Introduction to Scientific Computing
Revised: December 2008 (Erin McNelis)
Course Description
This introduction to the field of scientific computing will focus on using mathematical software and programming as tools in mathematical problem solving.
Objectives
1. model problems mathematically and use mathematical software to solve or simulate these problems
2. to develop algorithms and implement them in the appropriate software or programming language
3. to present algorithms and solutions to problems in a mathematically sophisticated manner using a
scientific documentation environment
4. to know the benefits and drawbacks of each of the computational tools used during the semester
Text
This course has no text book. Instead, handouts will be provided and documents can be download from the class web sites.
Grading ProcedureGrading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.
Attendance Policy
Attendance policy is left to the discretion of individual instructors, subject to general university policy.
Course Outline
- Preliminaries (about 3 days)
o Taylor polynomial approximation.
o Mean Value Theorem - Chapter 1 Power Tools of the Trade (about 8 days)
o Vectors and Plotting.
o Error.
o Designing Functions. - Chapter 2 Polynomial Interpolation (about 5 days)
o The Vandemonde Approach.
o The Newton Approach.
o Properties.
o Special Topics. - Chapter 3 Piecewise Polynomial Interpolation (about 5 days)
o Piecewise Linear Interpolation.
o Cubic Splines. - Supplemental Material on Least Squares Fitting to Data (about 6 days)
o Linear Regression.
o Polynomial Regression.
o Goodness of Fit. - Chapter 4 Numerical Integration (about 9 days)
o Newton Cotes Rules.
o Composite Rules.
o Adaptive Quadrature.
o Romberg Integration
o Special Topics - Supplemental Material on Numerical Differentiation (about 6 days)
o Difference Approximations
o Richardson's Extrapolation
o Special Topics