CS 137: Introduction to Scientific Computing

General Information

Time : TuTh 11:00-12:50pm
Location: Gates B03

Instructor: Oscar Gonzalez
Email Address: gonzalez@sccm.stanford.edu
Office Ph: 3-6317
Office Hrs: Gates 203, Tuesday 3-4pm and Wednesday 11am-12pm, or by appointment

Teaching Asst: Paul Tupper
Email Address: tupper@sccm.stanford.edu
Office Ph: 3-4101
Office Hrs: See below.

Assignments

Assignment 1 is due on July 1.
Assignment 2 is due on July 8.
Assignment 3 is due on July 15.
Assignment 4 is due on July 27.
Assignment 5 is due on August 3.
Assignment 6 is due on August 10.
Final is due on August 13.

Required Text

M.T. Heath (1997) Scientific Computing: An Introductory Survey, McGraw-Hill


The book is on reserve in the Math/CS library

Useful References

Matlab Primer, available online

Matlab Tutorial, available online

Prerequisites

Officially, CS106A and MATH103 or 113. We expect students to have a basic knowledge of linear algebra and calculus, and some basic programming skills.

Calculus

You should be comfortable with limits, differentiation, integration, and Taylor series.

Linear algebra

You should be comfortable with basic matrix arithmetic, understand what a matrix inverse is, be aware of various types of matrices (e.g. symmetric, positive-definite, orthogonal, singular) and know what eigenvalues are. A good reference is Linear Algebra and its Applications by Gilbert Strang.

Course Policies

Homeworks

• typically weekly
  
• to be submitted in class or box outside Gates 286
  
• due on date specified by 5:30pm
  
• late homeworks accepted only by prior arrangement
  

Exams

• no midterm
  
• take-home final due early in the exam period
  

Grading

• homework 60%
  
• take-home final 40%
  

Programming

Homework exercises that require programming should be written (unless you obtain prior approval) in Matlab, which is an easy-to-use scientific computing environment. Matlab is available in many computer labs around campus, and there is also a relatively inexpensive student version which can be purchased for personal use. No prior experience with Matlab is required for the successful completion of this course. The Matlab Primer and the Matlab Tutorial each provide a good introduction. Both commented source code and sample output should be submitted with programming assignments.

Topics

Finite-precision computer arithmetic
Linear algebraic equations
Nonlinear algebraic equations
Optimization problems
Interpolation problems
Numerical quadrature and differentiation
Ordinary differential equations
Eigenvalue problems

Tentative Class Schedule

Date	Topic	Reading
June 22	Introduction, Computer arithmetic	1.1-1.3
June 24	Linear algebraic equations: math review, direct methods	2.1-2.5
June 29	Linear algebraic equations: iterative methods	2.6,11.5,11.6,2.7
July 1	Nonlinear algebraic equations: math review, scalar case	5.1-5.2
July 6	Nonlinear algebraic equations: vector case	5.3-5.4
July 8	Parameter continuation: ideas, examples	class notes
July 13	Optimization problems: math review, vector case	6.1-6.3
July 15	Optimization problems: least squares	6.4,3.2-3.5
July 20	Interpolation problems	7.1-7.3
July 22	Numerical quadrature	8.1-8.5
July 27	Numerical differentiation	8.7-8.9
July 29	Initial-value problems for ordinary differential equations: math review, survey of methods	9.1,9.2,9.4,9.6
August 3	Initial-value problems for ordinary differential equations: accuracy, stability	9.3,9.7
August 5	Boundary-value problems for ordinary differential equations: math review, survey of methods	10.1-10.5
August 10	Eigenvalue problems	10.6,4.1-4.3
August 13	Take-home final exam due	.