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# Some basic practical applications of Calculus

I am currently studying Calculus on my own for fun. I enjoy different components of math and how they can be used to solve so many problems.

Many people, however, think I am crazy because I am studying mathematics in my spare time. Many people ask me "how will this ever be useful?" and many times I cannot think of an answer. Often, people do not understand the significance of certain things in math.

For example, I would explain to someone how the Gamma function is like an extension of the factorial. The usual response is "Okay, how is that useful?" When I attempt to explain, I then need to go into many other details about other concepts.

What are some basic uses for Calculus and its functions? I know that this is really vague, but I was hoping someone may help.

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Math doesn't have to be useful. You said it yourself: You study calculus because you just enjoy it. –  Javier Badia Apr 8 '12 at 23:48
But then, of course mathematics were probably initially used because it has a practical application. –  Argon Apr 9 '12 at 0:02
When they said "How it that useful?" and you answered "Who cares?", what did they say? –  Michael Hardy Apr 9 '12 at 1:25
I wonder how they'd respond if you asked in return how art is useful. –  KCd Apr 9 '12 at 2:20
That math happens to be useful is a nice side effect. That math actually works for modeling what we see in real life is a miracle in itself. –  Ｊ. Ｍ. Apr 14 '12 at 4:49

Here is a very general but broad class of applications: Suppose you have some quantity $q(t)$ that you want to model with respect to time, like maybe a population, or a chemical concentration, or an object's speed, or whatever. Quite often there will be a natural way to describe the quantity you're interested in by using a differential equation, i.e. an equation which relates the rate of change $\frac{dq}{dt}$ of the quantity to $q(t)$ itself.

Calculus can then be used to analyze the differential equation (which could be very complicated) and hopefully give a closed-form solution so that we can predict the quantity in the long term. If an explicit solution is found, calculus can again be used to analyze the solution to find maxima and minima, and all sorts of critical points of interest.

Differential equations aren't only useful for modelling quantities, but also positions. for example, in order to fully understand how a rocket ship blasts off into space, scientists need to take into account the fact that the burning of fuel means the mass is decreasing, and so the propulsion will cause a larger acceleration. This problem leads to solving a differential equation.

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I think it is useful to start from applications of mathematics it self. In my view mathematics has the following uses.

1. It has aesthetic value, i.e., it has beauty. Just as some people are attracted in the beauty of flowers, ornaments, young animals, music, painting,....mathematicians are attracted by the beauty of mathematics. Its beauty lies in expressing very complex relationships with compact mathematical models.

2. Mathematics is a tool(a technical language) of science and technology. Many disciplines such as engineering, physics, economics,...express their facts, principles, theory, etc in this language. It is difficult/impossible to study certain topics in other disciplines with out using the language of mathematics.

3. Mathematics trains the mind. It empowers the brain no matter what career you have.

4. Mathematics also has direct real life applications.

And calculus shares all these attributes of Mathematics.

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How do you find the GCF of 42 and 56?

Jan 4, 2017

The GCF of $42$ and $56$ is $14$.

Explanation:

One method for finding the GCF of two numbers goes as follows:

• Divide the larger number by the smaller to get a quotient and remainder.

• If the remainder is $0$ then the smaller number is the GCF.

• Otherwise repeat with the remainder and the smaller number.

So in our example:

$\frac{56}{42} = 1 \text{ }$ with remainder $14$

$\frac{42}{14} = 3 \text{ }$ with remainder $0$

So the GCF of $56$ and $42$ is $14$

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# Advanced Topic in Odes

1. Mar 11, 2014

### Marcoreus

Fint the modified equation when the implicit Euler method is applied to y'= f(y). If f(y)=λy, where λ is negative. what is the effect on the amplication factor?
=>

y ' = λ * y
dy / dx = λ * y
dy / y = λ dx
ln y = λ* x + C
y = Ae^( λ* x ), the constant factor does not depend on λ.
i SOLVE THIS FOR THE ACTUAL SOLUTIONS
NOW,
The implicit Euler scheme is given by:
y_(n+1)= y_n +hf(y_n+1 , t_n+1 )
For f(y)=λ y, we have:
y_(n+1)= y_n +hf(y_n+1 , t_n+1 )= y_n + h λ y_n+1
Solving this for y_n+1 (in general, this is not possible), we arrive at:
y_n+1 = y_n / (1-h λ)..............(eqn 1)

From (eqn 1), we can see that if |1−h λ|≥1, the solution is decaying (stable). Compare this to the actual solution of y(x)=Ae^(λ x).
If we have λ being negative, we would have:
y_n+1 = y_n / (1+h λ)..............(eqn 2)

Compare this to the actual solution of y(x)=Ae^(−λ x). What conclusion can i draw?
Trying it for λ= ±1 , what happens to stability.

Last edited: Mar 11, 2014
2. Mar 11, 2014

### Staff: Mentor

Your last equation is wrong. The equation before it is
ln y = λx + C
Exponentiating (making each side the exponent on e) gives
$$e^{ln y} = e^{λx + C} = e^{λx} \cdot e^C$$
Can you finish this?

What you have done is solve the DE using separation. I don't know what the "implicit Euler method" is, so you might not have solved this in the intended way.

3. Mar 11, 2014

### Staff: Mentor

BTW, your title made me think you had a question about classical poetry. Odes are poems in praise of someone. ODEs are ordinary differential equations.

4. Mar 11, 2014

### Marcoreus

Fint the modified equation when the implicit Euler method is applied to y'= f(y). If f(y)=λy, where λ is negative. what is the effect on the amplication factor?
=>

y ' = λ * y
dy / dx = λ * y
dy / y = λ dx
ln y = λ* x + C
y = Ae^( λ* x ), the constant factor does not depend on λ.
i SOLVE THIS FOR THE ACTUAL SOLUTIONS
NOW,
The implicit Euler scheme is given by:
y_(n+1)= y_n +hf(y_n+1 , t_n+1 )
For f(y)=λ y, we have:
y_(n+1)= y_n +hf(y_n+1 , t_n+1 )= y_n + h λ y_n+1
Solving this for y_n+1 (in general, this is not possible), we arrive at:
y_n+1 = y_n / (1-h λ)..............(eqn 1)

From (eqn 1), we can see that if |1−h λ|≥1, the solution is decaying (stable). Compare this to the actual solution of y(x)=Ae^(λ x).
If we have λ being negative, we would have:
y_n+1 = y_n / (1+h λ)..............(eqn 2)

Compare this to the actual solution of y(x)=Ae^(−λ x). What conclusion can i draw?
Trying it for λ= ±1 , what happens to stability.

5. Mar 11, 2014

### Simon Bridge

Welcome to PF;

Ode to ODEs

O My sweet ODE
How is it you can be
So beautiful and yet so deadly
To me

The method's Implicit Euler,
But deep-fried brain is oilier
Numerical iterations don't clean me up!
I'm soilier.

Variables separate
As we cogitate
But it's not the method no
But it's not the method no

By brain hurts so sweetly when you are around
Even when you make by head to pound
But O the joy when the general solution
is found.

Sweet ODE.

