Math 128B: Numerical Analysis (Spring 2013)

Department of Mathematics
University of California, Berkeley

Description: Second part of the course sequence on introductory numerical analysis: Iterative methods for linear systems; Approximation theory; Eigenvalue approximations; Solution of systems of equations; Numerical methods for ODEs and PDEs. Prerequisites: Math 128A or equivalent, basic MATLAB skills. Course control number: 54235.
Web page: http://persson.berkeley.edu/128B
Lecturer: Per-Olof Persson, persson@berkeley.edu, Evans 1089, Phone (510) 642-6947
Office hours: Wed 10:00am - 11:30am and Thu 3:30pm - 5:00pm in 1089 Evans
Lectures: TuTh 9:30-11:00am, Room 71 Evans
GSI and Discussion section: Anna Lieb, lieb.anna.m@gmail.com
Discussion section: Tu 4:00-5:00pm, Room B3A Evans
Office hours: Mon 4-5pm, Wed 3-4pm, in 1010 Evans
Exams: Midterm exam: Tue Mar 12, 9:30am-11:00am
Final Exam Group 10, Wed May 15, 11:30am-2:30pm
Textbook: R. L. Burden and J. D. Faires, Numerical Analysis, 9th edition, Brooks-Cole, 2010. ISBN-13: 978-0-538-73351-9; ISBN-10: 0-538-73351-9
or
R. L. Burden and J. D. Faires, Numerical Analysis, 8th edition, Brooks-Cole, 2004. ISBN-13: 978-0-534-39200-0; ISBN-10: 0-534-39200-8
Other reading: Lecture Slides (Note: These will be frequently updated)
Chapter 7 - Iterative Techniques in Matrix Algebra (Full page, 6 per page)
Chapter 8 - Approximation Theory (Full page, 6 per page)
Chapter 9 - Approximating Eigenvalues (Full page, 6 per page)
Chapter 10 - Numerical Solutions of Nonlinear Systems of Equations (Full page, 6 per page)
Chapter 11 - Boundary-Value Problems for Ordinary Differential Equations (Full page, 6 per page)
Chapter 12 - Numerical Solutions to Partial Differential Equations (Full page, 6 per page)

MATLAB Books
J. Dorfman, Introduction to MATLAB Programming, Decagon Press, Inc. Available at Krisha Copy Center on University Avenue, on demand for about $20 + tax. Please email them your order at orders@krishnacopy.com, with name and phone number, and it will be available for pick up later.
Otto and Denier, An Introduction to Programming and Numerical Methods in MATLAB (online version)
Quarteroni and Saleri, Scientific Computing with MATLAB and Octave (online version)
K. Sayood, Learning programming using MATLAB (online version)

Instructions for setting up a UC Berkeley Library Proxy Server for off-campus access to online books
MATLAB: The commercial software MATLAB will be used in the class, and there are various alternatives for using it:
  • MATLAB will be available during discussion sections in the computer lab B3A Evans
  • On computers owned by the university, the UC Berkeley Software Central provides MATLAB for free
  • The Mathworks provide student editions of MATLAB at a discounted rate
  • The free alternative Octave has some limitations but will be sufficient for most of the excercises in the class

