Math 128A: Numerical Analysis (Spring 2009)

Department of Mathematics
University of California, Berkeley
News: May 20: Here is the Final Exam (Sorry, no solutions! Happy to discuss the problems if you come by.)
Apr 6: Here are Midterm 2 and the solutions.
Feb 20: Here are Midterm 1 and the solutions.
Feb 12: Problems 2.6: 10 and 3.1: 21, 32 have been excluded from Homework 4.
Feb 12: See below for information about Midterm 1 next Friday. I will have extra office hours in Evans 1089 on Tue Feb 17 11am-12:30pm and Thu Feb 19 10am-12pm. No office hours after the exam on Fri Feb 20.
Jan 26: Here are the problems for Homework 1
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; Least square approximation. Prerequisites: Math 53 and 54, basic programming skills. Course control number: 54503.
Lecturer: Per-Olof Persson, persson 'at' berkeley 'dot' edu, Evans 1089, Phone (510) 642-6947
Office hours: Mon 12-2pm and Fri 12-2pm in Evans 1089
Lectures: MWF 10-11am, Room 160 Kroeber
GSIs and Discussion Sections: Justin Blanchard, 128A Web page, justinb 'at' math 'dot' berkeley 'dot' edu, Evans 1008
Sec 101: Wed 9-10am, Room B3A Evans
Sec 102: Wed 12-1pm, Room B3A Evans
Office hours: Tue 3-5pm, Thu 2-3pm in Evans 1008

Trevor Potter, 128A Web page, potter 'at' math 'dot' berkeley 'dot' edu, Evans 935
Sec 103: Wed 11-12am, Room B3A Evans
Sec 104: Wed 1-2pm, Room B3A Evans
Office hours: Tue 2-4pm and Fri 2-3pm in Evans 935

Ryan Hynd, ryanhynd 'at' math 'dot' berkeley 'dot' edu, Evans 1049
Sec 105: Wed 2-3pm, Room B3A Evans
Office hours: Tue 10am-12pm and Fri 11am-12pm in Evans 1049

Ask the GSI or the instructor about the username and password for the basement computer lab.
Textbook: R. L. Burden and J. D. Faires, Numerical Analysis, 8th edition, Brooks-Cole, 2005 (required).
J. Dorfman, Introduction to MATLAB Programming, Decagon Press, Inc (recommended). For online purchases, visit Decagon Press, and use the promotion code 128Sp2009 to receive the 35% discounted price ($29.22 + tax + shipping = $36.77), processed through PayPal and shipped 2nd-day Priority Mail.
Grading: The 10 best homeworks (15%)
Programming assignments (15%)
Midterm exams (20% + 20%)
Final exam (30%)

Grades of Incomplete will be granted only for dire medical or personal emergencies that cause you to miss the final, and only if your work up to that point has been satisfactory.
Policies, etc: Homeworks and programming assignments are due on Wednesdays during discussion. We will give no credit for written homework turned in after the due date and there will be no make up quizzes and exams. The only exception to this policy is medical or personal emergencies. All written assignments must be done individually, but if you get stuck after an honest attempt please ask the instructor, the GSIs, or other students for advise.

Basic programming skills are required for the programming assignments. The MATLAB programming language will be used, unless the GSI agrees on exceptions. It is highly recommended to take the one-credit course Math 98 for those with little previous programming experience.