"implicit eulers method" is a numerical method involving iteration.
... oh you found it - good :)

6. Mar 11, 2014

### Marcoreus

that was nice poem. i like it thanks

7. Mar 11, 2014

### Simon Bridge

Imagine my disappointment when I found the thread was not about Odes :(
... these are all good questions.
Before we pitch in ere, how about having a go at answering them?
Give it your best shot.

If you are stuck, try plotting a few points for some easy values of the parameters.

Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
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# Solutions Concentration And Molarity Phet Chemistry Lab Answer Key

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Wednesday 4/29/20 - Complete the rest of the Molarity worksheet. Conclusion Questions and Calculations, Concentration and Molarity Post-Lab Exercises. This website is provided for the convenience of students in Chem CP with Dr. The undiluted unknown #285 would therefore be twice that of the diluted, or 0. Complete Ionic and Net Ionic Equations: Home: Writing Complete Ionic Equations. Coordination Chemistry. You also need to provide spaces for up to 4 sets of titration data – 4 trials. The AP Chemistry science practices describe what a student should be able to do while exploring course concepts. Use mathematical and computational analysis to quantitatively express the concentration of solutions using the concepts such as molarity, percent by mass, and dilution. Class information. For review, we will also be looking at the two Acid-Base FRQ questions from last years exam. For example, to make a 1M salt water solution, one mole of salt is measured. giving the answer as S = ½ [Ag +] = 4. The Solution is Dilution. Facilitated group inquiry. Learn from step-by-step solutions for over 34,000 ISBNs in Math, Science, Engineering, Business and more. Solute concentration can be expressed quantitatively using a number of different units such as molarity, molality and parts per million (ppm). AP Syllabus/Class Policies > AP Chemistry Syllabus. A Geekout Marathon - Every Friday in February, groups of enthusiastic educators came together for a Geekout, a virtual meeting to focus on a topic related to Digital Learning. Beer’s Law Lab. top/readpdf/ phet-molarity-and-concentration-answer-key. Complete Ionic and Net Ionic Equations: Home: Writing Complete Ionic Equations. Determining the Concentration of a Diluted Solution If 0. Molarity Practice - on. Win Chemistry 120 views. Use your answer from #1 and #2 to find the moles of HCl that reacted. • prepare a dilute solution from a more concentrated one. We will cover acid and base definitions, pH, acid-base equilibria, acid-base properties of salts, and the pH of salt solutions. Use this HTML to embed a running copy of this simulation. pdf phet molarity and concentration answer key is available in our digital library an online access to it is set as public so you can download it instantly. Describe how you would prepare 1 L of a 1 M solution of sodium chloride. 1 M solution: Observations of the 0. Joshua Farley CHEM 1251L- 10/30/ Introduction This experiment focused on an essential quantitative technique that, when used effectively, can determine the concentration of an acid in a solution. On Friday, March 13, 2015 we will run a Geekout marathon. I am confused with the following problems, if possible please explain answer each question for me. If 100 ml of a saturated solution of KNO3 at 50oC is cooled to 10oC, how much precipitate will form? 45 minutes - Finish Notes: Concentration (change notes so students can make. 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In medicine, these skills are necessary to ensuring proper medicine dosage and treatment. pdf FREE PDF DOWNLOAD There could be some typos (or mistakes) below (html to pdf converter made them): concentration, is a measure of the concentration of a solute in a solution, or of any ChemTeam: Converting between "ppm" and molarity EXPERIMENT 12 Chemistry 110 Lab TITRATION PART I. Calculate the concentration of solutions in units of molarity (mol/L). Set up retort stand with ring clamp and Bunsen burner. Answer Key For 4th Grade Nys Common Core Mathematics Curriculum Lesson 1 Homework 4 2. For Trial 2(etc), Choose Cobalt (II) Nitrate (solid) & record its chemical formula Calculate the moles of solute required to saturate the solution using the molarity formula and record your result in. This banner text can have markup. Crystal Violet Lab/ Beer's Law Lab Resource Link Lab -- Data for Beer's Law 2017. Calculate the molarity of a solution made by diluting $125\rm~ ml$ of concentrated $\ce{HCl}$ with water to a total volume of $2\rm~ L$. Part A: Phet acid base solutions:. 400 M KOH is added to 100. classify mixtures into homogeneous and heterogeneous ones. Which of the solutions is the most concentrated? Explain your answer. pdf PhET - Forces Motion Basics in html5. The textbook provides an important opportunity for students to learn the core concepts of chemistry and understand how those concepts apply to their lives and the world around them. Selection File type icon File name Description Size Revision Time User; ĉ: Lab 5 Periodic Law Density only Version. Test Corrections Policy. The reason for this is because one liter of solution usually contains either slightly more or slightly less than 1 liter of solvent. (10) Science concepts. The undiluted unknown #285 would therefore be twice that of the diluted, or 0. Calculate the molality, mole fraction, mass % and ppm of NaOH in this solution. Introductory Chemistry, 6th Edition. 2 Notes and Practice- Finish for hw (P8 did not do) Koolade Lab (excused for absent students) HW: Finish 4. In chemistry, concentration is usually measured by the number of moles of substance dissolved in a liter of liquid. Previous: Some Definitions. This is called molarity and is expressed as mol/L or M (The formula is: M = moles/Liter). Part B: Stoichiometry Calculations Involving - Molar Concentration IMPORTANT: If a VOLUME is mentioned, and the problem involves a molarity, DO NOT assume that "22. 0x10-18 M so neglecting the additional sulfide ion is not a bad bet, but you could solve the equation exactly. Burets, glassware most commonly used in a technique called “titration,” are filled with solutions of various colors. Report this Question as Inappropriate. | bartleby. Click to begin next trial. This Mass Concentration of Solutions Interactive is suitable for 6th - 12th Grade. (Answer: 0. pHet Lab on Molarity and Concentration; Modeling Lab (Can get paragraph checked off tomorrow for Extension - must present to Coach Day to get stamped and checked) DUE TOMORROW Rate of Solubility Lab (one per group). We meet in Google Hangouts on Air for discussion followed by a questions and answer session. INTRODUCTION The molarity of an unknown acid will be determined using a method called "titration". Our team of designers, researchers, educators, and developers is dedicated to producing high quality STEM resources. We are going to focus on the reaction of Cu metal with various solutions. Acids and bases webquest answers pdf, save this pdf ebook to read acids and bases webquest answers pdf ebook at our collection get acids and bases webquest answers pdf file for free from our online. Our science question and answer board features hundreds of science experts waiting to provide answers to your questions. 5 grams of Fe2O3 by the following equation. To calculate the limiting reagent, enter an equation of a chemical reaction and press the Start button. Read Online Now circuits phet lab answer key Ebook PDF at our Library. Adding pure water to a saturated solution (with some s ettled solids) would cause the concentration of that solution to initially increase / decrease / remain the same, until it was no longer saturated then it would. and the Molarity of an Aqueous Solution? Purpose The purpose of this lab is to introduce students to the concepts of solutes, solvents, and molarity. We will be checking our email and voicemail regularly. 850 grams of ammonium nitrate are dissolved in 345 mL of solution? 11) Explain how you would make 675 mL of a 0. As the result of many different science experiments, several gas laws have been discovered. Unit 7 - Solutions/Concentration - Openers. Add some water and dissolve the salt. Preparing a solution is something that is very critical to many applications in science, medicine, cooking, engine matainence, and other fields. 0 L moles of solute = 48. Describe the relationship between the solution concentration and the. 4 L" should be used. Finish Lab Calculations. Molarity Quizziz Link Email me the following work: 1. A solution was made by dissolving 800. 00 M = moles of solute 12. What determines the concentration of a solution? Learn about the relationships between moles, liters, and molarity by adjusting the amount of solute and solution volume. Balancing Chemical Equations. It is a lab which can be easily completed in one class period. pdf" copy this link into your â€¦ CONCENTRATION AND MOLARITY PHET ANSWER â. school physics and chemistry. 20 - PhET Interactive Simulations. Solution The HCl concentration is near 40%, so a 100-g portion of this solution would contain about 40 g of HCl. 2010 academic year for Chemistry Department faculty, students, and staff at the that no student or faculty member has to go elsewhere for an answer about degree The Department of Chemistry provides key educational service to the Institute. -A concentrated solution contains a large amount of solute. web; books; video; audio; software; images; Toggle navigation. 