Math 128A Syllabus

Fall, 2005

Instructor: Prof. Ming Gu

Review of calculus, Taylor series with remainder. Error analysis: roundoff and truncation errors in numerical approximations and computer arithmetic. Algorithms and convergence (Chapter 1).

Nonlinear equations: bisection, fixed point, Newton and secant methods. Zeros of polynomials and Muller's method (Chapter 2).

Polynomial interpolation. Lagrange vs. Hermite. Divided differences. Splines (Chapter 3).

Numerical differentiation and integration: basic rules, extrapolation, adaptive and Gaussian strategies (Chapter 4).

Initial value problems for ordinary differential equations. Runge-Kutta and Adams methods. Introduction to stiff problems (Chapter 5).

Matrix computations: linear systems, LU factorization (Chapter 6).

Approximation theory: least squares, Householder QR factorization, and orthogonal polynomials (Sections 7.1, 9.3 and 8.1-2).

What's New

Final Exam will be from 12:30 to 3:30PM, on Dec. 19, at 2040 Valley LSB.

Per student suggestion, we will allow one new sheet of notes, as well as one-sheet notes from the two midterms, in the final exam.

Sample Final Exam is now available.

Due day extended for thoeretical and programming homework this week. Thoeretical hwk will be due this Friday, Oct. 21, and Programming #3 Wednesday of next week, Oct. 26.

Due day for homework this week (Sections 3.1,3.2, and 3.3) has been extended to Oct. 7.

Sample Midterm I .

We will allow a one-page cheat sheet in the midterm exam as well as hand-held calculators.

Programming homework assignment:

Programming Homework , due Wed., Sept. 14 in discussion.

Programming Homework , due Wed., Sept. 28 in discussion.

Programming Homework , due Wed., Oct. in discussion.

Programming Homework , due Dec. 7 in discussion. Note that this is a large assignment, so please start early.

Reading and Homework Schedule

Lecture ----- Date ----- Reading ----- Exercises

01 8/30 1.1,1.2 1.1: 1d, 4d, 6, 8, 12, 18, 20. ,24, 26. 1.2: 1ace, 2, 4, 5ace,6ace,10,12ab,15ab,16ab,18,20.
02 9/1 1.3 1a, 2cd,6, 8, 13, 16
03 9/6 2.1-2 2.1: 2b,10,12,14; 2.2: 1,2,4,6,8,12,18,22,23,24.
04 9/8 2.3-4 2.3: 2,4,6ab,8ab,16,26,28; 2.4: 2,4,6,10,14.
05 9/13 2.5 2,4,13,14
06 9/15 2.6,3.1 2.6: 2.a, 6, 8, 10; 3.1: 2, 4, 6.a, 8.a
07 9/20 3.1, 3.2 Section 3.1: 25, 32; Section 3.2: 2, 4, 6, 8, 10, 11, 20
08 9/22 3.3 Section 3.3: 2ab, 6, 10, 11.
09 9/27
9/29 --- Midterm #1: -- --Chaps. 1-2, Sections 3.1-3.3
10 10/4 3.4 Section 3.4: 3a, 4a, 11, 12, 20, 22, 26.
11 10/6 3.5 Section 3.5: 3a, 4, 5.
12 10/11 4.1 2, 4, 6, 8, 22, 26
13 10/13 4.2-4.3 Section 4.2: 6, 8, 10, 12. Section 4.3: 2, 14, 16, 18, 20.
14 10/18 4.4-4.5 Section 4.4: 12, 24, 26. Section 4.5: 14, 15
15 10/20 4.6, 4.7 Section 4.6: 4, 6. Section 4.7: 6, 8.
16 10/25 4.8-4.9 Section 4.8: 10, 14. Section 4.9: 4, 6, 7, 8. Due Nov. 2.
17 10/27 Review
11/1 --- Midterm #2: Chaps. 1-4
18 11/3 5.1-2 Section 5.1: 2.ab, 4.bc, 6, 8.ab. Section 5.2: 2.ab, 4.ab, 6.c, 8.c, 12. Due: Thursday, Nov. 10
19 11/8 5.3-4 Section 5.3: 2.b, 10. Section 5.4: 2.a, 10.a, 27, 31. Due: Wed. Nov 16.
20 11/10 5.5 2.a. Due: Wed. Nov 16.
21 11/15 5.6-7 Section 5.6: 2.a, 9. Section 5.7: 2.a, 4 (without doing exercise 3). Due Nov. 23.
22 11/17 5.8-9 Section 5.9: 2.a. Due Nov. 23.
23 11/22 5.10 Prog. Assignment Due Dec. 7.
11/24 Thanksgiving Break
24 11/29 5.11,6.1 Sec. 5.11: 2.d, 12, 15. Sec. 6.1: 6.a, 10. Due: Dec. 7.
25 12/1 6.2-3 Sec. 6.2: 10a, 32. Sec. 6.3: 2.bd, 6, 13. Due: Dec. 7.
26 12/6 6.4-5
27 12/8 Review
-- 12/19 --- Final Exam: Chaps. 1-6, 7.1, 9.3, and 8.1-2

