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[–][deleted]  (3 children)

[deleted]

[–][S] 0 points1 point  (2 children)

Sorry for the late reply. First, thanks for responding to this - didn't think anyone would. Second, could you provide an example of how to apply the E-L equation to take these functions down to an ODE?

[–] 1 point2 points  (0 children)

Here is a functional

S = \int 1/2 m x'2 - 1/2 k x2 dt

The E-L equation says take d/dt dL/dx' - dL/dx = 0

Here:

dL/dx' = m x'

d/dt dL/dx' = m x''

dL/dx = -k x

So the ODE you need to solve is

mx'' - - kx = 0 mx'' + kx = 0

You should be able to solve that ODE.

[–][S] 0 points1 point  (8 children)

So, I was told to use the Hamiltonian method for #1, 2.

Quite frankly, I don't think I've felt this lost in a math course before. This is a summer class, so the progress is accelerated, but no one in our class is able to follow the professor. He's jumping around the chapters in our required text (this hw problem dealt with topics not really covered in the book). Any advice on what I should do in order to actually learn some Diff Eq?

[–][deleted]  (7 children)

[deleted]

[–][S] 0 points1 point  (6 children)

I am an undergrad. This course is listed as a 300 level course, so I'm not sure if it's necessarily an introduction course to Diff. Eqn's. But I'm taking it as an equivalent course, so I can transfer credits to the university I'm a full-time student at. The equivalent course to my university is titled "Introduction to Diff Eqn's" and it's a 200 level course. So I'm not sure why they're listed as equivalents.

The book we're using is, "Introductory Differential Equations using Sage" by David Joyner and Marshall Hampton.

[–][deleted]  (5 children)

[deleted]

[–][S] 0 points1 point  (0 children)

Copy/Paste from course website: Course Catalog’s Description
First and second order differential equations with applications, linear differential equations, power series solutions, Laplace transforms.

Course Objectives Upon completing the course, students should be able to:

 Describe the basic existence and uniqueness conditions for ordinary differential equations, and their physical significance.
Solve first and second order differential equations by direct integration, transform, and power series methods.
Use software to study differential equations numerically, taking note of the reasons for different numerical methods.
Classify equilibria and dynamics for two-dimensional systems of differential equations (if time).


"This is a topic driven course, and I would like to do much more than this! But the above are the basics."

[–][S] 0 points1 point  (3 children)

Also, I'd love to hear your recommendation.

[–][deleted]  (2 children)

[deleted]

[–][S] 0 points1 point  (1 child)

Shoot, I don't know if I have the heart to do that. The prof's not a bad guy - he's not intentionally trying to lose the class. I probably shouldn't have complained to you guys if I wasn't prepared to take action against him, but I was just wondering if it was my own incompetency with mathematics or if there was something else going on.