No books or notes are allowed on the midterm and final exams. Please let me know as soon as possible if you need any special accommodations for the exams.
Other webpages: Fall 2008, Lecturer Ming Gu
Spring 2008, Lecturer Ming Gu
Other links: UCB Math 98 Introduction to MATLAB Programming, Spring 2009, by Maxim Trokhimtchouk
MATLAB Online Documentation
Exams: Midterm exam 1: Friday February 20, in class 10-11am
Midterm exam 2: Monday April 6, in class 10-11am
Final exam: Saturday May 16, 8-11am
Midterm 1 info: The exam will be in class 10-11am on Friday February 20.
No books, no notes, and no calculator are allowed on the exam.
Midterm 1 will cover the following:
  • Textbook chapters 1-3.2
  • Homeworks 1-4
  • Programming assignment 1
  • MATLAB codes for lecture 1-11
Practice exams:
Midterm 2 info: The exam will be in class 10-11am on Monday April 6.
No books, no notes, and no calculator are allowed on the exam.
Midterm 2 will cover the following:
  • Textbook chapters 1-5.4
  • Homeworks 1-9
  • Programming assignments 1-2
  • MATLAB codes for lectures 1-27
Practice exams:
Final Exam info: The exam will be in 105 Stanley 8-11am on Saturday, May 16.
No books, no notes, and no calculator are allowed on the exam.
The final exam will cover the following:
  • Textbook chapters 1-6, 7.1, 8.1-8.2
  • Homeworks 1-15
  • Programming assignments 1-4
  • MATLAB codes for lectures 1-44
Practice exams:
MATLAB Codes: Lecture 2: num2bin.m
Lecture 4: bisection.m, bisection_table.m
Lecture 5: fixedpoint.m, fixedpoint_table.m, fixedpoint_plot.m, fixedpoint_demo.m
Lecture 6: newton.m, newton_table.m, newton_plot.m
Lecture 8: steffensen.m, steffensen_table.m
Lecture 9: horner.m, muller.m, muller_table.m, muller_plot.m
Lecture 10: neville.m
Lecture 11: divideddifference.m
Lecture 14: ncspline.m, ccspline.m, splineeval.m, diffsplineeval.m, spline_demo.m
Lecture 15: diff_demo.m
Lecture 16: rich_demo.m
Lecture 19: romberg.m
Lecture 20: adaptive_demo.m
Lecture 21: gaussquad.m
Lecture 22: simpsondouble.m, gaussdouble_demo.m
Homework 9: laguerrequad.m
Programming Assignment 3: pendplot.m
Lecture 27: rk4.m
Lecture 28: rkf.m
Lecture 35: rk4stability.m
Lecture 37: gausselim.m
Lecture 40: lu_demo.m, mkM.m, mkP.m
Lecture 42: vecnorm_demo.m, matnorm_demo.m
Syllabus:
Lec Date Topic Slides Reading Other
01 Wed 1/21 Introduction, Review of Calculus Full, 6pp, TeX 1.1  
02 Fri 1/23 Round-off Errors and Computer Arithmetic Full, 6pp, TeX 1.2  
03 Mon 1/26 Algorithms and Convergence Full, 6pp, TeX 1.3  
04 Wed 1/28 The Bisection Method Full, 6pp, TeX 2.1 HW1 Due
05 Fri 1/30 Fixed-Point Iteration Full, 6pp, TeX 2.2  
06 Mon 2/02 Newton's Method Full, 6pp, TeX 2.3  
07 Wed 2/04 Error Analysis for Iterative Methods Full, 6pp, TeX 2.4 HW2 Due
08 Fri 2/06 Accelerating Convergence Full, 6pp, TeX 2.5  
09 Mon 2/09 Zeros of Polynomials and Müller's Method Full, 6pp, TeX 2.6  
10 Wed 2/11 Interpolations and the Lagrange Polynomial Full, 6pp, TeX 3.1 HW3 Due
11 Fri 2/13 Divided Differences Full, 6pp, TeX 3.2  
  Mon 2/16 Presidents' Day Holiday - No lecture      
12 Wed 2/18 Hermite Interpolation Full, 6pp, TeX 3.3 HW4, PA1 Due
