MTH 436 Spring 06 -- Tips for the Final Exam My dear students, our Final Exam is scheduled for Thursday, May 11, 7 pm - 10 pm, in Tyler 106. The Final is comprehensive and covers all classes and all homework assignments. As part of your preparation for the Final, review tips for Exam 1 and Exam 2: For the last portion of the material, you should, as always, know statements of all theorems, propositions, definitions, as well as all important examples. The following questions seem like good candidates. -- State and prove the Weierstrass M-Test. -- Use the Weierstrass M-Test to prove uniform convergence of a given series in a given region. -- State the theorem about the region of convergence of a power series. Find the radius of convergence for a given power series. Examine convergence at the endpoints of the interval of convergence. -- Define Taylor polynomials, remainders, and the Taylor series of a function f at a point x0. Find the Taylor series at some point for a not-too-complicated function. -- State the Taylor Theorem with the Remainder in the Form of Lagrange. Use it to prove convergence of a given Taylor series. -- State and prove Cauchy Condition for Uniform Convergence of a Series of Functions (Th 46.1) -- State and prove Theorems 47.1, 47.2 -- Prove Prop. 48.2. I hope you all enjoy the Final and get As!