18.085 | Fall 2008 | Graduate

Computational Science and Engineering I


Course Meeting Times

Lectures: 3 sessions / week, 1 hour / session

Recitations: 1 session / week, 1 hour / session


Calculus of Several Variables (18.02) and Differential Equations (18.03) or Honors Differential Equations (18.034)

Course Outline

This course has four major topics:

  • Applied linear algebra (so important!)
  • Applied differential equations (for engineering and science)
  • Fourier methods
  • Algorithms (lu, qr, eig, svd, finite differences, finite elements, FFT)

My Goals for the Course

I hope you will feel that this is the most useful math course you have ever taken. I will do everything I can to make it so. This will not be like a calculus class where a method is explained and you just repeat it on homework and a test. The goals are to see the underlying pattern in so many important applications—and fast ways to compute solutions.

Assignments and Exams

This course has ten problem sets, three one-hour exams, and no final exam. You may use your textbook and notes on the exams.


Let me try to say this clearly: my life is in teaching, to help you learn. Grades have come out properly for 20 years (almost all A-B). I will NOT spend the semester thinking about grades. I hope you don’t either. The homeworks will be important and I plan 3 exams and no final. Those exams are open book and a chance for you to bring key ideas together.


The textbook for this course is:

Strang, Gilbert. Computational Science and Engineering. Wellesley, MA: Wellesley-Cambridge Press, 2007. ISBN: 9780961408817. (Table of Contents)

Information about this book can be found at the Wellesley-Cambridge Press Web site, along with a link to Prof. Strang’s new “Computational Science and Engineering” Web page developed as a resource for everyone learning and doing Computational Science and Engineering.


1 Four special matrices
R1 Recitation 1
2 Differential eqns and Difference eqns
3 Solving a linear system
4 Delta function day!
R2 Recitation 2
5 Eigenvalues (part 1)
6 Eigenvalues (part 2); positive definite (part 1)
7 Positive definite day!
R3 Recitation 3
8 Springs and masses; the main framework
9 Oscillation
R4 Recitation 4
10 Finite differences in time; least squares (part 1)
11 Least squares (part 2)
12 Graphs and networks
R5 Recitation 5
13 Kirchhoff’s Current Law
14 Exam Review
R6 Recitation 6
15 Trusses and ATCA
16 Trusses (part 2)
17 Finite elements in 1D (part 1)
R7 Recitation 7
18 Finite elements in 1D (part 2)
19 Quadratic/cubic elements
20 Element matrices; 4th order bending equations
R8 Recitation 8
21 Boundary conditions, splines, gradient and divergence (part 1)
22 Gradient and divergence (part 2)
23 Laplace’s equation (part 1)
R9 Recitation 9
24 Laplace’s equation (part 2)
25 Fast Poisson solver (part 1)
26 Fast Poisson solver (part 2); finite elements in 2D (part 1)
R10 Recitation 10
27 Finite elements in 2D (part 2)
28 Fourier series (part 1)
R11 Recitation 11
29 Fourier series (part 2)
30 Discrete Fourier series
31 Examples of discrete Fourier transform; fast Fourier transform; convolution (part 1)
R12 Recitation 12
32 Convolution (part 2); filtering
33 Filters; Fourier integral transform (part 1)
34 Fourier integral transform (part 2)
R13 Recitation 13
35 Convolution equations: deconvolution; convolution in 2D
36 Sampling Theorem

Course Info

As Taught In
Fall 2008
Learning Resource Types
Lecture Videos
Problem Sets with Solutions
Exams with Solutions
Course Introduction
Programming Assignments