Instructor: Jingrun Chen
Office: South Hall 6705
Office hours: 13:30-15:00 TR or by appointment
E-mail: cjr@math.ucsb.edu
Teaching Assistant:
Jon Karl Sigurdsson, jonksig@math.ucsb.edu Office: South Hall 6431-S
Office hours: 12:00-13:00, Monday
Computer Laboratory: 17:00-18:50 in Gaviota Lab (Phelps Hall 1529), Thursday
Textbook: Numerical Analysis, by Richard L. Burden and J. Douglas Faires, 8th edition.
Prerequisites: Math 5 A, B, and C, or equivalent. Knowledge of a computer language suitable for numerical computing, such as FORTRAN, C, C++, or Matlab.
Homework: Homework will be assigned on Tuesday, and will be collected at the beginning of the class on the following Tuesday. Late homework will not be accepted. Late homework will not be accepted. If you have a predictable absence, you will need to hand it in earlier. The homework will generally consist of some theoretical questions, and some computational assignments. You will be required to write a program to solve certain problems. The program must be given to me as part of the assignment, together with the output of the program, in the format indicated in the assignment, and an interpretation of the results whenever necessary. You can write the programs either in FORTRAN, C, C++, or Matlab. The book comes with a CD that contains the code for the problems. You may use this code as a guide, but you must write your own original code for the assignments. No credit will be given for using the code in the CD.
Grading policy:
Homework | 35% |
Midterm | 25% |
Final | 40% |
Course description: This is the first part of a three-quarters introductory course on Numerical Analysis. This quarter we will study numerical methods for the solution of nonlinear algebraic equations, interpolation, extrapolation, numerical differentiation and integration, and numerical solution of ordinary differential equations. Although the emphasis will be in applications, the course will have a strong theoretical component. By the end of the course, the following will be expected:
1. Convergence of a numerical algorithm.
2. A solid knowledge of Approximation Theory:
1. Polynomial Interpolation.
2. Numerical Integration: Design and implementation of quadrature rules.
3. Numerical Differentiation: Design and implementation of differentiation formulas of arbitrary order of accuracy.
4. Estimation of the error in a given approximation.
3. Solution of Differential Equations:
1. Design and implementation of solvers for Ordinary Differential Equations (ODEs).
2. Being able to obtain the stability region of a multistep method for ODEs.
3. Estimation of the error and the stability properties of a given method.
4. Solid programming skills.
Computer Laboratory: In order to use the computer laboratory, you must go to Phelps 1523 (between 9am and 5pm) and get a sticker in your ID. You can check the lab schedule here.
For those of you unfamiliar with Matlab, you may want to check: A practical Introduction to Matlab by Mark S. Gockenbach. You can find a lot of documentation at the MathWorks homepage, specially in their support page.
You should try and do a search on the Internet, since there are a lot of sites dedicated to Matlab, and programming in general.
I wrote the homework assignments and the solutions using a program called LaTeX. If you want to learn more about this program, you can find some information and tutorials at the following homepages:
1. The LaTeX Project.
2. Text processing using LaTeX.
Tentative Syllabus: We will cover Chap. 1, 2, 3, 4 and 5 during this quarter.
Week 1 & 2: Mathematical Preliminaries and Error Analysis, Chap. 1
Review of Calculus, Note
Round-off Errors and Computer Arithmetic
Algorithms and Convergence, Note
Numerical Software and Introduction to programming with Matlab, numericaldev.m & finitesum.m
Week 3 , 4 & 5: Solutions of Equation in One Variable, Chap. 2
The Bisection Method, Note, bisec.m, f.m (Right Click and Save)
Fixed-Point Iteration, Note
Newton's Method, Note
Error Analysis for Iterative Methods
Zeros of Polynomials and Muller's Method
Week 5 & 6: Interpolation and Polynomial Approximation, Chap. 3
Interploation and the Lagrange Polynomial
Divided Differences
Hermite Interpolation
Week 7 & 8: Numerical Differentiation and Integration, Chap. 4
Numerical Differentiation
Richardson's Extrapolation
Elements of Numerical Integration
Composite Numerical Integration
Week 9, 10 & 11: Initial-Value Problems for Ordinary Differential Equations
The Elementary Theory of Initial-Value Problems
Euler's Method
Higher-Order Taylor Methods
Runge-Kutta Methods
Multistep Methods
Higher-Order Equations and Systems of Differential Equations
Homework Assignment: Guidelines for Programming Assignments