Homework, Quizzes, and Programming Assignments:
HW QZ PA Date Problems, 9th Ed Problems, 8th Ed Problems, 9th Int. Ed
1     Tue 01/29 7.1: 1abc, 2a, 4, 13
7.2: 2f, 6f, 10f, 11, 19
7.3: 2b, 4b, 14
7.4: 2b, 9
7.1: 1abc, 2a, 4, 13
7.2: 2f, 4f, 8f, 9, 17
7.3: 2b, 4b, 10b, 22, 23
7.1: 1bac, 2b, 4, 13
7.2: 1f, 5f, 9f, 11, 19
7.3: 1b, 3b, 14
7.4: 1b, 9
2     Tue 02/05 7.5: 2b, 4b, 9, 10b
7.6: 11, 13
7.4: 2b, 4b, 9, 10b
7.5: 11, 13
7.5: 2b, 4b, 9, 10b
7.6: 11, 13
3 1   Tue 02/12 8.1: 5, 14
8.2: 2f, 11, 12c, 14
8.1: 5, 14
8.2: 2f, 11, 12c, 14
8.1: 5, 14
8.2: 2f, 11, 12c, 14
4     Tue 02/19 8.3: 1d, 3d, 8, 9
8.4: 2, 8a, 10
8.3: 1d, 3d, 8, 9
8.4: 2, 8a, 10
8.3: 1d, 3d, 8, 9
8.4: 2, 8a, 10
5 2 1 Tue 02/26 8.5: 5, 7cd, 15, 16
8.6: 6, 9
8.5: 5, 7cd, 15, 16
8.6: 6, 9
8.5: 6, 7dc, 15, 16
8.6: 6, 9
6     Tue 03/05 No homework No homework No homework
7 3 2 Tue 03/19 9.1: 4cd, 10, 11, 15
9.2: 12, 13
9.4: 2a, 3d
PDF 9.1: 4cd, 10, 11, 15
9.2: 12, 13
9.4: 2a, 3d
      Spring Break Spring Break Spring Break Spring Break
8     Thu 04/04 9.5: 2a, 8, 9
10.1: 5, 12
10.2: 2d, 9
9.4: 2a, 8, 9
10.1: 5, 12
10.2: 2d, 9
9.5: 2a, 8, 9
10.1: 5, 12
10.2: 2d, 9, 13
9     Tue 04/09 10.3: 2c, 9, 10
10.4: 2b, 6
10.5: 9, 10
10.3: 2c, 9, 10
10.4: 2b, 6
10.5: 9, 10
10.3: 2c, 9, 10
10.4: 2b, 6
10.5: 9, 10
10 4 3 Tue 04/16 11.1: 4b, 7, 8
11.2: 2, 4b, 6
11.3: 2, 4b, 7, 10
11.1: 4b, 7, 8
11.2: 2, 4b, 6
11.3: 2, 4b, 7, 10
11.1: 4b, 7, 8
11.2: 2, 4b, 6
11.3: 2, 4b, 7, 10
11     Tue 04/23 11.4: 2, 7
11.5: 1, 6, 9, 10, 12
11.4: 2, 7
11.5: 1, 6, 9, 10, 12
11.4: 2, 7
11.5: 1, 6, 9, 10, 12
12 5 4 Tue 04/30 12.2: 2, 4, 13
12.3: 2, 6
12.2: 2, 4, 13
12.3: 2, 6
12.2: 2, 4, 13
12.3: 2, 6
Syllabus:
Lec Date 9th Ed Section, Topic 8th Ed
1 Tue 01/22 7.1: Norms of Vectors and Matrices
7.2: Eigenvalues and Eigenvectors
7.1
7.2
2 Thu 01/24 7.3: The Jacobi and Gauss-Siedel Iterative Techniques
7.4: Relaxation Techniques for Solving Linear Systems
7.3
3 Tue 01/29 7.5: Error Bounds and Iterative Refinement 7.4
4 Thu 01/31 7.6: The Conjugate Gradient Method 7.5
5 Tue 02/05 8.1: Discrete Least Squares Approximation 8.1
6 Thu 02/07 8.2: Orthogonal Polynomials and Least Squares Approximation 8.2
7 Tue 02/12 8.3: Chebyshev Polynomials and Economization of Power Series 8.3
8 Thu 02/14 8.4: Rational Function Approximation 8.4
9 Tue 02/19 8.5: Trigonometric Polynomial Approximation 8.5
10 Thu 02/21 8.6: Fast Fourier Transforms 8.6
11 Tue 02/26 9.1: Linear Algebra and Eigenvalues
9.2: Orthogonal Matrices and Similarity Transformations
9.1
12 Thu 02/28 9.3: The Power Method 9.2
13 Tue 03/05 9.4: Householder's Method 9.3
14 Thu 03/07 Review  
15 Tue 03/12 Midterm Exam - In class, 71 Evans, 9:30-11:00am  
16 Thu 03/14 9.5: The QR Algorithm 9.4
17 Tue 03/19 10.1: Fixed Points for Functions of Several Variables 10.1
18 Thu 03/21 10.2: Newton's Method
10.3: Quasi-Newton Methods
10.2
10.3
    Spring Break 3/25-3/29 - No lectures  
19 Tue 04/02 10.4: Steepest Descent Techniques
10.5: Homotopy and Continuation Methods
10.4
10.5
20 Thu 04/04 11.1: The Linear Shooting Method 11.1
21 Tue 04/09 11.2: The Shooting Method for Nonlinear Problems 11.2
22 Thu 04/11 11.3: Finite-Difference Methods for Linear Problems
11.4: Finite-Difference Methods for Nonlinear Problems
11.3
11.4
23 Tue 04/16 11.5: The Rayleigh-Ritz Method 11.5
24 Thu 04/18 12.1: Elliptic Partial Differential Equations 12.1
25 Tue 04/23 12.2: Parabolic Partial Differential Equations 12.2
26 Thu 04/25 12.3: Hyperbolic Partial Differential Equations 12.3
27 Tue 04/30 Review  
28 Thu 05/02 Review  
    Reading/Review/Recitation Week 05/6-05/10 - No lectures  
  Wed 05/15 Final Exam - 106 Stanley, 11:30am - 2:30pm  

