Course:
- Lecture: MTWR 12:30PM-1:35PM, GIRV 2108
- Webpage: You're looking at it!
- Textbook: Numerical Analysis, Burden and Faires, ISBN 0-534-39200-8
Lecturer:
- Name: Pat Plunkett
- Office: 6432L, South Hall
- Email: plunkett@math.ucsb.edu
- Office Hours: T 1:35PM-3:35PM
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:
- Convergence of a numerical algorithm: What it means, and how to determine whether the algorithm converges or not.
- A solid knowledge of Approximation Theory:
- Polynomial Interpolation.
- Numerical Integration: Design and implementation of quadrature rules.
- Numerical Differentiation: Design and implementation of differentiation formulas of arbitrary order of accuracy.
- Estimation of the error in a given approximation.
- Solution of Differential Equations:
- Design and implementation of solvers for Ordinary Differential Equations (ODEs).
- Being able to obtain the stability region of a multistep method for ODEs.
- Estimation of the error and the stability properties of a given method.
- Solid programming skills.
Grading:
- Homework: 30%
- Midterm: 30%
- Final: 40%
Homework:
- Homework will be assigned on Thursdays, and will be due one week later. Late homework will not be accepted. 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 in any programming language, but Matlab or Octave is strongly recommended. 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.
Final:
- The final will be a take-home project. You will choose a project from a pool which I will provide. These will be due Monday, Aug. 1.
Computer Laboratory:
- The computer labs in Phelps Hall (Leadbetter, Mesa, Miramar, Gaviota) have MatLab installed on each computer. Click on each link to see a schedule for the lab. There is at least one lab open every day from 8AM-5PM.
Resources:
- For those of you unfamiliar with MatLab or programming, check out the resources page.