498 M If the volume had been specified as 1. • Lab #1: Introduction to the Chemistry Laboratory (PDF Format) • Math Skills Packet Answer Key (PDF Format) • PhET Concentration Interactive Simulation. concentration and molarity phet chemistry labs answers key PDF may not make exciting reading, but concentration and molarity phet chemistry labs answers key is packed with valuable instructions, information and warnings. 0 g of solute added eAll beakers contain 10. What is the final concentration of the solution produced when 225. Solute Name Formula Volume added, Total volume, Final Added V1 V2 Concentration, Concentration, C2 C1 Drink Mix NA Cobalt(II) nitrate Cobalt(II) chloride Potassium dichromate Potassium chromate Nickel(II) chloride Copper(II) sulfate Potassium permanganate. Square brackets are used to represent the concentration of a solution. building an atom phet simulation sheet answers Alistair MacLean Public Library File ID a94693e Creator : LibreOffice simulation build an atom answer key pdf excellent book is always being the. Kay's General Chemistry. 0768 g mol¯ 1 x = 2. Find the number of moles of solute in e. 5 M solution? 69. Concentration Lab. Use your answer from #1 and #2 to find the moles of HCl that reacted. atozteacherstuff. Ready to teach your class about molar mass and solution concentration? Make time for an interactive resource that will challenge their reasoning and problem-solving skills. Record the exact "Concentration of Soln'" in Data Table 1. Suspensions, colloids and solutions. mL of the unknown with 2. INTRODUCTION The molarity of an unknown acid will be determined using a method called "titration". Unit 10: Solutions-Key Regents Chemistry '14-'15 Mr. Design a procedure for creating a solution of a given concentration. This is called molarity and is expressed as mol/L or M (The formula is: M = moles/Liter). Answer Key For 4th Grade Nys Common Core Mathematics Curriculum Lesson 1 Homework 4 2. 200g of Mg (s). We will cover acid and base definitions, pH, acid-base equilibria, acid-base properties of salts, and the pH of salt solutions. You have remained in right site to begin getting this info. 5 moles of sodium hydroxide to water to make 2. Click on “Cu” and then click on the blue box to put the Cu in to the solutions and then click again to take it out. Alexandra Barry, Kasey Rowe, Katie Silberstein, Sarah King, Victoria Lee, 2010. Build an Atom. ; Molarity, concentration in mol/L or mol L-1, is given the symbol c (sometimes M). That is because by measuring the volume of the solution, you can use the molarity to calculate exactly how much solute is contained in the sample. UNIT #9: MOLARITY SOLUBILITY CURVES DILUTIONS COLLIGATIVE PROPERTIES OF SOLUTIONS 1. I Can Answer Key: File Size: 113 kb: File Type: pdf: Download File  Online Resources. moles HCl molarity = M = volume HCl(in liters) 5. pptx: File. 5 L) of the solution is about five times greater than that in a 100 g portion, or 5 × × 40 = 200 g. Due Thursday, November 7. Solutions, Dilutions, Concentrations and Molarity. review your calculations for preparation of 10. Procedure: PhET Simulations à Play With Sims à Chemistry à Acid-Base Solutions à The concentration of the acids and bases used in the at 0. The iodine test is utilized to test for the presence of starch. 00-M solution of copper nitrate, Cu(NO 3) 2, is diluted to a volume of 1. Worksheet Reaction Rates Chemistry A Study Of Matter Answers. In this lesson plan, adaptable for grades 5-12, students use an interactive simulation called Concentration to explore the concentration of different solutes and solvents. Nbme 15 Questions And Answers. Point out that the greater the molarity of the solution, the greater the concentration is of the solute within the solvent. WE ARE ON EXTENDED SCHOOL & OFFICE CLOSURE DUE TO THE COVID-19. Bring any questions you have to discuss before the quiz tomorrow. Concentrated hydrochloric acid is $37\% \ce{HCl}$ by mass and has a density of \$1. 0 M means the concentration of the sucrose solution is 3. 01 M solution of HNO 3? (A) 1 (C) 13 (B) 2 (D) 14 ____40. 075M and a 0. molarity by dilution answer key. pdf PhET - The Moving Man JAVA. 50 moles of NaCl? 2. LABORATORY #2: Molarity Lab Introduction: A solution consists of one or more substances (Solutes) that are dissolved in a liquid. 3g of LiNO3) 4) Using the following equation: Fe2O3 + 3 H2 -----> 2 Fe + 3 H2O. Conceptual Chemistry is designed to challenge and stimulate the intellect of the motivated science student in grades 10, 11, or 12. This work is licensed under a Creative Commons Attribution 4. What is the relationship between concentration and color? 5. 1b) Molarity Name_____ CHEMISTRY: A Study of Matter 7. It is categorised under Classic literature and is a tale of sexual obsession toward a gender that was considered inappropriate in the society. You will be completing the Molarity and Concentration PhET Lab in a group of 3. Dilution is a decrease in a solution's concentration, whereas concentration is an increase in a solution's concentration. In Section 9. Mastering Chemistry Fractional Precipitation of Metal Carbonates Tutorial *Solubility Graded Homework #3 Questions 58-69 from the Solubility homework set posted on Carmen. 6mL of the 8. 0 L moles of solute = 48. concentration = 2 mol/L. Record the exact “Concentration of Soln’” in Data Table 1. Even on this basic laboratory experiment requires of those standard obligations,. Students do a micro-titration of six NaOH solutions of increasing concentration with 1. The molar concentration (M) of a solution is defined as the number of moles of solute (n) per liter of solution (i. moles liter Working with Solutions Diluting Solutions The molarity of a solution and its volume are inversely proportional. When all measurements have been recorded, plot concentration vs. Report "Molarity Worksheet #1 - KEY. Our science question and answer board features hundreds of science experts waiting to provide answers to your questions. Preparing a solution of known concentration. Click Activity 1. This precipitation reaction is described by the following equation: 2 Na 3 PO 4 (aq) + 3 CaCl 2 (aq) --> 6 NaCl (aq) + Ca 3 (PO 4) 2 (s). 09988 M solution of Na 2 CO 3 is allowed to evaporate until the solution volume is reduced to 45. pdfFREEPDFDOWNLOADNOW!!!Source#:answerstophetphlab. Solving the last equation for #x#, we find that #x=2. Notice that the answer does not depend on the identity of the solute. 1az Fse Engine Repair Manual. We most often represent the concentration of solutions in the lab in units of molarity. as concentration of a weak base increases, the pH (increases/decrease/remains constant) increases. (C) calculate the concentration of solutions in units of molarity. Chemistry CP provides students with a comprehensive study of the nature of matter and the changes it undergoes. geometric optics phet lab answer key - PDF Free Download Answer Key For Universal Gravitation Phet Lab - In this site is not the similar as a solution manual you buy in a book stock or. Adding pure water to a saturated solution that has no settled solids would cause the concentration of that solution to increase / decrease / remain the same. See more ideas about High school chemistry, Chemistry class and Chemistry. When all the solid is. atozteacherstuff. This corresponded to a concentration of 0. 3 Thinking Like a Scientist. Chapter 7: “Solutions” Worksheet and Key Define the following terms: mixture aqueous solutions colloids suspensions heterogeneous homogenous solvent solute saturated solution solubility molarity molality Henry’s law Osmosis Osmotic pressure Osmolarity Osmolality Diffusion SEE LECTURE NOTES FOR DEFINITION ANSWERS 1. The Project Director will make a copy of the Lab and share it with the other two members of the group. Molarity Worksheet W 331 Everett Community College Student Support Services Program What is the molarity of the following solutions given that: 1) 1. Describe how you would prepare 1 L of a 1 M solution of sodium chloride. Explain how solution color and concentration are related. Virtual Titration Lab. Title Investigation of a Solution's Color (Qualitative and Quantitative) - Guided Inquiry Activity: Description Learning goals for this guided inquiry activity include for students to be able to, (1) Describe the relationship between solution concentration and color intensity for various metal ions; (2) Sketch absorbance vs. Unit Outline. Molarity Practice Worksheet (With answer key!!) Giant Molarity/Molality/Freezing Point Depression and Boiling Point Elevation Packet (With answer key! There's some stuff in here that we didn't go over like dilutions, so if it doesn't look familiar, it's probably not from our unit!) Molarity Practice Problems and Answer Key. More information and offline downloads. What you get: Worksheets-Molarity problems (9 problems)-Molarity Problems 2 (16 problems)-Molarity Extra Practice (35 problems)-How to read a Solubility chart (a tutorial on one side and practice on the back) All worksheets are complete with typed answer keys Labs-Molarity Lab (3 unknown solutions - students attempt to calculate the molarity. So depending on what exactly you are searching, you will be able to choose ebooks copy of chemistry. SHOW YOUR WORK! Wednesday 4/29/20 - Complete the rest of the Molarity worksheet. holt's nut wizard inc dr gounev's general chemistry page lebanon moph cheap san storage solutions coro mozart viseu portugal muzyka bikta raszka stupi de vanzare ieftinirea vietsub running man ep 154 online sara hopper soccer spicy beef pepper asparagus udon noodles ludmila kiseleva neujahrsempfang bee 2013 nfl custom slot car pit boxes burgo. INTRODUCTION The molarity of an unknown acid will be determined using a method called "titration". 