18.085 Mathematical Methods for Engineers (aka Computational Science and Engineering, CSE) I, Spring 2008
Prerequisites: 18.02, 18.03 or 18.034
Units: 309
Lectures: MWF 12 in 4370
Office hours: To be announced
The class website for Spring 2008 is at Stellar: 18.085 Spring 2008
Syllabus from S2007 (to be updated) (PDF)
 Course information (to be updated)

The course is an introduction to mathematical and computational methods useful in engineering applications. The focus is on understanding some of the basic analytical and numerical techniques for solving boundary value problems. There are three parts to the course:
1. Applications of linear algebra: Linear systems, matrix factorizations (LU, QR, SVD, SDS^{1}), calculation of eigenvalues, least squares approximation, mechanical oscillations, mechanical structures, networks. 2. Boundary value problems: Origin of boundaryvalue problems, wave equation, heat/diffusion equation, Laplace's equation, separation of variables, SturmLiouville problem, orthogonal functions, Chebyshev/Legendre/Hermite polynomials. 3. Fourier methods: Discrete Fourier Transform and FFT, spectral methods, Galerkin and finite element methods, wavelets and signal processing.
The course is based on the first four chapters of G. Strang's Computational Science and Engineering (check CSE web site by Prof. Strang.) Additional recommended books will be announced later. There will be three openbook midterm exams and several problem sets that will count towards the final grade. There will be no final exam. Matlab will be used for numerical computations throughout the course.  Assignments, notes, and updates (from S2007)

03/12/07: Quiz #1 (PDF). Solutions for Quiz #1 (PDF).
04/18/07: Quiz #2 (PDF). Solutions for Quiz #2 (PDF).
05/16/07: Quiz #3 (PDF).
 Matlab and linear algebra resources

Short Matlab tutorial.
Matlab at MIT.
"Matlab Guide" by D. Higham and N. Higham is a nice introduction to Matlab.
For linear algebra background, check Prof. Strang's video lectures and 18.06 web site.  Information on previously offered 18.085