Numerical Methods (Math 465/565 - Fall 2020)
This course will introduce you to the fundamental ideas in the analysis of numerical methods.
- Floating point number systems, or Why do we worry about Numerical Analysis?
- Numerical root-finding, or How do we solve cos(x)=x ?
- Systems of linear equations using Gaussian Elimination and decomposition methods
- Interpolation and curve fitting, or If it looks like a parabola, it might be a cubic!
- Numerical integration
- Basic course information
- Recommended and suggested textbooks
- Homework Assignments
- Grading policy (subject to change)
Send me an e-mail
Please send me an e-mail at email@example.com so that I can compile an e-mail list for the class. At the very least, include a subject header that says "Math 465/565". You may leave the message area blank, if you wish, or send me a short note about what you hope to get out of this course.
Basic course information
|Instructor||Prof. Donna Calhoun|
|Place||Virtual meeting - see Blackboard for Zoom link|
|Office Hours||Wednesday 12:00 - 1:30|
|Prerequesites||Math 301 or Math 333, and Math 365|
Recommended and suggested textbooks
- A Friendly Introduction to Numerical Analysis, by Brian Bradie. Pearson Prentice Hall, (2006) (required).
- An Introduction to Numerical Analysis, 2nd Edition, by Kendall Atkinson. Wiley Press, (1989) , ((suggested)) (suggested).
- Analysis of Numerial Methods, by Eugene Isaacson and Herbert Keller. Dover Books on Mathematics, (1994) (suggested).
- Numerical Computing with Matlab, by Cleve Moler. Mathworks, Inc., (2004) (suggested).
- Learning Matlab, by Toby A. Driscoll. The Society for Industrial and Applied Mathematics, (2009) (suggested).
The schedule below shows different material for Wednesday and Friday. Because we have two sections of this course, I will cover the same material on both days, and make what is listed as "Friday" material available asynchronously. That means that if you are in the Friday section, you can expect to cover the material listed under Wednesday.
|Week #1 (Aug. 24)||
Wednesday (8/26) -- Chapter 1.1 : Getting started
Friday (8/28) -- Section 1.2 : Convergence (available asynchronously)
|Week #2 (Aug. 31)||
Wednesday (9/2) -- Representation of floating point numbers (Section 1.3)
Friday (9/4) -- Numerical consequences of floating point representations
|Week #3 (Sep. 7)||
Wednesday (9/9) -- Worksheet problems on rates of convergence and floating point arithmetic
Friday (9/11) -- Programming tips and Pitfalls (async.)
|Week #4 (Sep. 14)||
Wednesday (9/16) -- Introduction to Root-finding (sync.)
Friday (9/17) -- TBA (async.)
|Week #5 (Sep. 21)||
Wednesday (9/23) -- Bisection Algorithm (sync.)
Friday (9/25) -- Method of False Position (async.)
|Week #6 (Sep. 28)||
Wednesday (9/30) -- Fixed Point iteration (sync.)
Friday (10/2) -- TBA (async.)
|Week #7 (Oct. 5)||
Wednesday (10/7) -- Newton's Method (sync.)
Friday (10/9) -- Acceleration methods : Steffensen's Method (async.)
|Week #8 (Oct. 12)||
Wednesday (10/14) -- Linear Systems; Gaussian Elimination; LU decomposition (sync.)
Friday (10/16) -- Stability of Gaussian Elimination (async.)
|Week #9 (Oct. 19)|
|Week #10 (Oct. 26)|
|Week #11 (Nov. 2)|
|Week #12 (Nov. 9)|
|Week #13 (Nov. 16)|
|Week #14 (Nov. 30)|
|Week #15 (Dec. 7)|
Homework projects are designed to enforce mathematical concepts and to build and improve programming skills. Homeworks will be due roughly every two weeks, by midnight of the due date. Homework is to be submitted to Dropbox folders which will be setup for each student.
Due Sept. 2
Due Sept. 21
Due Oct. 16
This exam will be open notes and open book
|Final Exam||Date: TBA
The final exam will be comprehensive
You can find the Final Exam calendar here.
Grading policy (subject to change)
Homeworks and quizzes will count for 25% of your final grade, and each of the midterms and the final will be 25% each of your final grade.