Course 18.086: Mathematical Methods for Engineers II (Spring 2009)

Directions: The homework will have a written portion, and a computational portion. Please turn in your solutions to the written part in class together with plots and answers from the computational parts, and send your code to Hila Hashemi, with an informative subject, e.g., "Pset 2".

Problem Set 5 (due Friday, May 1, 2009, at 2pm): 8.2 exercises 4,5,6

Problem set 4 (due Friday, April 17, 2009, at 2pm): pdf

Problem set 3 (due Wednesday, April 1, 2009, at 2pm): pdf

Here are solutions to problem set 2: pdf

Here is some code:

Problem set 2 (due Friday, March 6, 2009, at 2pm): pdf

Here are solutions to problem set 1: pdf

Here is some code:

Problem set 1 (due on February 20, 2009, at 2pm):

Some students have expressed confusion regarding problem 8. Here's a clarification: K refers to the Toeplitz matrix defined on pages 1 and 2 of the text. The problem is a model of heat flow with fixed boundary conditions. You are asked to compare various numerical approximations for accuracy, and this means you should find out how far a given approximation is from the true solution exp(-KT) - "how far" means take an L2 norm of the error vector, i.e., sum the squares of the components and take the square root. You may find it useful when computing this exponential to use the diagonalization, so your computer doesn't spend several hours unnecessarily. The eigenvalues and eigenvectors are given on page 56 of the text. In order to find the order of accuracy and leading coefficient, you should choose two different time steps for the same time interval, and compare the errors you get. Hopefully, the answers will resemble something reasonable.