Grading and policies: Homework: Weekly homework is posted on the course web page, and it is in general due in each Tuesday discussion section. Group discussions about the homework are encouraged, but each student must write his/her own solutions and not copy them from anyone else. Late homework will not be accepted, but the two lowest scores will be dropped when computing the grade.

Quizzes: There will be a total of 6 quizzes given in the Tuesday discussion sections. They will consist of chosen homework problems, possibly with minor modifications. There will be no make-up quizzes, but the quiz with lowest score will be dropped when computing the grade.

Programming Assignments: There will be a total of 4 programming assignments, based on the MATLAB programming language. Group discussions about the assignments are encouraged, but each student must write his/her own computer codes and report, and not copy them from anyone else. Late submissions will not be accepted, and all 4 assignments will count towards the grade.

Exams: There will be one in-class midterm exam, scheduled for Tuesday March 12 between 9:30 - 11am. The final exam will be given on Wednesday May 15 between 11:30am - 2:30pm (final exam group 15). The exams are "closed book". In particular, you may not bring textbooks, notebooks, or calculators. If there is an emergency alarm during the midterms or the final exam, leave the exam at the desk and walk out. You may of may not be allowed back to complete the work.

Grade corrections: The grades for exams or quizzes will be changed only if there is a clear error on the part of the grader, such as adding up marks incorrectly. Problems must be brought to the attention of the GSI immediately after the exams are returned.

Grades: The final grade will be based on weekly homework assignments and quizzes (20%), the programming assignments (20%), the Midterm exam (20%), and the Final exam (40%). If it improves your grade, we will count the Midterm exam (0%) and the Final exam (60%). This allows you to miss the midterm exam, but your chances are improved if you take it.

Incomplete grades: Incomplete "I" grades are almost never given. The only justification is a documented serious medical problem or genuine personal/family emergency. Falling behind in this course or problems with workload in other courses are not acceptable reasons.

Special arrangements: If you are a student with a disability registered by the Disabled Student Services (DSS) on UCB campus and if you require special arrangements during exams, you must provide the DSS document and make arrangements via email or office hours at least 10 days prior to each exam, explaining your circumstances and what special arrangements need to be done. Also see your GSI as soon as possible to make arrangements for the homeworks/quizzes.