645:572 Computational Mathematics II

645:572 Computational Mathematics II / 640:497 Advanced Computational Mathematics - Spring 2021
Department of Mathematical Sciences
Rutgers University, Camden, NJ

Textbooks:

E. Suli and D. Mayers, An Introduction to Numerical Analysis , Cambridge University Press, 2003.
A. Ralston and P. Rabinowitz, A First Course in Numerical Analysis, Second Edition, Dover Publications

Class meetings: Wednesdays 6:00PM - 8:50PM Online
Instructor: Steve Alessandrini, sma@rutgers.edu
Office hours: Before class.
Prerequisites:

(Undergraduate) advanced calculus, linear algebra, and differential equations.
Knowledge of C++. Tutorial
C++ Style Guide for Scientific Computing
This course is suitable for graduate students and advanced undergraduates who have the prerequisites.
It is preferred that the first semester 645:571 is taken before 645:572.

Course description:

This one-year sequence covers various numerical techniques for solving mathematical problems on a computer. The first semester 645:571 covers the IEEE internal representation of floating point numbers, interpolation, root finding, numerical integration, numerical differentiation, and function minimization. The second semester 645:572 covers numerical linear algebra and the numerical solution of differential equations. The material is presented so that topics build on one another and applications are given to illustrate the use of the techniques.

Course outline.

Handouts: (PDF Format)

Course Information
Chapter 1: Matrices and Systems of Linear Equations

Part 1: pp 1-9 (1/20/2021)
Part 2: pp 10-21 (1/27/2021)

Read: Edward Rozema, "Why Should We Pivot in Gaussian Elimination?", The College Mathematics Journal, Vol. 19, No. 1 (Jan., 1988), pp. 63-72.

Chapter 2: The Matrix Eigenvalue Problem

Part 6: pp 47-58 (3/3/2021)
MATLAB:

Applications (references)

Tournament Rankings:

T. Jech,"The Ranking of Incomplete Tournaments: A Mathematician's Guide to Popular Sports," American Mathematical Monthly, Vol. 90, No. 4, April 1983, pp. 246-266.
J. P Keener, "The Perron-Frobenius Theorem and the Ranking of Football Teams" SIAM Review, Vol.35, No.1, March 1993, pp.80-93.
M. Stob, "A Supplement to 'A Mathematician's Guide to Popular Sports'," American Mathematical Monthly, Vol. 91, No. 5, May 1984, pp. 277-282.

Google:

Chapter 3: Ordinary Differential Equations

Bibliography

Homework Assignments: See Canvas

Notes:

First Class: Wednesday 1/20
The three 2-hour exams will be given on Canvas from 6:00 pm - 8:00pm on the following Wednesdays: 2/10/21, 3/10/21, 4/14/21
Spring Break: Wednesday 3/17 (No Class)
Last Class: Wednesday 4/28
Final Exam: Wednesday 5/12 on Canvas from 6:00 pm - 9:00pm

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Last Revised 7:11PM EST 04/28/2021