TAM 542 Homework 6
Due April 13 2016
Recommended Reading: Chapter 7 and Chapter 9 in Strauss.
Problem 1 on page 196 of Strauss.
Problem 6 on page 196 of Strauss.
Problem 18 on page 197 of Strauss.
Problem 4 on page
TAM 542 Homework 4
Due March 9 2016
Recommended Reading: Chapter 4 and Chapter 11 in Strauss.
Problem 4 on page 87 of Strauss.
Problem 3 on page 90 of Strauss.
Problem 17 on page 100 of Strauss.
Consider the eigenva
TAM 542 Homework 5
Due March 30 2016
Recommended Reading: Chapter 7 and Chapter 12 in Strauss.
Use the Fourier transform to solve
for < x < ,
ut = uxx + ux
u(x, 0) = (x).
Use Fourier transform to find the solution of
u + u = (x),
TAM 542 Homework 2
Due Wednesday, February 17 2016
Solve the diffusion equation on the real line with initial condition u(x, 0) = (x) = ex for x > 0 and
(x) = 0 for x < 0.
Solve the wave equation on the real line with initial condition
TAM 542 Homework 7
Due April 20 2016
Recommended Reading: Calculus of Variations notes by Peter Olver.
Write the Euler Lagrange (E-L) equation for stationary points of the integral
Obtain the stationary point for boundary c
TAM 542 Homework 1
Due Wednesday, February 3, 2016
In this homework assignment, u, v are real-valued functions of x = (x1 , x2 , . . . , xn ), F is a Rn -valued function
of x, denotes the gradient vector, F denotes the matrix with (i, j) entry x
TAM 542 Homework 3
Due Wednesday, February 24 2016
This homework is a continuation of the class notes on obtaining the Poissons integral formula solution of
the Laplaces equation on a disk in the complex plane.
Let x = r cos and y = r sin . Show
TAM 542 MATHEMATICAL METHODS II
Prof. Prashant G. Mehta
MW 5:00-6:00pm, or by appointment
Regular office hours in 359 CSL
Introduction to the Calculus of Variations
by Peter J. Olver
University of Minnesota
Minimization principles form one of the most wide-ranging means of formulating mathematical models governing the equilibrium configurations of physical s