Math 128A: Numerical Analysis (Spring 2014)

Department of Mathematics
University of California, Berkeley

Description: Basic concepts and methods in numerical analysis: Solution of equations in one variable; Polynomial interpolation and approximation; Numerical differentiation and integration; Initial-value problems for ordinary differential equations; Direct methods for solving linear systems. Prerequisites: Math 53 and 54, basic programming skills. Course control number: 54186.
Web pages: http://math.berkeley.edu/~persson/128A (this page)
https://bcourses.berkeley.edu/courses/1195558 (for announcements, messages, discussions, etc)
Lecturer: Per-Olof Persson, persson@berkeley.edu, Evans 1089, Phone (510) 642-6947
Office hours: in 1089 Evans,
  • Tue 11:00 - 12:30pm (primarily 10B students)
  • Wed 2:00 - 3:30pm (general)
  • Thu 11:00 - 12:30pm (primarily 128A students)
Lectures: TuTh 9:30-11:00am, Room 4 LeConte
Exams: Midterm exam: Thu Mar 13, 9:30am-11:00am
Final exam: Wed May 14, 11:30am-2:30pm (group 10)
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
Chapter 1 - Mathematical Preliminaries and Error Analysis (Full page, 6 per page)
Chapter 2 - Solutions of Equations in One Variable (Full page, 6 per page)
Chapter 3 - Interpolation and Polynomial Approximation (Full page, 6 per page)
Chapter 4 - Numerical Differentiation and Integration (Full page, 6 per page)
Chapter 5 - Initial-Value Problems for Ordinary Differential Equations (Full page, 6 per page)
Chapter 6 - Direct Methods for Solving Linear Systems (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

The course Math 98: Introduction to MATLAB programming will not be offered this semester. However, the course material from last semester might be useful.
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 is sufficient for all excercises in the class

Homework, Quizzes, and Programming Assignments:
HW QZ PA Date Problems, 9th Ed 8th Ed changes
1     Tue 01/28 1.1: 1c, 4a, 5, 14, 19, 28b
1.2: 1ah, 4c, 9, 12, 15cd, 16cd
1.1: 28b -> 1.1: 26
2 1   Tue 02/04 1.3: 1a, 6, 7, 16
2.1: 1, 10, 15
2.2: 3bd, 11abf
 
3     Tue 02/11 2.3: 6a, 8a, 16
2.4: 2a, 4a, 6
2.5: 1d, 5, 14a
 
4 2   Tue 02/18 2.6: 2b, 4b
3.1: 5a, 7a
3.2: 1a

3.1: 7a -> 3.1: 9a
3.2: 1a -> 3.1: 7a
5   1 (PDF, Solutions) Tue 02/25 3.3: 3a, 5a, 17
3.4: 2a, 4a, 9, 11a
3.5: 4c, 6c, 8c
4.1: 6a, 8a, 22, 29
3.3 -> 3.2
3.4 -> 3.3
3.5 -> 3.4
6 3   Tue 03/04 4.2: 1d, 2d, 8
4.3: 2a, 4a, 6a, 8a, 16
4.4: 2a, 4a, 26a
 
7   2 (PDF, Solutions) Tue 03/11 4.5: 2a, 4a, 13
4.6: 1ab, 9
4.7: 1ab, 2ab, 3ab, 4ab, 7, 8
4.8: 1a, 2a, 10
 
8 4   Tue 04/01 4.9: 2a, 4a, 6, 9
5.1: 1a, 4ac, 6
5.2: 2b, 4b, 9
 
9     Tue 04/08 5.3: 2b, 4b
5.4: 2b, 14b, 30, 31
5.9: 2c, 4b
 
10 5 3 (PDF, Solutions) Tue 04/15 5.5: 3bd, 4bd
5.6: 1ac, 4ac, 12
5.10: 1, 2, 5, 8
 
