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Teaching

  • 18.303 - Linear PDE
  • 18.085 - CSE
  • 18.06 - Linear Algebra
  • 18.03 - ODE
  • 18.085 Mathematical Methods for Engineers (aka Computational Science and Engineering, CSE) I, Spring 2008

    Prerequisites: 18.02, 18.03 or 18.034
    Units: 3-0-9
    Lectures: MWF 12 in 4-370
    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)

    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 boundary-value problems, wave equation, heat/diffusion equation, Laplace's equation, separation of variables, Sturm-Liouville 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 open-book mid-term 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.

    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).

    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.

    Fall 2006 course web site
    OCW
    Prof. Strang's CSE web site