Assigned readings are sections in the course textbook: Mathews, J. H., and K. D. Fink. *Numerical Methods Using MATLAB®*. 3rd ed. Upper Saddle River, NJ: Prentice Hall, 1998. ISBN: 9780132700429.

LEC # | TOPICS | READINGS |
---|---|---|

1 |
Introduction Computer Architecture Number Representations Recursion |
Sections 1.1-1.2 |

2 |
Error Propagation Error Estimation Condition Numbers |
Sections 1.2-1.3 |

3 |
Linear Systems of Equations: Cramer’s Rule Gaussian Elimination |
Section 1.3 |

4 |
Linear Systems: Gaussian Elimination Pivoting LU Factorization Error Analysis |
Sections 3.1-3.2 |

5 |
Linear Systems: Tri-Diagonal Systems Special Matrices |
Sections 3.3-3.4 and 3.6 |

6 |
Linear Systems: Iterative Methods Convergence of Iterative Schemes |
Section 3.4 |

7 |
Roots of Non-linear Equations: Bisection Newton-Ralphson Iteration |
Section 3.7 |

8 |
Interpolation of Functions by Polynomials Lagrange Interpolation Triangular Family |
Sections 2.1-2.4 |

9 |
Numerical Differentiation and Integration Error Estimates |
Sections 4.1-4.4 |

10 |
Ordinary Differential Equations Initial Value Problems: Euler and Runge-Kutta Methods |
Sections 6.1-6.2 and 7.1-7.3 |

11 |
Ordinary Differential Equations (cont.) Boundary Value Problems: Finite Difference Methods |
Sections 9.1-9.2 and 9.4-9.5 |

12 |
Minimization Problems Least Square Approximation Optimization |