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Entrance Guide, Math 527 This document is a summary of prerequisites that we shall particularly rely on in this class. From first-year calculus, we will heavily use 1. Improper integrals. You should know how improper integrals are defined and how to calculate them. You should understand what is meant by convergence and divergence of improper integrals and how to use the comparison theorem to prove convergence and divergence. Of particular use Z 0 e - st dt = ( 1 s , if s > 0. diverges , if s 0. Z 1 1 t p dt = ( 1 p - 1 , if p > 1. diverges , if p 1. 2. Infinite series and power series. You should understand convergence and divergence of infinite series and comparison and ratio tests for convergence and divergence. You should understand power series, finding intervals of convergence for power series, Tay- lor series. 3. Linear Algebra. Vectors, matrices, matrix multiplication, determinants, eigenvectors and eigenvalues. The remainder of this sheet summarizes some things you should know from ordinary di±erential equations. I have written these down in fairly general form, but you should be generally familiar with the ideas as applied to second-order equations. Don’t panic if you forget the mechanics of calculating solutions in these methods. You will learn di±erent techniques and get an opportunity to relearn as we go through the ODE material of the
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entranceguide - Entrance Guide, Math 527 This document is a...

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