16 L of solution. Resonance Formal Charges Bond Energies. Please contact staff via email or telephone. Design a procedure for creating a solution of a given concentration. and 12:00 noon at CCHS & LaBallona Elementary School and 9:00 am - 12:00 at the Office of Child Development. Upon completion of this lab, the student should be able to • proficiently calculate molarities for solutions. Of note is the PhET simulation of acid–base chemistry that allows students to change the concentration and acid strength (effectively the K a of the acid) while watching the pH and the particulate representation change (Box , LO 6. AP Chemistry Course Planning and Pacing Guide 2 Zinc, iron, tin, and lead are extracted by the reaction with carbon or carbon monoxide. HW - 1) None Day 104 - Tuesday, 2/11 - Today we practiced calculating the molarity of solutions such as Mt. Beer's Law Practice. 2 Practice and Koolade Lab. Students will demonstrate an understanding of the nature of properties of various types of chemical solutions. The solution concentration molarity is used a great deal by the chemist. Acid And Base Activity. concentration. Worksheet 5 ¢€" Solutions Electrolytes and Concentration The name from Concentration Worksheet, source:yumpu. This is inquiry-based lab in which students are asked to investigate the properties of hard and soft water with regards to the activity of soap. Notice that the answer does not depend on the identity of the solute. The Project Director will make a copy of the Lab and share it with the other two members of the group. 0 g of water. 5 mL of a 0. Smaller pieces of magnesium metal will react more rapidly than larger pieces because more reactive surface exists. Proper solution making requires basic math skills, accurate measurement, and the ability to follow instructions. 8 g K 2 SO 4 b. The hydrogen ion concentration of this solution, in moles per. 2010 academic year for Chemistry Department faculty, students, and staff at the that no student or faculty member has to go elsewhere for an answer about degree The Department of Chemistry provides key educational service to the Institute. Suspensions, colloids and solutions. · Begin with a strong acid and lower the pH probe into the beaker. We will be checking our email and voicemail regularly. Go To: (Either Google PhET, or find link on my Chem II Unit 11 Page) PhET Simulations Play With Sims Chemistry Acid-Base Solutions Notation: Acids are abbreviated HA, with the H representing the proton (H+) the acid donates to the solution. Therefore, adding water makes the solution less concentrated. Students should focus on the effect of additions of solids and water on saturated solutions. The Learning Goals and Success Criteria documents are the key guide to the instructional program for each unit. TEACHING MODE. By measuring the absorbance of a set of standard solutions of known concentrations, you can create a calibration curve that shows how the response of the instrument (absorbance) changes with concentration. 0mL of HCl (aq) 70. You do not need to write the questions. 850 L of a 5. increase / decrease / remain. solute that dissolves in a given quantity of a solvent at a specified temperature and pressure to produce a saturated solution. 50 M, NOT 2. Concentration of Solutions and Molarity The concentration of a solution is a measure of the amount of solute that is dissolved in a given quantity of solvent. Finish Lab Calculations. Crystal Violet Lab/ Beer's Law Lab Resource Link Lab -- Data for Beer's Law 2017. Balloons/Static Electricity. pdf PhET - Concentration in html5. 00 M solution, how many moles of solute will be needed if 12. To create the 0. We are going to focus on the reaction of Cu metal with various solutions. Class information. 4 L" is justified only if the substance being referred to is a gas AND if the key phrase "at STP" is mentioned along with the volume. It will need one set of spaces to list the name, type, appearance, and nominal concentration of the vinegar you choose and the molarity of the sodium hydroxide. Alexandra Barry, Kasey Rowe, Katie Silberstein, Sarah King, Victoria Lee, 2010. The book also includes a number of innovative features, including interactive exercises and real. Unit 10: Solutions-Key Regents Chemistry '14-'15 Mr. The AP Chemistry science practices describe what a student should be able to do while exploring course concepts. 0 liter of a 1. 50 M, NOT 2. We will be checking our email and voicemail regularly. Materials needed: PhET website. 2 (concentrations) Ch. 50 liters of solution. The textbook provides an important opportunity for students to learn the core concepts of chemistry and understand how those concepts apply to their lives and the world around them. 195 g of cholesterol, C 27 H 46 O, in 0. concentration. This is defined as "neutral" and corresponds to a pH level of 7. Report this Question as Inappropriate. Resource Topic: Stoichiometry The Mole, Molarity, and Density. 4 L" is justified only if the substance being referred to is a gas AND if the key phrase "at STP" is mentioned along with the volume. Molarity and Serial Dilutions Teacher Handout Module Overview One of the most important skills in science is to calculate dilutions. building an atom phet simulation sheet answers Alistair MacLean Public Library File ID a94693e Creator : LibreOffice simulation build an atom answer key pdf excellent book is always being the. Dilutions and Concentrations by Jessie A. , a low molarity acid and high molarity acid can react differently and at different speeds. Start studying Chemistry Chapter 16: Molarity. If you have extra time, you can try to make one more solution with the exactly perfect concentration based upon your observations. Calculate the molarity of a solution prepared by dissolving 6. 1az Fse Engine Repair Manual. Volumetric analysis is a widely-used quantitative analytical method. This is called molarity and is expressed as mol/L or. are a great way to gain specifics of operating certain products. molarity by dilution answer key. Concentration PhET WebLab KEY What students are saying As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students. In order to increase the percent yield of product, increasing the limiting reactant, possibly, is the most effective. 5 mL of a 0. When aqueous solutions of sodium phosphate and calcium chloride are mixed together, an insoluble white solid forms. View concentration and molarity phet answer key from SCIENCE 2031 at University of Colorado, Denver. 010 (10 -2 ) Molar. Chapter 18 “Reaction Rates and Equilibrium”. 50 liters of solution. These practices are categorized into skills, which form the basis of the tasks on the AP Exam. This is called molarity and is expressed as mol/L or M (The formula is: M = moles/Liter). 5 L) of the solution is about five times greater than that in a 100 g portion, or 5 × × 40 = 200 g. We also acknowledge previous National Science Foundation support under. Molarity and Serial Dilutions Teacher Handout Module Overview One of the most important skills in science is to calculate dilutions. Using your general scheme for calculating the concentration of diluted solutions devised in key question 1, calculate the resulting concentration (ppm Zn) for each solution A-E above. The solution contained 868. Vocabulary: acid – a chemical that forms a salt when mixed with a base. Notes_Chemical. Acid/Base Solutions. Name: _____ Part 4: Calculating Molarity. Experiment 16. 3366 g of HCl? Outline the steps necessary to answer the question. The molarity, M, of a solution is defined as the number of moles of solute in one liter of solution (Equation 1). Even on this basic laboratory experiment requires of those standard obligations,. pdf phet molarity and concentration answer key is available in our digital library an online access to it is set as public so you can download it instantly. Concentration Lab. Volumetric analysis is a widely-used quantitative analytical method. Titrations - A Laboratory method that is used to find the concentration of an unknown solution by undergoing a specific chemical reaction of known stoichiometric proportions with a solution of known concentration. 0 M means the concentration of the sucrose solution is 3. I run a very high-energy, interactive lab/class. The Learning Goals and Success Criteria documents are the key guide to the instructional program for each unit. This website is provided for the convenience of students in Chem CP with Dr. 6mL of the 8. building an atom phet simulation sheet answers Alistair MacLean Public Library File ID a94693e Creator : LibreOffice simulation build an atom answer key pdf excellent book is always being the. Created Date: 5/8/2013 3:16:42 PM. The LibreTexts libraries are Powered by MindTouch ® and are supported by the Department of Education Open Textbook Pilot Project, the UC Davis Office of the Provost, the UC Davis Library, the California State University Affordable Learning Solutions Program, and Merlot. Solutions Packet Questions Answer Key Assigned as HW on 4/17/18. 10 L of solution. 125 M K 2 SO 4 21. pdf FREE PDF DOWNLOAD NOW!!! Source #2: solutions worksheet 1 molarity answer key. Resource Topic: Stoichiometry The Mole, Molarity, and Density. 8 M NH3, molality: 22. Dilution is a decrease in a solution's concentration, whereas concentration is an increase in a solution's concentration. c) The solvent is the substance doing the dissolving, usually water. Phet_Conc_Lab_3. 850 L of a 5. You will be completing the Molarity and Concentration PhET Lab in a group of 3.

