MATH 257 Study Guide - Midterm Guide: Gibbs Phenomenon, Fourier Series
Document Summary
Be sure that this examination has 8 pages (5 problems). Write your last name on top of each page. Submit only this booklet, with solution written in space provided (you may use adjacent page(s)). Solutions on scratch paper will not be graded. A 2-sided self-prepared letter-size formula sheet is allowed. In case of an exam disruption such as a re alarm, leave the exam papers in the room and exit quickly and quietly to a pre-designated location. [20] problem 1: find the coe cients of fourier cosine series of the function f (x) = 1, Solve the following problem for the laplace equation in the rectangle: U(x, y) = 0, ux(0, y) = ux(4, y) = uy(x, 0) = 0, u(x, 3) = f (x), where f (x) is given in problem 1. explicitly. You may state results you know, e. g. , eigenbasis, without derivation. ] [remark: you do not have to do all steps of separation of variables.