Lecture -----	Date -----	Reading -----	Exercises
01	8/30	1.1,1.2	1.1: 1d, 4d, 6, 8, 12, 18, 20. ,24, 26. 1.2: 1ace, 2, 4, 5ace,6ace,10,12ab,15ab,16ab,18,20.
02	9/1	1.3	1a, 2cd,6, 8, 13, 16
03	9/6	2.1-2	2.1: 2b,10,12,14; 2.2: 1,2,4,6,8,12,18,22,23,24.
04	9/8	2.3-4	2.3: 2,4,6ab,8ab,16,26,28; 2.4: 2,4,6,10,14.
05	9/13	2.5	2,4,13,14
06	9/15	2.6,3.1	2.6: 2.a, 6, 8, 10; 3.1: 2, 4, 6.a, 8.a
07	9/20	3.1, 3.2	Section 3.1: 25, 32; Section 3.2: 2, 4, 6, 8, 10, 11, 20
08	9/22	3.3	Section 3.3: 2ab, 6, 10, 11.
09	9/27
	9/29	---	Midterm #1: -- --Chaps. 1-2, Sections 3.1-3.3
10	10/4	3.4	Section 3.4: 3a, 4a, 11, 12, 20, 22, 26.
11	10/6	3.5	Section 3.5: 3a, 4, 5.
12	10/11	4.1	2, 4, 6, 8, 22, 26
13	10/13	4.2-4.3	Section 4.2: 6, 8, 10, 12. Section 4.3: 2, 14, 16, 18, 20.
14	10/18	4.4-4.5	Section 4.4: 12, 24, 26. Section 4.5: 14, 15
15	10/20	4.6, 4.7	Section 4.6: 4, 6. Section 4.7: 6, 8.
16	10/25	4.8-4.9	Section 4.8: 10, 14. Section 4.9: 4, 6, 7, 8. Due Nov. 2.
17	10/27	Review
	11/1	---	Midterm #2: Chaps. 1-4
18	11/3	5.1-2	Section 5.1: 2.ab, 4.bc, 6, 8.ab. Section 5.2: 2.ab, 4.ab, 6.c, 8.c, 12. Due: Thursday, Nov. 10
19	11/8	5.3-4	Section 5.3: 2.b, 10. Section 5.4: 2.a, 10.a, 27, 31. Due: Wed. Nov 16.
20	11/10	5.5	2.a. Due: Wed. Nov 16.
21	11/15	5.6-7	Section 5.6: 2.a, 9. Section 5.7: 2.a, 4 (without doing exercise 3). Due Nov. 23.
22	11/17	5.8-9	Section 5.9: 2.a. Due Nov. 23.
23	11/22	5.10	Prog. Assignment Due Dec. 7.
	11/24	Thanksgiving Break
24	11/29	5.11,6.1	Sec. 5.11: 2.d, 12, 15. Sec. 6.1: 6.a, 10. Due: Dec. 7.
25	12/1	6.2-3	Sec. 6.2: 10a, 32. Sec. 6.3: 2.bd, 6, 13. Due: Dec. 7.
26	12/6	6.4-5
27	12/8	Review
--	12/19	---	Final Exam: Chaps. 1-6, 7.1, 9.3, and 8.1-2