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)
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.
||Four special matrices
||Differential eqns and Difference eqns
||Solving a linear system
||Delta function day!
||Eigenvalues (part 1)
||Eigenvalues (part 2); positive definite (part 1)
||Positive definite day!
||Springs and masses; the main framework
||Finite differences in time; least squares (part 1)
||Least squares (part 2)
||Graphs and networks
||Kirchhoff's Current Law
||Trusses and ATCA
||Trusses (part 2)
||Finite elements in 1D (part 1)
||Finite elements in 1D (part 2)
||Element matrices; 4th order bending equations
||Boundary conditions, splines, gradient and divergence (part 1)
||Gradient and divergence (part 2)
||Laplace's equation (part 1)
||Laplace's equation (part 2)
||Fast Poisson solver (part 1)
||Fast Poisson solver (part 2); finite elements in 2D (part 1)
||Finite elements in 2D (part 2)
||Fourier series (part 1)
||Fourier series (part 2)
||Discrete Fourier series
||Examples of discrete Fourier transform; fast Fourier transform; convolution (part 1)
||Convolution (part 2); filtering
||Filters; Fourier integral transform (part 1)
||Fourier integral transform (part 2)
||Convolution equations: deconvolution; convolution in 2D