Course Meeting Times
Lectures: 3 sessions / week, 1 hour / session
Recitations: 1 session / week, 1 hour / session
Prerequisites
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.
Grades
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.
Text
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.
Calendar
LEC # | TOPICS |
---|---|
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 A^{T}CA |
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 |