13 Fri 2/20 Midterm #1   1-3.2 Midterm #1
14 Mon 2/23 Cubic Spline Interpolation Full, 6pp, TeX 3.4  
15 Wed 2/25 Numerical Differentiation Full, 6pp, TeX 4.1 HW5 Due
16 Fri 2/27 Richardson's Extrapolation Full, 6pp, TeX 4.2  
17 Mon 3/02 Elements of Numerical Integration Full, 6pp, TeX 4.3  
18 Wed 3/04 Composite Numerical Integration Full, 6pp, TeX 4.4 HW6 Due
19 Fri 3/06 Romberg Integration Full, 6pp, TeX 4.5  
20 Mon 3/09 Adaptive Quadrature Methods Full, 6pp, TeX 4.6  
21 Wed 3/11 Gaussian Quadrature Full, 6pp, TeX 4.7 HW7, PA2 Due
22 Fri 3/13 Multiple Integrals Full, 6pp, TeX 4.8  
23 Mon 3/16 Improper Integrals Full, 6pp, TeX 4.9  
24 Wed 3/18 The Elementary Theory of Initial-Value Problems Full, 6pp, TeX 5.1 HW8 Due
25 Fri 3/20 Euler's Method Full, 6pp, TeX 5.2  
    Spring Break 3/23-3/27      
26 Mon 3/30 Higher-Order Taylor Methods Full, 6pp, TeX 5.3  
27 Wed 4/01 Runge-Kutta Methods Full, 6pp, TeX 5.4 HW9 Due
28 Fri 4/03 Error Control and the Runge-Kutta-Fehlberg Method Full, 6pp, TeX 5.5  
29 Mon 4/06 Midterm #2   1-5.4 Midterm #2
30 Wed 4/08 Multistep Methods Full, 6pp, TeX 5.6  
31 Fri 4/10 Variable Step-Size Multistep Methods Full, 6pp, TeX 5.7  
32 Mon 4/13 Extrapolation Methods Full, 6pp, TeX 5.8  
33 Wed 4/15 Higher-Order Equations and Systems of Differential Equations Full, 6pp, TeX 5.9 HW10/11, PA3 Due
34 Fri 4/17 Stability Full, 6pp, TeX 5.10  
35 Mon 4/20 Stiff Differential Equations Full, 6pp, TeX 5.11  
36 Wed 4/22 Linear Systems of Equations Full, 6pp, TeX 6.1 HW12 Due
37 Fri 4/24 Pivoting Strategies Full, 6pp, TeX 6.2  
38 Mon 4/27 Linear Algebra and Matrix Inversion Full, 6pp, TeX 6.3  
39 Wed 4/29 The Determinant of a Matrix Full, 6pp, TeX 6.4 HW13 Due
40 Fri 5/01 Matrix Factorization Full, 6pp, TeX 6.5  
41 Mon 5/04 Special Types of Matrices Full, 6pp, TeX 6.6  
42 Wed 5/06 Norms of Vectors and Matrices Full, 6pp, TeX 7.1 HW14, PA4 Due
43 Fri 5/08 Discrete Least Squares Approximation Full, 6pp, TeX 8.1  
44 Mon 5/11 Orthogonal Polynomials and Least Squares Approximation Full, 6pp, TeX 8.2  
  Sat 5/16 Final Exam   1-6, 7.1, 8.1-2  Final Exam
Homework:
HW Due Date Exercises
1 Wed 1/28 1.1: 1c, 4a, 5, 14, 19, 26
1.2: 1ah, 4c, 9, 12, 15cd, 16cd
2 Wed 2/04 1.3: 1a, 6, 7, 16
2.1: 1, 10, 15
2.2: 3bd, 11abf
3 Wed 2/11 2.3: 6a, 8a, 16
2.4: 2a, 4a, 6
2.5: 1d, 5, 14a
4 Wed 2/18 2.6: 2b, 4b
3.1: 5a, 7a, 9a
3.2: 3a, 5a, 17
5 Wed 2/25 3.3: 2a, 4a, 9, 11a
6 Wed 3/04 3.4: 4c, 6c, 8c
4.1: 6a, 8a, 22, 29
4.2: 1d, 2d, 8
7 Wed 3/11 4.3: 2a, 4a, 6a, 8a, 16
4.4: 2a, 4a, 26a
4.5: 2a, 4a, 13
8 Wed 3/18 4.6: 1ab, 9
4.7: 1ab, 2ab, 3ab, 4ab, 7, 8
4.8: 1a, 2a, 10
9 Wed 4/01 4.9: 2a, 4a, 6, 9
5.1: 1a, 4ac, 6
5.2: 2b, 4b, 9
10 Wed 4/15 5.3: 2b, 4b
5.4: 2b, 14b, 30, 31
11 Wed 4/15 5.5: 3bd, 4bd
5.6: 1ac, 4ac, 12
12 Wed 4/22 5.9: 2c, 4b
5.10: 1, 2, 5, 8
13 Wed 4/29 5.11: 9, 10, 12, 15
6.1: 5d, 10, 20ab
6.2: 2d, 4d, 31
14 Wed 5/06 6.3: 2a, 6, 14
6.4: 2b, 6, 8, 11
6.5: 2a, 4a, 6a, 8a, 11a
6.6: 2bc, 4b
15 Practice Only 7.1: 1abc, 2a, 4, 13
8.1: 1, 2
8.2: 1d, 2d, 3d, 4d
Programming Assignments:
PA Due Date Assignment
1 Wed 2/18 PDF
2 Wed 3/11 PDF
3 Wed 4/15 PDF
4 Wed 5/06 PDF