# Syllabus

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## 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 |