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Numerical Methods (Math 465/565 - Fall 2020)

This course will introduce you to the fundamental ideas in the analysis of numerical methods.

Send me an e-mail

Please send me an e-mail at 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
Time Wednesday/Friday 10:30-11:45
Place Virtual meeting - see Blackboard for Zoom link
Office Hours Wednesday 12:00 - 1:30
Prerequesites Math 301 or Math 333, and Math 365

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Recommended and suggested textbooks

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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
Codes written or demonstrated in class :
solve_for_x.m  -- Matlab code for root-finding algorithm shown in class
Codes written or demonstrated in class :
solve_for_x.ipynb  -- Jupyter notebook code for root-finding algorithm shown in class
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)

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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

Assignment :
Updates to homework :
 --  (8/28/2020) Problem 1 : Changed superscript to subscript; Problem 2 : Include 'h' in formula.

Homework #2

Due Sept. 21

Assignment :
Updates to homework :
 --  (9/13/2020) Add one more problem; clarified a second problem.
 --  (9/15/2020) Fixed a few typos.

Homework #3

Due Oct. 16

Assignment :
Updates to homework :
 --  (10/7/2020) Add Math 565 problem; removed one problem.

Homework #4

Due 12/2

Assignment :
Updates to homework :
 --  (11/25/2020) Added clarification to problem #1.

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Midterm Date: TBA

This exam will be open notes and open book

Final Exam Date: no date

In lieu of a final exam, you will have a final homework set, due during finals week.

You can find the Final Exam calendar here.

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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.

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