11     Tue 04/22 5.11: 9, 10, 12, 15
6.1: 5d, 10, 20ab
6.2: 2d, 4d, 31
 
12 6 4 (PDF, Solutions) Tue 04/29 6.3: 6a, 10, 18
6.4: 2b, 6, 8, 11
6.5: 2a, 4a, 6a, 8a, 11a
6.6: 2bc, 4b
6.3: 6a, 10, 18 -> 6.3: 2a, 6, 14
Syllabus:
Lec Date 9th Ed Section, Topic 8th Ed
1 Tue 01/21 1.1: Review of Calculus
1.2: Round-off Errors and Computer Arithmetic
1.1
1.2
2 Thu 01/23 1.3: Algorithms and Convergence 1.3
3 Tue 01/28 2.1: The Bisection Method
2.2: Fixed-Point Iteration
2.1
2.2
4 Thu 01/30 2.3: Newton's Method and Its Extensions 2.3
5 Tue 02/04 2.4: Error Analysis for Iterative Methods
2.5: Accelerating Convergence
2.4
2.5
6 Thu 02/06 2.6: Zeros of Polynomials and Müller's Method 2.6
7 Tue 02/11 3.1: Interpolations and the Lagrange Polynomial
3.2: Data Approximation and Neville's Method
3.1
3.1
8 Thu 02/13 3.3: Divided Differences
3.4: Hermite Interpolation
3.2
3.3
9 Tue 02/18 3.5: Cubic Spline Interpolation
4.1: Numerical Differentiation
3.4
4.1
10 Thu 02/20 4.2: Richardson's Extrapolation 4.2
11 Tue 02/25 4.3: Elements of Numerical Integration
4.4: Composite Numerical Integration
4.3
4.4
12 Thu 02/27 4.5: Romberg Integration
4.6: Adaptive Quadrature Methods
4.5
4.6
13 Tue 03/04 4.7: Gaussian Quadrature
4.8: Multiple Integrals
4.7
4.8
14 Thu 03/06 4.9: Improper Integrals 4.9
15 Tue 03/11 Review  
16 Thu 03/13 Midterm Exam - In class, 4 LeConte, 9:30-11:00am  
17 Tue 03/18 5.1: The Elementary Theory of Initial-Value Problems
5.2: Euler's Method
5.1
5.2
18 Thu 03/20 5.3: Higher-Order Taylor Methods 5.3
    Spring Break 3/24-3/28 - No lectures  
19 Tue 04/01 5.4: Runge-Kutta Methods
5.9: Higher-Order Equations and Systems of Differential Equations
5.4
5.9
20 Thu 04/03 5.5: Error Control and the Runge-Kutta-Fehlberg Method
5.6: Multistep Methods
5.5
5.6
21 Tue 04/08 5.7: Variable Step-Size Multistep Methods
5.10: Stability
5.7
5.10
22 Thu 04/10 5.11: Stiff Differential Equations 5.11
23 Tue 04/15 6.1: Linear Systems of Equations
6.2: Pivoting Strategies
6.1
6.2
24 Thu 04/17 6.3: Linear Algebra and Matrix Inversion 6.3
25 Tue 04/22 6.4: The Determinant of a Matrix
6.5: Matrix Factorization
6.4
6.5
26 Thu 04/24 6.6: Special Types of Matrices 6.6
27 Tue 04/29 Review  
28 Thu 05/01 Review  
    Reading/Review/Recitation Week 5/5-5/9 - No lectures  
  Wed 05/14 Final Exam - 220 Hearst Gym, 11:30am-2:30pm  
GSIs and Discussion Sections:
Sec Time Room GSI E-mail Office Office hours
101 Tue 8 - 9am B3A Evans C. Melgaard chrismelgaard@berkeley.edu 1039 Evans M 1-2pm, F 4-5pm
102 Tue 11 - 12pm B3A Evans D. Anderson davidanderson@berkeley.edu 737 Evans M 1:30-3:30pm
103 Tue 12 - 1pm B3A Evans D. Anderson davidanderson@berkeley.edu 737 Evans M 1:30-3:30pm
104 Tue 1 - 2pm B3A Evans M. Fortunato meiref@math.berkeley.edu 1065 Evans M 3:30-4:30pm, Th 4-5pm
105 Tue 2 - 3pm B3A Evans M. Pejic mpejic@math.berkeley.edu 824 Evans F 3-5pm
106 Tue 3 - 4pm B3A Evans M. Pejic mpejic@math.berkeley.edu 824 Evans F 3-5pm
107 Tue 4 - 5pm B3A Evans C. Melgaard chrismelgaard@berkeley.edu 1039 Evans M 1-2pm, F 4-5pm
108 Tue 5 - 6pm B3A Evans M. Fortunato meiref@math.berkeley.edu 1065 Evans M 3:30-4:30pm, Th 4-5pm
MATLAB Codes: Lecture 1: num2bin.m
Lecture 3: bisection.m, bisection_table.m
Lecture 3: fixedpoint.m, fixedpoint_table.m, fixedpoint_plot.m, fixedpoint_demo.m, newton.m, newton_table.m, newton_plot.m
Lecture 5: steffensen.m, steffensen_table.m, horner.m, muller.m, muller_table.m, muller_plot.m
Lecture 7: neville.m
Lecture 8: divideddifference.m
Lecture 9: ncspline.m, ccspline.m, splineeval.m, diffsplineeval.m, spline_demo.m
Lecture 9: diff_demo.m, rich_demo.m
Lecture 12: romberg.m
Lecture 12: adaptive_demo.m, gaussquad.m
Lecture 13: simpsondouble.m, gaussdouble_demo.m
Homework 7: laguerrequad.m
Programming Assignment 3: pendplot.m
Lecture 19: rk4.m, rkf.m
Lecture 21: rk4stability.m
Lecture 23: gausselim.m
Lecture 25: lu_demo.m, mkM.m, mkP.m

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 Thursday March 13 between 9:30 - 11:00am. The final exam will be given on Wednesday May 14 between 11:30am - 2:30pm (final exam group 10), in 220 Hearst Gym. 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.