CS 371 Introduction to Computational Mathematics
Watch a video introduction to the course on YouTube.
Objectives
This course is intended as an introduction to the computational methods and issues encountered
when solving realistic examples in scientific computation.
Intended Audience
CS 371 is intended for students interested in the computational aspects that one would encounter
in solving various mathematical and scientific problems. Students are expected to be interested in
both mathematics and computer science.
Related Courses
Prerequisites: (One of CS 116, 134, 136, 138, 145 taken fall 2010 or earlier, CS 146), MATH 235 or 245, 237 or 247; Not open to General Mathematics students.
Antirequisites: CS 335, 337, 370, ECE 204.
Successors: CS 473, 475, 476.
Cross-listed as: AMATH 341, CM 271.
Hardware/Software
Used in course: Matlab.
References
Numerical Analysis, 8th ed., by R. Burden and J. Faires, Publ.: Brooks Cole (optional). Course notes are required.
Schedule
3 hours of lectures per week. Normally available in Winter and Spring.
Notes
1. CS 371 may be substituted for CS 370 in any degree plan or for prerequisite purposes; lab is not scheduled and students
are expected to find time in open hours to complete their work.
Outline
Floating Point Number Systems (3 hours)
Pitfalls of computation, errors in computation.
Polynomial Interpolation (9 hours)
Converting discrete data to continuous functions, Lagrange interpolation, piecewise approximation, spline and b-spline interpolation.
Numerical Integration (6 hours)
Converting continuous problems into discrete data, quadrature rules, Monte Carlo integration.
Fourier Approximation (9 hours)
Fourier series, discrete Fourier transform, fast Fourier transform (FFT), applications for image processing, JPEG, MPEG.
Linear Systems (9 hours)
Solution of linear systems (LU factorization), condition number of a matrix, solving overdetermined systems, least squares fitting, QR factorization.
