645:572 Computational Mathematics II / 640:497 Advanced Computational Mathematics -
Spring
2021
Department of Mathematical Sciences
Rutgers University, Camden, NJ
- 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.
- Handouts: (PDF Format)
- Course
Information
- Chapter 1: Matrices and Systems of Linear Equations
- 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
Last Revised 7:11PM EST 04/28/2021