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text:
Prealgebra (7th Edition)

$-54$
$-6\times9$ is the same as the opposite of $6\times9$, which in turn is the same as $9+9+9+9+9+9$. So if $9\times6$ is $54$, just take the opposite to get the solution, $-54$.


text:
## Fixing a plotting problem over a fixed axes

Hans123

### Hans123 (view profile)

님이 질문을 제출함. 19 Aug 2019
최근 활동 darova

### darova (view profile)

님이 답변함. 19 Aug 2019
darova

### darova (view profile)

님이 답변을 채택함.
I want the below spirals to be evenly spaced (in both x and y axes). I am hoping distance between the rows and columns of the helical spirals to be the same, while each center will lie on the same line. I am not sure how to use MATLAB to calculate that for me. The radius of the helical spirals will change and I think there is way to use MATLAB to evenly space them out rather than manually calculating the distance of them.
The axes will always be constrained from -255 to 255, so only radius stays the same.
I pasted the code and what the spirals look from the xy axes
I am hoping the spacing between each row would be constant so that the spirals lie on the same line
Code
clc; clear; close all
%
% prompt2 = 'Layer Height: ';
% height = input(prompt2);
height = 250;
% prompt3 = 'Number of Layers: ';
% numlayer = input(prompt3);
spirals = (1:10:61);
num = 1:1:7;
for columns=1:4
for rows = 1:length(spirals)
center = -250 + (spirals(rows))*num(rows); % this was calculated to work only for this radius
indent =255 - (columns*30);
gap=height./columns;
d=height;
r = spirals(rows);
z=linspace(0,d,1000);
t=(2*pi/gap)*z;
x=r*cos(t)+center;
y=r*sin(t)+ indent;
hold on
plot3(x,y,z,'o','MarkerSize',2)
xlim([-255 255])
ylim([-255 255])
zlim([1 255])
grid on
ylabel('\it Increasing Layer Height \leftarrow')
end
end

표시 이전 댓글 수: 4
Hans123

### Hans123 (view profile)

19 Aug 2019
Currently, my plot has overlapping of the spirals. The goal is to get rid of that overlapping. I want to know how I can make MATLAB understand the necessarcy distance so that there is no overlap between rows.
The reason I want MATLAB to solve fit the spirals on the axes, rather than manually calculating the required distance, is because I intend to change the radius of each spiral on each row later. I do not wish to recalculate the distance again
darova

### darova (view profile)

19 Aug 2019
What if radius of spirals too big for
ylim([-255 255])
Hans123

### Hans123 (view profile)

19 Aug 2019
the radius for the spirals being picked will adhere to the limit. My problem is getting rid of the overlap of the spirals. Please let me know how I could do it.

