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:
Ways to run matlab:
Syllabus: Programming for numerical calculations, round-off error, approximation and interpolation, numerical quadrature, matrix computations, and numerical solutions of ordinary differential equations.
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 |
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| 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 | |||||||