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 rootfinding, 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
 Lectures
 Homework Assignments
 Exams
 Grading policy (subject to change)
Send me an email
Please send me an email at donnacalhoun@boisestate.edu so that I can compile an email 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 
Time  Wednesday/Friday 10:3011:45 
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).
Lectures
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 Rootfinding (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 Assignments
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.
Homework #1 
Due Sept. 2

Homework #2 
Due Sept. 21

Homework #3 
Due Oct. 16

Exams
TBA
Midterm  Date: TBA 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.