<video><caption><image_2>The image is a photograph of a whiteboard with a handwritten text written on it. The text reads "We are tempted to consider 8 = 1-1 = 2". The text is written in black marker and is centered on the whiteboard. On the right side of the image, there is a logo of the company "CDEEP" and the company's logo on the top right corner. The background is blurred, but it appears to be a classroom or classroom setting.</caption><caption><image_3>The image is a whiteboard with black text written on it. The text reads "We are tempted to consider" and is written in a cursive font. Below the text, there is a logo of the Indian government, which is a shield with a crown on top. On the right side of the image, there are two lines of text that read "CEEP" and "CDEEP". On the bottom right corner, there appears to be a logo for the company. The background of the whiteboard is plain white.</caption></video><transcript><audio_4>to consider s equal to 1 minus z inverse what it means is we are approximating the derivative by taking the difference between the</transcript><caption><image_5>The image is a photograph of a whiteboard with a handwritten note on it. The note reads "We are tempted to consider 8 = 1-2". The note is written in black marker and is written on a white paper. On the right side of the whiteboard, there is a logo of the Central Bank of India (CBI) and a stamp that reads "CBIEP". The background of the image is blurred, but it appears to be a classroom or a classroom setting.</caption><transcript><audio_6>now we do not need to go too far to see that this is not adequate as far as our conditions go in fact all that we need to do is to write z in terms of</transcript><video><caption><image_7>The image is a whiteboard with black text written on it. The text reads "We are tempted to consider" and is written in a cursive font. Below the text, there is a list of equations written in black marker. The equations are arranged in a grid-like pattern, with each equation written in the same font as the rest of the text. The background of the whiteboard is plain white. On the right side of the image, there are two logos, one for CDEEP and the other for the company.</caption><caption><image_8>The image shows a whiteboard with a handwritten equation written on it. The equation is written in black marker and is written on a piece of paper. The text on the whiteboard reads "We are tempted to consider" and there is a logo of the Indian government on the top right corner. The background of the image is blurred, but it appears to be a classroom or a classroom setting.</caption><caption><image_9>The image is a photograph of a whiteboard with a mathematical equation written on it. The equation is written in black marker and is surrounded by various mathematical symbols. The text on the whiteboard reads "We are tempted to consider" and there is a logo of the Indian Institute of Technology (CDEEP) on the top right corner. The background of the image is blurred, but it appears to be a classroom or a classroom setting.</caption><caption><image_10>The image is a screenshot from a video titled "We are tempted to consider". It shows a whiteboard with a mathematical equation written on it. The equation is written in black marker and is surrounded by other mathematical equations. The background of the image is white and there is a logo of the Indian government on the top right corner. The image appears to be taken in a classroom or a classroom setting.</caption><caption><image_11>The image is a whiteboard with a mathematical equation written on it. The equation is written in black marker and is written as "We are tempted to consider". Below the equation, there is a logo of the Indian Institute of Technology (CDEEP) and the text "CDEEP IT Bombay". The background of the whiteboard is plain white.</caption></video><transcript><audio_12>s so the inverse is clearly 1 minus s and therefore z is 1 by 1 minus s if we take this transformation to be true and then we only need to substitute s equal to j omega and then we have 1 by 1 minus j omega does not even have a magnitude of 1.</transcript><transcript><audio_13>so mod of 1 by 1 minus j omega so we have failed on a very important count anyway and in fact this transformation you know we should have this is if this is z</transcript><transcript><audio_14>then the imaginary axis should have gone to the unit circle and anyway this is not going to be so you know a simple approximation like this</transcript> to consider s equal to 1 minus z inverse what it means is we are approximating the derivative by taking the difference between the now we do not need to go too far to see that this is not adequate as far as our conditions go in fact all that we need to do is to write z in terms of s so the inverse is clearly 1 minus s and therefore z is 1 by 1 minus s if we take this transformation to be true and then we only need to substitute s equal to j omega and then we have 1 by 1 minus j omega does not even have a magnitude of 1. so mod of 1 by 1 minus j omega so we have failed on a very important count anyway and in fact this transformation you know we should have this is if this is z then the imaginary axis should have gone to the unit circle and anyway this is not going to be so you know a simple approximation like this
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