Lectures: MWF 8:10-9:00 AM, 105 Stanley
Prerequisites: Math 53 and 54 or equivalent
Required Text: Numerical Analysis, 9th 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 solution 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.
Piazza forum: link to 128A
Grading:
| programming assignments: | 10% | (all scores count) |
| homework: | 5% | (lowest score dropped) |
| quizzes: | 15% | Sep 17, Oct 1, Oct 15, Oct 29, Nov 12, Dec 3 (in section, lowest score dropped) |
| Midterm 1: | 20% | Monday, October 6 (in class) |
| Midterm 2: | 20% | Friday, November 14 (in class) |
| Final exam: | 30% | Monday, Dec 15, 7-10 PM (location TBA) |
More Details: 11 homework assignments, 4 programming assignments, 6 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 count for both. 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 | Wed | Fri | |||
|---|---|---|---|---|---|
| 8/29 1.1 |
Overview, example of unstable recurrence, MVT, Rolle's theorem, Extreme value theorem/algorithm | ||||
| 9/1 | holiday | 9/3 1.1 |
IVT, Taylor's theorem, tricks for bounding R, maximum error, meaning of R | 9/5 1.1,1.2 |
avoiding circular reasoning, error bounds for integrals, floating-point arithmetic |
| 9/8 1.2, 1.3 |
floating-point arithmetic, absolute and relative error, quadratic formula, two algorithms for evaluating polynomials | 9/10 1.3, 2.1 |
error propagation, rate of convergence,
bisection method HW 1 due |
9/12 1.3, 2.1 |
convergence order examples, ln(1+x)=O(x), convergence rate of bisection method |
| 9/15 2.2 |
fixed point iteration, discuss HW 2.2.11, proof of fixed point theorem, error estimates | 9/17 2.3 |
Newton's method: graphical derivation, proof of
convergence, why it's so fast HW 2 due, Quiz 1 |
9/19 2.3, 2.4 |
secant method, false position, order of convergence, quadratic convergence in fixed point iteration when g'(p)=0 |
| 9/22 2.4, 2.5 |
multiple roots, modified Newton, accelerating convergence, Aitken's method/proof, Steffensen's method/proof | 9/24 2.6, 3.1 |
Horner's method, Mueller's method, polynomial
interpolation
HW 3 due, PA 1 due |
9/26 3.1, 3.2 |
polynomial interpolation, Neville's method |
| 9/29 3.2, 3.3 |
recap of Neville's method, divided differences | 10/1 3.3, 3.4 |
forward/backward differences, Hermite interpolation HW 4 due, Quiz 2 |
10/3 | Review |
| 10/6 | Midterm 1, (chapters 1-3) | 10/8 4.1 |
numerical differentiation, n+1 point formula, examples | 10/10 4.1-2 |
2nd order derivatives, Richardson extrapolation |
| 10/13, 4.3 | quadrature: trapezoidal rule, Simpson's rule, degree of accuracy, Newton-Cotes formulas | 10/15, 4.4-5 | composite quadrature, Romberg integration, Euler-Maclaurin formula HW 5 due, Quiz 3 |
10/17, 4.5 | recap/overview of quadrature, Euler-Maclaurin, Romberg integration |
| 10/20, 4.7 | Gaussian quadrature, Legendre polynomials, Gram-Schmidt procedure, proof that degree of precision = 2n-1 | 10/22, 4.7, 4.6 | recap of Gaussian quadrature, proof that zeros are real and distinct, arbitrary intervals, adaptive quadrature
HW 6 due, PA 2 due |
10/24, 4.8, 4.9 | multiple integrals, improper integrals |
| 10/27, 5.1 | (guest lecture by Danny Hermes) theory of ODE's, Lipschitz continuity, well-posed problems, examples |
10/29, 5.2 | (guest lecture by Ming Gu) Euler's method, convergence proof HW 7 due, Quiz 4 |
10/31, 5.2, 5.3 | How to compute/bound derivatives of the unknown solution, Taylor methods, local truncation error |
| 11/3, 5.4 | Runge-Kutta methods, Butcher array/tableau, truncation error of general explicit 2-stage RK scheme | 11/5, 5.6 | (guest lecture by Weihua Liu) multistep methods, derivation of Adams-Bashforth and Adams-Moulton HW 8 due |
11/7, 5.10 |
(guest lecture by Weihua Liu) stability of multistep methods |
| 11/10, 5.6, 5.10 | truncation error of multistep methods, stability+consistency=convergence | 11/12 | Review HW 9 due, Quiz 5 |
11/14 | Midterm 2 (chapters 4 and 5, only sections in which homework has been assigned) |
| 11/17, 5.9, 5.11 | higher-order equations and systems, stiff equations, Prothero-Robinson example | 11/19, 5.11, 5.5 | linear stability analysis, adaptive stepsize control PA 3 due |
11/21, 6.1-3 | Gaussian elimination, pivoting, matrix inversion |
| 11/24, 6.5 | LU factorization, forward/back-substitution, counting flops | 11/26 | no main lecture, yes discussion sections HW 10 due |
11/28 | holiday |
| 12/1, 6.6 | positive definite matrices, Cholesky factorization, tridiagonal matrices | 12/3, 3.5 | cubic spline interpolation PA 4 due, Quiz 6 (5.9, 5.11, 6.1, 6.2, 6.3, 6.5) |
12/5 | Review |
| 12/8 | RRR Week. (HW 11 due Monday in my office hours, or arrange with your GSI) | ||||
| 12/15 | Final Exam, 7-10 PM, 105 Stanley | ||||