## Math 128A - Numerical Analysis

Instructor: Jon Wilkening
Office: 1051 Evans
Office Hours: Mon 10:15-11:45, Fri 3:30-4:30

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:

• 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.

 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