mat315w08review2 - Mat 315 Review for Exam 2 The first exam...

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Mat 315 Review for Exam 2 February 25, 2008 The first exam is Monday, March 3. The exam will cover sections 6.2-6.6. You should study your homework assignments, the notes for the class and the examples and proofs in the book. You definitely should know the definitions of the following terms: f n f pointwise f n f uniformly on A f n converges pointwise to f f n converges uniformly to f power series radius of convergence Also know the following theorems: Criterion for Uniform Convergence ( )Theorem 6.2.6: The uniform limit of continuous functions is continuous Theorem 6.3.1: Hypotheses that guarantee that (lim f n ( x )) = lim f n ( x ) ( ) Theorem 6.4.2: The uniform sum of continuous functions is continuous. Theorem 6.4.3: Hypotheses that guarantee that ( f n ( x )) = f n ( x ) Theorem 6.4.4: Cauchy Criterion for Uniform Convergence of Series ( ) Corollary 6.4.5: Weierstrass M
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