exsheet0 - Mathematical Methods I Dr Gordon Ogilvie Example...

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Mathematical Methods I Natural Sciences Tripos, Part IB Dr Gordon Ogilvie Michaelmas Term 2008 Example Sheet 0 This is a revision sheet. If you did NST Mathematics A or B last year you should be able to do the questions already (let me know if I have made an incorrect assumption here, especially if you did Course A). If you did the Mathematical Tripos last year you will have to read up on Fourier Series for question 3. Some of the material will be touched on in the ±rst couple of lectures, so you might prefer to wait until then. 1. (a) Let h be a function of one variable. Working from Frst principles, di±erentiate with respect to x the function I ( x ) = i x a h ( y ) d y , where a is a constant. (b) Let f ( x, y ) be a function of two variables. Working from Frst principles, dif- ferentiate with respect to x the function J ( x ) = i x a f ( x, y ) d y . 2. Let g ( x, y, z ) be a function of three variables. Working to O ( δx, δy, δz ), write down the Taylor expansion of
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exsheet0 - Mathematical Methods I Dr Gordon Ogilvie Example...

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