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## 답변 수: 1

darova

### darova (view profile)

님의 답변 19 Aug 2019
채택된 답변

See attached file
dy = max(spirals);
indent = linspace(-255+dy, 255-dy,4);
y=r*sin(t)+ indent(columns);
FOr thicker line use:
plot(x,y,'linewidth',2)

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Translated by


text:
# Archive for category Programming

### svg2pdf and svg2eps (convert svg to pdf or eps from the command line)

I’ve been working on a new makefile for my latex projects. The goal is to have single-source builds of dvi, pdf, and xhtml documents. I ran into a problem of generating figures. latex expects eps graphics, pdflatex expects pdf figures, and latexml expects png figures (or will try to generate them). In order to generate documents with make, I need a way to generate eps and pdf figures from svg sources (I usually use inkscape to make my figures). Inkscape can be run from the command line, but I dont want to install inkscape on my server because that will require installing a ton of libraries that don’t make sense to have on a server with no graphical interface.

As it turns out, writing such a command line tool is very easy with librsvg and cairo. Carl Worth of redhat has produced a nice demo of svg2pdf which can be found at freedesktop.org. I cloned his project, create a cmake project out of it, and made a trivial modification to turn it into svg2eps as well.

You can find my code at git://git.cheshirekow.com/svg2x.git and there’s some doxygen documentation Doxygen documentation.

### Generating HTML pages from Latex

While latex is pretty much “not designed” for web content, it is very useful to generate a web-version of a latex document. The purpose of latex is clearly for typesetting layouts on a pre-defined page, but when you want to share the information with others, it’s generally a lot easier for them to go to a webpage then it is to download and open a PDF. In addition, it’s generally easier to view a webpage than a PDF because the content is continuous, and one can scroll around and click hyperlinks in a way that is far more fluid than on a PDF.

Now that MathML and SVG are becoming more supported by web browsers, there is a strong case for sharing mathy documents on the web in addition to paper documents (or PDFs, which are only slightly more readable than paper).

To this end, I’ve been evaluating various different Latex to HTML converters. I’ve tried the following on Linux (Ubuntu):

By far my favorite is LaTeXML. It generates crisp, simple pages using MathML and CSS, making it easy to customize the style. It doesn’t support a whole lot of packages that I generally would like to use (like algorithm2e), but then again none of them do. Also, the ArXiV project is working on a branch of LaTeXML so there is promise that it will grow quickly to support a lot of the best packages.

## Document Setup

My current approach to generating both PDFs and HTMLs from latex source is to use separate top-level documents for both. The directory structure looks something like this:

 document |- document_html.tex |- document_pdf.tex |- document.tex |- preamble_common.tex |- preamble_html.tex |- preamble_pdf.tex \- references.bib

The two versions of document_[output].tex are the top-level files. They look like this:

1 2 3 4 5 6 7 8 %document_html.tex   \documentclass[10pt]{article} \input{preamble_common} \input{preamble_html} \begin{document} \input{document} \end{document}

The pdf version is the same but it uses preamble_pdf as an input. Note that in latex you cannot nest \include directives, but you can nest \input directives. Also, \include inserts a page-break so there is no need to use them here. Rather document.tex may \include it’s chapters as tex files or the like.

## Makefile

To ease the process of generating the different types, I’m using a makefile.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 # The following definitions are the specifics of this project PDF_OUTPUT := document.pdf HTML_OUTPUT := document.html   PDF_MAIN := document_pdf.tex HTML_MAIN := document_html.tex   COMMON_TEX := document.tex \ preamble_common.tex   PDF_TEX := $(COMMON_SRC) \ document_pdf.tex \ preamble_pdf.tex HTML_TEX :=$(COMMON_SRC) \ document_html.tex \ preamble_html.tex   BIB := references.bib       # these variables are the dependencies for the outputs PDF_SRC := $(PDF_TEX)$(BIB) HTML_SRC := $(HTML_TEX)$(BIB)   # the 'all' target will make both the pdf and html outputs all: pdf html   # the 'pdf' target will make the pdf output pdf: $(PDF_OUTPUT) # the 'html' target will make the html output html:$(HTML_OUTPUT)   # the pdf output depends on the pdf tex files # we use a shell script to optionally run pdflatex multiple times until the # output does not suggest that we rerun latex $(PDF_OUTPUT):$(PDF_TEX) @echo "Running pdflatex on $(PDF_MAIN)" @pdflatex$(basename $(PDF_MAIN)) >$(basename $(PDF_MAIN))_0.log @echo "Running bibtex" @-bibtex$(basename $(PDF_MAIN)) > bibtex_pdf.log @echo "Checking for rerun suggestion" @for ITER in 1 2 3 4; do \ STABELIZED=cat$(basename $(PDF_MAIN)).log | grep "Rerun"; \ if [ -z "$$STABELIZED" ]; then \ echo "Document stabelized after$$ITER iterations"; \ break; \ fi; \ echo "Document not stabelized, rerunning pdflatex"; \ pdflatex$(basename $(PDF_MAIN)) >$(basename $(PDF_MAIN))_$$ITER.log; \ done @echo "Copying pdf to target file" @cp (basename (PDF_MAIN)).pdf (PDF_OUTPUT) # the html output depends on the html tex files # we have to process all of the bibliography files separately into xml files, # and then include them all in the call to the postprocessor (HTML_OUTPUT): (HTML_TEX) @echo "Running latexml on (HTML_MAIN)" @latexml (HTML_MAIN) --dest=(basename (HTML_OUTPUT)).xml > (basename (HTML_MAIN)).log 2>&1 @BIBSTRING=""; \ for BIBFILE in (BIB); do \ echo "Running latexml on$$BIBFILE"; \ XMLFILE=basename "$$BIBFILE" .bib.xml; \ LOGFILE=basename "$$BIBFILE" .bib_html.log; \ latexml $$BIBFILE --dest=$$XMLFILE > $$LOGFILE 2>&1; \ BIBSTRING="$$BIBSTRING --bibliography=$$XMLFILE"; \ done; \ echo$$BIBSTRING > bibstring.txt @echo "postprocessing with cat bibstring.txt" @latexmlpost$(basename $(HTML_OUTPUT)).xml cat bibstring.txt --dest=$(HTML_OUTPUT) --css=navbar-left.css   # the 2>/dev/null redirects stderr to the null device so that we don't get error # messages in the console when rm has nothing to remove clean: @-rm -v *.log 2>/dev/null @-rm -v *.out 2>/dev/null @-rm -v *.aux 2>/dev/null @-rm -v *.xml 2>/dev/null @-rm -v *.pdf 2>/dev/null @-rm -v *.html 2>/dev/null @-rm -v bibstring.txt 2>/dev/null

Some notes on the makefile. I execute bibtex ignoring errors (the dash symbol before ‘bibtex’) because bibtex will exit with an error if it doesn’t find any citations, or if there is no bibliography. Each iteration of pdflatex is output to a logfile named “document_pdf_<i>.log” where “<i>” is the iteration number. The output of pdflatex and bibtex is supressed by dumping it to the logfile (I the verbosity useless to have in the console).

The shell script in the PDF recipe iterates up to four times. The first thing it does is greps the output of the most recent run pdf latex looking for the line where latex recommends that we “Rerun” latex. If it finds such a line it sets the shell variable STABELIZED to that string. Otherwise it gets the empty string. Then we test to see if the string is empty. If it’s empty, we’re done so we break the loop. If it’s not, then we rerun pdflatex.

