**Lectures:** MWF 2:10-3:00 PM, Stanley 105

**Prerequisites:** Math 53 and 54 or equivalent

**Required Text:** Numerical Analysis, 9th or 10th Edition, by Burden/Faires

**Matlab resources:**

- Christos Xenophontos, A Beginner's Guide to MATLAB (online)
- Otto and Denier, An Introduction to Programming and Numerical Methods in MATLAB (online)
- Quarteroni and Saleri, Scientific Computing with MATLAB and Octave (online version)
- K. Sayood, Learning programming using MATLAB (online version)
- How to set up a UC Berkeley Library Proxy Server (off-campus access to online books)

**Ways to run matlab:**

- MATLAB will be available during discussion sections in the computer lab B3A Evans
- The University has a site license you can use to install it on your own computer. You can download MATLAB here and obtain a student license here.

**Syllabus:** Programming for numerical calculations, round-off
error, approximation and interpolation, numerical quadrature, matrix
computations, and numerical
solutions of ordinary differential equations.

- Error anlysis, roundoff error and computer arithmetic, algorithms and convergence (Chapter 1)
- Nonlinear equations: bisection, Newton and secaont methods (Chapter 2)
- Polynomial interpolation and approximation (Chapter 3)
- Numerical differentiation and integration (Chapter 4)
- Initial value problems for ordinary differential equations (Chapter 5)
- Matrix computations: linear systems, matrix factorizations, norms (Chapter 6, 3.5, 7.1)

**Course Material:** I will post handouts and assignments on
bCourses.
Please e-mail me if you do not have access to the bCourses page by Friday, Aug 24.

**Grading:**

programming assignments: | 12% | (all scores count) |

homework: | 6% | (lowest score dropped) |

quizzes: | 12% | Sep 4, Sep 25, Oct 16, Nov 6, Nov 27 (in section, lowest score dropped) |

Midterm 1: | 20% | Wednesday, October 3 (in class) |

Midterm 2: | 20% | Wednesday, November 7 (in class) |

Final exam: | 30% | Thursday, Dec 13, 3-6 PM (location TBA) |

**More Details:** 13 homework assignments, 4 programming
assignments, 5 quizzes. My grade cutoffs are usually around 90 A, 85
A-, 80 B+, 75 B, 70 B-, 65 C+, 60 C, 50 D. Your lowest midterm grade
will be replaced by your grade on the final if you do better on the
final. If you miss a midterm for any reason (illness, family
emergency, didn't study, etc.), the final will used to replace
the midterm. Only one midterm grade can be replaced this way.
Homework and programming assignments are due at the beginning of
discussion section. Quizzes will be given in section.
* Late assignments and missed quizzes cannot be made up.*
Collaboration is encouraged in discussing ideas, but you are not
allowed to share code or written solutions of homework. If you are
caught cheating, you will receive an F in the course and be reported
to the university.

**Detailed syllabus** (will be updated as the semester progresses)

Mon | Tues | Wed | Fri | |||||
---|---|---|---|---|---|---|---|---|

8/22 Lec01, 1.1 |
Overview, example of unstable recurrence, Mean Value Theorem, Rolle's Theorem | 8/24 Lec02, 1.1 |
Extreme Value Theorem, Intermediate Value Theorem, extrema of |f(x)|, MVT for integrals | |||||

8/27 Lec03, 1.1 |
Taylor's theorem, meaning of R, maximum error, error bounds for integrals, composition of power series | 8/28 |
8/29 Lec04, 1.1-2 |
error bounds for integrals, floating point numbers | 8/31 Lec05, 1.2 |
floating point arithmetic, correct rounding, absolute and relative error, quadratic formula revisited | ||

9/3 |
Holiday | 9/4 |
Hw01 Quiz1 |
9/5 Lec06, 1.3 |
algorithms, pseudo-code, polynomial evaluation, error propagation, rates of convergence | 9/7 Lec07, 1.3,2.1 |
ln(1+x)=O(x), generalizations, bisection method (theory, algorithm, convergence rate) | |

9/10 Lec08, 2.2 |
fixed-point iteration, existence, uniqueness, convergence | 9/11 |
Hw02 | 9/12 Lec09, 2.3 |
fixed-point algorithm, max number of steps, Newton's method, convergence | 9/14 Lec10, 2.3 |
convergence of Newton, secant method, false position, example of Newton failing | |

9/17 Lec11, 2.4 |
linear/quadratic convergence, convergence rate of fixed point iteration, multiple roots, modified Newton | 9/18 |
Hw03 Prog1 |
9/19 Lec12, 2.5-6 |
Accelerating convergence, Aitkin's method, Steffensen's method, Horner's method/long division | 9/21 Lec13, 2.6 |
Horner's method, deflation, Muller's method, finding complex roots, examples | |

9/24 Lec14, 3.1 |
Weierstrass theorem, Lagrange interpolation, approximation theorem, example of bounding errors | 9/25 |
Hw04 Quiz2 |
9/26 Lec15, 3.2-3 |
Neville's method, divided differences | 9/28 Lec16, 3.3-4 |
alternative paths through the difference table, coalescing nodes, osculating polynomials, hermite interpolation | |

10/1 Lec17 |
Hw05 due, Midterm review, unified view of remainder theorems, repeated nodes, examples | 10/2 |
10/3 |
Midterm 1 | 10/5 Lec18 |
|||

10/8 Lec19 |
10/9 |
Hw06 Prog2 |
10/10 Lec20 |
10/12 Lec21 |
||||

10/15 Lec22 |
10/16 |
Hw07 Quiz3 |
10/17 Lec23 |
10/19 Lec24 |
||||

10/22 Lec25 |
10/23 |
Hw08 | 10/24 Lec26 |
10/26 Lec27 |
||||

10/29 Lec28 |
10/30 |
Hw09 Prog3 |
10/31 Lec29 |
11/2 Lec30 |
||||

11/5 Lec31 |
Hw10 due | 11/6 |
Quiz4 |
11/7 |
Midterm 2 | 11/9 Lec32 |
||

11/12 |
Holiday | 11/13 |
Hw11 | 11/14 Lec33 |
11/16 |
class cancelled (air quality) | ||

11/19 |
class cancelled (air quality) | 11/20 |
11/21 |
No class | 11/23 |
Holiday | ||

11/26 Lec34 |
Lec35 posted on bCourses | 11/27 |
11/28 Lec36 |
11/29: Hw12 due | 11/30 Lec37 |
|||

12/3 Lec38 |
12/4 |
Prog4 Quiz5 |
12/5 RRR |
12/5: no class, 12/6: Hw13 due | 12/7 RRR |
review session | ||

12/10 | Thurs, 12/13: Final Exam, 3-6 PM |