MATH 2Z03 Chapter Notes - Chapter 5: Convolution, Analytic Function, Periodic Function
2 Aug 2018
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4. 2 inverse transform and transforms of derivatives. Most of these laplace formulas are in the back of the book. Convolution equation (not on exam):for a periodic function, f (t) with period, t, the transform is: t t d t. Impulse, where (0) = and (anything else) = 0. Chapter 5 series solutions of linear differential equations. When you are evaluating this type of question, you only need to find the particular solution. The reason why you keep incrementing the starting n is because the first term will have an x0 before differentiation. When you differentiate a constant, it will always become 0. Frobenius"s theorem actually says to guess: y x r x. I describe what those mean here, but you generally won"t need to. However, most of the time (i. e. when your function is analytic), you"ll be dealing with an r = 0 and 0.