The shell script in the HTML recipe iterates over each of the (potentially multiple, potentially zero) bibliography files, processing each of them with latexml. It then appends the string “–bibliography=<filename>.xml” to the BIBSTRING shell variable. The last thing it does is echos the contents of that shell variable to the file “bibstring.txt”. This so so that subsequent commands by make can find it.

### ImgClip (xclip for images)

Here is a little python script I wrote to emulate xclip for image files. xclip, if you don’t know, is a simple command line tool for setting/retrieving text from the clipboard. For instance the following command

ls -l | xclip -i -selection clipboard

copies the current directory listing to the gnome clipboard, where it can then be ctrl + v pasted into a forum post, email, etc.

I really wanted something that does the same for image files. Unfortunately the following does not work:

cat image.png | xclip -i -selection clipboard

I’m not sure of the details of how the gnome clipboard works… but this doesn’t do it. I discovered a way to do it easily using pygtk. Here is a python script that does exactly what I want:

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 #! /usr/bin/python   import pygtk pygtk.require('2.0') import gtk import os import sys   def copy_image(f): assert os.path.exists(f), "file does not exist" image = gtk.gdk.pixbuf_new_from_file(f)   clipboard = gtk.clipboard_get() clipboard.set_image(image) clipboard.store()     copy_image(sys.argv[1]);

P.S. I pasted this code into this post using the following command

cat imgclip.py | xclip -i -selection clipboard

Make sure to set the script to executable

chmod +x imgclip.py

And then use it like this

./imgclip.py /path/to/some/image.png


text:
### 统计代写|贝叶斯分析代写Bayesian Analysis代考|Bayesian Analysis

statistics-lab™ 为您的留学生涯保驾护航 在代写贝叶斯分析Bayesian Analysis方面已经树立了自己的口碑, 保证靠谱, 高质且原创的统计Statistics代写服务。我们的专家在代写贝叶斯分析Bayesian Analysis代写方面经验极为丰富，各种代写贝叶斯分析Bayesian Analysis相关的作业也就用不着说。

• Statistical Inference 统计推断
• Statistical Computing 统计计算
• (Generalized) Linear Models 广义线性模型
• Statistical Machine Learning 统计机器学习
• Longitudinal Data Analysis 纵向数据分析
• Foundations of Data Science 数据科学基础

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Bayes Theorem

Bayes theorem is based on the conditional probability law:
$$\mathrm{P}[\mathrm{A} \mid \mathrm{B}]=\mathrm{P}[\mathrm{B} \mid \mathrm{A}] \mathrm{P}[\mathrm{A}] / \mathrm{P}[\mathrm{B}]$$
where $\mathrm{P}[\mathrm{A}]$ is the probability of A before one knows the outcome of the event $B, P[B \mid A]$ is the probability of $B$ assuming what one knows about the event $A$, and $P[A \mid B]$ is the probability of $A$ knowing that event $B$ has occurred. $\mathrm{P}[\mathrm{A}]$ is called the prior probability of $\mathrm{A}$, while $\mathrm{P}[\mathrm{A} \mid \mathrm{B}]$ is called the posterior probability of A.

Another version of Bayes theorem is to suppose $X$ is a continuous observable random vector and $\theta \in \Omega \subset R^{m}$ is an unknown parameter vector, and suppose the conditional density of $X$ given $\theta$ is denoted by $f(X \mid \theta)$. If $X=\left(X_{1}, X_{2}, \ldots, X_{n}\right)$ represents a random sample of size $n$ from a population with density $f(X \mid \theta)$, and $\xi(\theta)$ is the prior density of $\theta$, then Bayes theorem expresses the posterior density as
$$\xi(\theta \mid \mathrm{X})=\mathrm{C} \prod_{i=1}^{i=} f\left(x_{i} \mid \theta\right) \xi(\theta), \quad \mathrm{X}{i} \in \mathrm{R} \text { and } \theta \in \Omega$$ where the proportionality constant is $c$, and the term $\prod{i=1}^{i=n} f\left(x_{i} \mid \theta\right)$ is called the likelihood function. The density $\xi(\theta)$ is the prior density of $\theta$ and represents the knowledge one possesses about the parameter before one observes X. Such prior information is most likely available to the experimenter from other previous related experiments. Note that $\theta$ is considered a random variable and that Bayes theorem transforms one’s prior knowledge of $\theta$, represented by its prior density, to the posterior density, and that the transformation is the combining of the prior information about $\theta$ with the sample information represented by the likelihood function.
‘An essay toward solving a problem in the doctrine of chances’ by the Reverend Thomas Bayes $^{1}$ is the beginning of our subject. He considered a binomial experiment with $n$ trials and assumed the probability $\theta$ of success was uniformly distributed (by constructing a billiard table) and presented a way to calculate $\operatorname{Pr}(a \leq \theta \leq b \mid \mathrm{X}=\mathrm{p})$, where $\mathrm{X}$ is the number of successes in $n$ independent trials. This was a first in the sense that Bayes was making inferences via $\xi(\theta \mid \mathrm{X})$, the conditional density of $\theta$ given $x$. Also, by assuming the parameter as uniformly distributed, he was assuming vague prior information for $\theta$. The type of prior information where very little is known about the parameter is called noninformative or vague information.

It can well be argued that Laplace ${ }^{2}$ is the greatest Bayesian because he made many significant contributions to inverse probability (he did not know of Bayes), beginning in 1774 with ‘Memorie sur la probabilite des causes par la evenemens,’ with his own version of Bayes theorem, and over a period of some 40 years culminating in ‘Theorie analytique des probabilites.’ See Stigler ${ }^{3}$ and Chapters 9-20 of Hald ${ }^{4}$ for the history of Laplace’s contributions to inverse probability.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|The Binomial Distribution

Where do we begin with prior information, a crucial component of Bayes theorem rules? Bayes assumed the prior distribution of the parameter is uniform, namely
$$\xi(\theta)=1,0 \leq \theta \leq 1 \text {, where }$$
$\theta$ is the common probability of success in $n$ independent trials and

$$f(x \mid \theta)=\left(\begin{array}{l} n \ x \end{array}\right) \theta^{x}(1-\theta)^{n-x}$$
where $x$ is the number of successes $x=0,1,2, \ldots, n$. For the distribution of $X$, the number of successes is binomial and denoted by $X \sim \operatorname{Binomial}(\theta, n)$. The uniform prior was used for many years; however, Lhoste ${ }^{5}$ proposed a different prior, namely
$$\xi(\theta)=\theta^{-1}(1-\theta)^{-1}, 0 \leq \theta \leq 1$$
to represent information which is noninformative and is an improper density function. Lhoste based the prior on certain invariance principals, quite similar to Jeffreys. ${ }^{6}$ Lhoste also derived a noninformative prior for the standard deviation $\sigma$ of a normal population with density
$$f(x \mid \mu, \sigma)=(1 / \sqrt{2 \pi} \sigma) \exp -(1 / 2 \sigma)(x-\mu)^{2}, \mu \in R \text { and } \sigma>0$$
He used invariance as follows: he reasoned that the prior density of $\sigma$ and the prior density of $1 / \sigma$ should be the same, which leads to
$$\xi(\sigma)=1 / \sigma$$
Jeffreys’ approach is similar in that in developing noninformative priors for binomial and normal populations, but he also developed noninformative priors for multi-parameter models, including the mean and standard deviation for the normal density as
$$\xi(\mu, \sigma)=1 / \sigma, \mu \in R \text { and } \sigma>0$$
Noninformative priors were ubiquitous from the 1920 s to the 1980 s and were included in all the textbooks of that period. For example, see Box and Tiao, $^{10}$ Zellner, ${ }^{11}$ and Broemeling. ${ }^{12}$ Looking back, it is somewhat ironic that noninformative priors were almost always used, even though informative prior information was almost always available. This limited the utility of the Bayesian approach, and people saw very little advantage over the conventional way of doing business. The major strength of the Bayesian way is that it a convenient, practical, and logical method of utilizing informative prior information. Surely the investigator knows informative prior information from previous related studies.

