CPSC 653-600: Computer Methods in Applied Sciences (Fall 07)

Instructor	Vivek Sarin, 309C HRBB, 458-2214
Lecture	TR, 11:10am-12:25pm, 126 HRBB
Office Hours	TR, 12:30-1:30pm
Prerequisites	One of these: CPSC 442 or MATH 417 or equivalent. Contact me if you have questions.
Textbook	Afternotes on Numerical Analysis by G. W. Stewart

Announcements

• Look out for important announcements here

Description

This course introduces techniques for computational solution of scientific and engineering problems; the following topics will be covered in varying depths:

- Number representation and errors

- Linear systems

- Nonlinear equations

- Interpolation

- Numerical integration

- Ordinary differential equations

- Partial differential equations

Homework will consist of theoretical problems as well as programming exercises using MATLAB. You are expected to learn basic MATLAB during the early part of the course (this is not at all difficult).

Outline

- Introduction: Algorithms, Errors, Error propagation, MATLAB

- Floating-point Computation: Floating-point numbers, Floating-point arithmetic (basic operations), Numerical instabilities

- Matrix Computations: Basic concepts, Solving linear systems, Conditioning

- Polynomial Interpolation: The Vandermonde approach, The Newton representation, Cubic Splines

- Numerical Integration: The Newton-Cotes rules, Composite rules, Spline quadrature, Gaussian quadrature

- Nonlinear Equations: Bisection method, Newton's method, Secant method

- Initial Value Problem for Ordinary Differential Equations: Basic concepts, Euler's method, The Runge-Kutta methods

- Partial Differential Equations: Finite difference methods

Homework

Homework assignments will be given once every couple of weeks. They will be posted in the Lecture Schedule section below. 

Matlab

You are expected to learn basic MATLAB during the early part of the course. CS majors should use their accounts on department machines to access MATLAB. Non-CS majors with no access to MATLAB in their respective departments should contact the CS system administrators for accounts. MATLAB documentation can be found at the MathWorks web site.

Grading

The final grade will depend upon your performance on homework, midterms, and final examination as follows:

Homework	25%
Midterm I	25%
Midterm II	25%
Final	25%

Homework policy: 1 day late: -10%, 2 day late: -20%, 3 day late: -40%, 4 or more days late homework will not accepted

Exams: All exams are open-book/open-notes

Scholastic dishonesty

University regulations (Section 42) define scholastic dishonesty to include acquiring answers from any unauthorized source, working with another person when not specifically permitted, observing the work of other students during any exam, providing answers when not specifically authorized to do so, informing any person of the contents of an exam prior to the exam, and failing to credit sources used. Disciplinary actions range from grade penalty to expulsion. 

Lecture Schedule (Tentative)

Handouts, homework assignments, solutions, etc., will be available here.

	Tuesday	Thursday		Tuesday	Thursday
Aug. 28	Nonlinear Equations	Nonlinear Equations	Sept. 4	Nonlinear Equations	Nonlinear Equations
Sept. 11	Floating Point Computation	Floating Point Computation	Sept. 18	Floating Point Computation	Floating Point Computation
Sept. 25	Linear Systems	Linear Systems	Oct. 2	Interpolation	Exam 1
Oct. 9	Interpolation	Interpolation	Oct. 16	Interpolation	Integration
Oct. 23	Integration	Integration	Oct. 30	Integration	Ordinary Diff. Eqns
Nov. 6	Ordinary Diff. Eqns	Ordinary Diff. Eqns	Nov. 13	Exam 2	Ordinary Diff. Eqns
Nov. 20	Partial Diff. Eqns	Thanksgiving	Nov. 27	Partial Diff. Eqns	Partial Diff. Eqns
Dec. 4	Partial Diff. Eqns		Dec. 7: Final Exam (3-5pm)

Updated by Vivek Sarin on August 20, 2007