General course description

Instructor: Da Kuang

TA: Wei Zhu

- Floating-point system
- Nonlinear equations with one variable
- Interpolation methods
- Numerical integration
- Linear systems / LU factorization
- Matlab/Octave programming

- (Officially) Required: R. L. Burden and J. D. Faires, Numerical analysis, 9th or 10th edition.
- Recommended: Michael Heath, Scientific Computing, 2nd edition.
- A good summary (or cheat-sheet) of the required textbook in slides: [link]
- A more practical treatment: Cleve Moler, Numerical Computing with Matlab.
- Matlab tutorial: [link]
- Additional references (posted here as the course proceeds):
- Floating-point system: [Slides from EE103]
- Nonlinear equations with one variable: [Slides from EE103]
- LU factorization: [Slides from EE103]
- Cholesky factorization: [Slides from EE103]
- Vector norms: [Slides from EE103]
- Matrix norms: [Slides from EE103]
- Conditioning and stability: [Slides from EE103]

- 60% Homework
- 20% Midterms
- 20% Final exam

- No late homework allowed. However, there are no penalties for medical reasons or emergencies. You must submit a doctor's note or an official letter explaining the emergency.

All the students must observe the conduct code.

Date | Mon | Wed | Fri |
---|---|---|---|

Sep 25 |
Course overview / Logistics | ||

Sep 28 Sep 30 Oct 2 |
Nonlinear equations (bisection, fixed-point) Reading: BF 2.1, 2.2 / MH 5.2.1, 5.2.2 |
Matlab/Octave introduction (example data set) HW1 out |
Nonlinear equations (convergence order and rates) Reading: BF 2.4 / MH 5.1.2 |

Oct 5 Oct 7 Oct 9 |
Nonlinear equations (Newton's method) Reading: BF 2.3 / MH 5.2.3 |
Nonlinear equations (secant method) Reading: BF 2.3 / MH 5.2.4 HW1 due; HW2 out |
Nonlinear equations (summary, pitfalls) Reading: BF 2.4 / MH 5.1.1 |

Oct 12 Oct 14 Oct 16 |
Conditioning and stability Reading: BF 7.1 / MH 1.2, 2.3.1 |
Floating-point numbers Reading: BF 1.2 / MH 1.3 HW2 due |
Case study Midterm review |

Oct 19 Oct 21 Oct 23 |
Midterm I [10%] |
Linear systems (Gaussian elimination) Reading: BF 6.1 / MH 2.2.1, 2.2.2 HW3 out |
Linear systems (LU factorization) Reading: BF 6.5 / MH 2.2.3 |

Oct 26 Oct 28 Oct 30 |
Linear systems (LU factorization) Reading: BF 6.5 / MH 2.2.3 |
Linear systems (pivoting) Reading: BF 6.2 / MH 2.2.4 HW3 due; HW4 out |
Linear systems (Cholesky factorization) Reading: BF 6.6 / MH 2.4 |

Nov 2 Nov 4 Nov 6 |
Linear systems (Jacobi, Gauss-Seidel) Reading: BF 7.3 / MH 11.5.2, 11.5.3 |
Matrix norms Reading: BF 7.1 / MH 2.3.2, 2.3.3 HW4 due |
Singular value decomposition (very briefly) Midterm review Reading: BF 9.6 / MH 4.5 |

Nov 9 Nov 11 Nov 13 |
Midterm II [10%] |
(Veterans Day holiday) | Examples for SVD Principal component analysis (Data) (Script) |

Nov 16 Nov 18 Nov 20 |
Matrix condition number Reading: BF 7.5 / MH 2.3.3 HW5 out |
Interpolation (monomial, Lagrange) Demo Reading: BF 3.1 / MH 7.1 - 7.2.2 |
Interpolation (Newton, cubic spline) Reading: BF 3.3, 3.5 / MH 7.2.3, 7.3.2 |

Nov 23 Nov 25 Nov 27 |
Numerical integration (Newton-Cotes, composite rules) Reading: BF 4.3, 4.4 / MH 8.2, 8.4.1 HW5 due; HW6 out |
(Cancelled) | (Thanksgiving) |

Nov 30 Dec 2 Dec 4 |
Numerical integration (error analysis) |
Numerical integration (extrapolation methods) HW6 due |
Demos for PCA and cubic splines Course review |

Dec 7 |
Final exam [20%]3pm-6pm |