## COURSE DESCRIPTION

The goal of this course is to give you:

- practical experience with common computational methods in engineering, and
- enough theoretical understanding to know when those methods can go wrong

Review of linear algebra, applications to networks, structures, and estimation, finite difference and finite element solution of differential equations, Laplace's equation and potential flow, boundary-value problems, Fourier series, discrete Fourier transform, convolution. Frequent use of MATLAB in a wide range of scientific and engineering applications.

This class is suitable for masters students, advanced undergraduates, or anyone interested in building a foundation in computational science.

**Prerequisites:** Calculus and some linear algebra

**Text Book:** *Computational Science and Engineering* by Gilbert Strang

**Grades:** 50% problem sets, 50% three in-class quizzes. Lowest problem set score will be dropped.

**Problem Sets:** Will be due in class.

# SCHEDULE

Event | Date | Related Documents |
---|---|---|

PSET 1 | Due Feb 21 | Solutions |

PSET 2 | Due Feb 28 | Solutions, Code for problem 5, Code for problem 6 |

Quiz 1 | Mar 7 in class | Practice Problems, Practice Solutions Quiz 1 solutions |

PSET 3 | Due Mar 21 | Solutions |

PSET 4 | Due Apr 4 | Wave file. Solutions |

Quiz 2 | Apr 11 in class | Practice Quiz (with solutions) Quiz 2 solutions |

PSET 5 | Due Apr 25 | Solutions |

PSET 6 | Due May 2 | Solutions |

Quiz 3 | May 9 in class | Practice Quiz, Practice Solutions |

# Syllabus

Day | Topics (page numbers) |
---|---|

Feb 5 | Truss stability problem (185-188, 192-193) Linear algebra basics (685-689) |

Feb 7 | Rank-nullity theorem (690) |

Feb 12 | Resistor network problem (142-151) Linear equations, Ax=b (686-687) LU decomposition (78, 26-30) |

Feb 14 | LU operation count (32-33) |

Feb 21 | Best fit problems Least squares Normal Equations |

Feb 26 |
Gram-Schmidt (80-81) QR decomposition (79-81) |

Feb 28 | Eigenvalues and eigenvectors Positive definite matrices Error analysis in solving Ax=b Condition number Singular value decomposition |

Mar 5 | Singular value decomposition (continued) Pseudoinverse Review |

Mar 7 | Quiz 1 |

Mar 12 | Frequency identification problem Complex numbers, vectors, and matrices Fourier basis Discrete Fourier Transform |

Mar 14 | Discrete Fourier Transform (continued) |

Mar 19 | Radioactive decay problem Forward Euler Backward Euler Trapezoidal Rule |

Mar 21 | Mass spring problem Leapfrog methods |

Apr 2 | Elastic membrane problem Boundary value problems Dirac Delta |

Apr 4 | Finite element method in 1d |

Apr 9 | Finite element method in 2d |

Apr 11 | Quiz 2 |

Apr 18 | Fourier series |

Apr 23 | Fourier series and boundary value problems |

Apr 25 | Potential flow |

Apr 30 | TBD |

May 2 | TBD |

May 7 | Review |

May 9 | Quiz 3 |

May 14 | TBD |

May 16 | TBD |