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|The Normal Distribution

Of course, the normal density plays an important role as a model for time series. For example, as will be seen in future chapters, the normal distribution will model the observations of certain time series, such as autoregressive and moving average series. How is informative prior information expressed for the parameters $\mu$ and $\sigma$ (the mean and standard deviation)? Suppose a previous study has $m$ observations $x=\left(x_{1} x_{2}, \ldots, x_{m}\right)$, then the density of X given $\mu$ and $\sigma$ is
\begin{aligned} &f(x \mid \mu, \sigma) \propto\left[\sqrt{m} / \sqrt{2 \pi \sigma^{2}}\right] \exp -\left(m / 2 \sigma^{2}\right)(\bar{x}-\mu)^{2} \ &{\left[(2 \pi)^{-(n-1) / 2} \sigma^{-(n-1)}\right] \exp -\left(1 / 2 \sigma^{2}\right) \sum_{i=1}^{i=m}\left(x_{i}-\bar{x}\right)^{2}} \end{aligned}
This is a conjugate density for the two-parameter normal family and is called the normal-gamma density. Note it is the product of two functions, where the first, as a function of $\mu$ and $\sigma$, is the conditional density of $\mu$ given $\sigma$, with mean $\bar{x}$ and variance $\sigma^{2} / m$, while the second is a function of $\sigma$ only and is an inverse gamma density. Or equivalently, if the normal is parameterized with $\mu$ and the precision $\tau=1 / \sigma^{2}$, the conjugate distribution is as follows: (a) the conditional distribution of $\mu$ given $\tau$ is normal with mean $\bar{x}$ and precision $\mathrm{m} \tau$, and (b) the marginal distribution of $\tau$ is gamma with parameters $(m+1) / 2$ and $\sum_{i=1}^{i=m}\left(x_{i}-\bar{x}\right)^{2} / 2=(m-1) S^{2} / 2$, where $S^{2}$ is the sample variance. Thus, if one knows the results of a previous experiment, the likelihood function for $\mu$ and $\tau$ provides informative prior information for the normal population.

For example, the normal serves as the distribution of the observations of a first-order autoregressive process
$$Y(t)=\theta Y(t-1)+W(t), t=1,2, \ldots$$
where
$$W(t), t=1,2, \ldots$$
is a sequence of independent normal random variables with mean zero and precision $\tau$, and $\tau>0$. It is easy to show that the joint distribution of the $n$ observations from the AR(1) process is multivariate normal with mean vector

0 and variance covariance matrix with diagonal entries $1 / \tau\left(1-\theta^{2}\right)$ and $k$-th order covariance $\operatorname{Cov}[Y(t), Y(t+k)]=\theta^{k} / \tau\left(1-\theta^{2}\right),|\theta|<1, k=1,2, \ldots$

Note it is assumed the process is stationary, namely, $|\theta|<1$. Of course, the goal of the Bayesian analysis is to estimate the processes autoregressive parameter $\theta$ and the precision $\tau>0$. For the Bayesian analysis, a prior distribution must be assigned to $\theta$ and $\tau$, which in the conjugate prior case is a normal-gamma. The posterior analysis for the autoregressive time series results in a univariate $t$-distribution for the distribution of $\theta$ as will be shown in Chapter $5 .$

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|Bayes Theorem

X(θ∣X)=C∏一世=1一世=F(X一世∣θ)X(θ),X一世∈R 和 θ∈Ω其中比例常数为C, 和项∏一世=1一世=nF(X一世∣θ)称为似然函数。密度X(θ)是先验密度θ并且表示在观察 X 之前对参数所拥有的知识。这种先验信息最有可能从其他先前的相关实验中提供给实验者。注意θ被认为是一个随机变量，并且贝叶斯定理转换了一个人的先验知识θ，由它的先验密度表示，到后验密度，并且转换是关于先验信息的组合θ用似然函数表示的样本信息。

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|The Binomial Distribution

X(θ)=1,0≤θ≤1， 在哪里
θ是成功的常见概率n独立试验和

F(X∣θ)=(n X)θX(1−θ)n−X

X(θ)=θ−1(1−θ)−1,0≤θ≤1

F(X∣μ,σ)=(1/2圆周率σ)经验−(1/2σ)(X−μ)2,μ∈R 和 σ>0

X(σ)=1/σ
Jeffreys 的方法与为二项式和正态总体开发非信息先验的方法相似，但他也为多参数模型开发了非信息先验，包括正态密度的均值和标准差

X(μ,σ)=1/σ,μ∈R 和 σ>0

## 统计代写|贝叶斯分析代写Bayesian Analysis代考|The Normal Distribution

F(X∣μ,σ)∝[米/2圆周率σ2]经验−(米/2σ2)(X¯−μ)2 [(2圆周率)−(n−1)/2σ−(n−1)]经验−(1/2σ2)∑一世=1一世=米(X一世−X¯)2

0 和带对角线条目的方差协方差矩阵1/τ(1−θ2)和ķ- 阶协方差这[是(吨),是(吨+ķ)]=θķ/τ(1−θ2),|θ|<1,ķ=1,2,…

## 有限元方法代写

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## MATLAB代写

MATLAB 是一种用于技术计算的高性能语言。它将计算、可视化和编程集成在一个易于使用的环境中，其中问题和解决方案以熟悉的数学符号表示。典型用途包括：数学和计算算法开发建模、仿真和原型制作数据分析、探索和可视化科学和工程图形应用程序开发，包括图形用户界面构建MATLAB 是一个交互式系统，其基本数据元素是一个不需要维度的数组。这使您可以解决许多技术计算问题，尤其是那些具有矩阵和向量公式的问题，而只需用 C 或 Fortran 等标量非交互式语言编写程序所需的时间的一小部分。MATLAB 名称代表矩阵实验室。MATLAB 最初的编写目的是提供对由 LINPACK 和 EISPACK 项目开发的矩阵软件的轻松访问，这两个项目共同代表了矩阵计算软件的最新技术。MATLAB 经过多年的发展，得到了许多用户的投入。在大学环境中，它是数学、工程和科学入门和高级课程的标准教学工具。在工业领域，MATLAB 是高效研究、开发和分析的首选工具。MATLAB 具有一系列称为工具箱的特定于应用程序的解决方案。对于大多数 MATLAB 用户来说非常重要，工具箱允许您学习应用专业技术。工具箱是 MATLAB 函数（M 文件）的综合集合，可扩展 MATLAB 环境以解决特定类别的问题。可用工具箱的领域包括信号处理、控制系统、神经网络、模糊逻辑、小波、仿真等。