Office: HSB 241C

Office hours: 9:30 AM to 11:30 AM, Mondays.

- Spectral method
- Finite Element method
- Finite Volume method

*Spectral Methods in MATLAB*, by Lloyd N. Trefethen*Introduction to Finite and Spectral Element Methods using MATLAB*, C. Pozrikidis*Finite Volume Methods for Hyperbolic Problems*, by Randall J. Leveque

Evaluation | Homework | Quiz | Project |

Points | 65 | 10 | 25 |

There will be a total of \(13\) homework (each worth 5 points) due roughly weekly. Homework will be posted on this website and will be

To save trees and keep track of submission on time, students need to send their homework through email to with the subject reading 2018_CMS_HW_#_firstname, where # needs to be replaced with the homework number (between \(1\) and \(13\)) and firstname is to be replaced with your first name in lower case. Details on how to submit the computing part of the homework will be elaborated in the homework itself. No collaboration is allowed for homework.

The grader will expect you to express your ideas clearly, legibly, and completely, often requiring complete English sentences rather than merely just a long string of equations or unconnected mathematical expressions. This means you could lose points for poorly written proofs or answers. Clear exposition is a crucial ingredient of communication. Clarity of thought and presentation is more important in mathematics & sciences than any other field. The only way to master exposition is by repeated practicing.

- https://www.sharelatex.com/
- https://www.overleaf.com/

There will be a short surprize (3-5 minutes) quiz once in a while and will account for \(10\%\) of your total grade.

This could be a work arising out a published article or from material/discussions in class. The project is due April 30th. More details will be provided by the middle of February.

Week |
Monday/Tuesday |
Homework |

Jan 16: Lecture 1 | Floating point arithmetic, Numerical Linear Algebra, Finite Difference, Interpolation | Homework 1: Jan 29 |

Feb 4: Lecture 2 | Spectral Methods: Chapter 1, 2, 3 of Trefethen | Homework 2: Feb 12 |

Feb 12: Lecture 3 | Spectral Methods: Chapter 4, 5, 6 of Trefethen | Homework 3: Feb 19 |

Feb 19: Lecture 4 | Spectral Methods: Chapter 7, 8, 9, 10 of Trefethen | Homework 4: Feb 26 |

Feb 26: Lecture 5 | Quadrature; Euler Maclaurin | Homework 5: Mar 5 |

Mar 13: Lecture 6 | Finite Element Methods: Chapter 1 of Pozrikidis | Homework 6: Mar 19 |

Mar 26: Lecture 7 | Finite Element Methods: Chapter 2 of Pozrikidis | Homework 7: Apr 2; RK4 |

Apr 2 & 3: Lecture 8 & 9 | Iterative methods for solving linear systems | Homework 8: Apr 9 |

Apr 9 & 10: Lecture 10 & 11 | Boundary Integral Method Representation of solution using Green's function |
Homework 9: Apr 16 |

Apr 16 & 17: Lecture 12 & 13 | Fast solvers for Boundary Integral Method Gerenalized Rybicki Press Low Rank Direct solver |
Homework 10: Apr 25 |

Apr 23: Lecture 14 | Finite Volume Method | Homework 11: Apr 30 Project: Apr 30 |