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Numerical Analysis (Math 465/565)


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 donnacalhoun@boisestate.edu 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 Tuesday/Thursday 9:00-10:15
Place MG 124
Office Hours Wednesday 10AM-12PM and 1PM-3PM
Prerequesites Math 301 or Math 333

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Recommended and suggested textbooks

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Lectures

Week #1 (Aug. 26)
Tuesday --  Introduction to Numerical Analysis
Lecture slides :
Introduction to Numerical Analysis  (pdfhtml)
Thursday --  Root-finding : Bisection
Lecture slides :
Bisection  (pdfhtml)
Codes written or demonstrated in class :
bisection.m

Week #2 (Sept. 2)
Tuesday --  Fixed point iteration
Lecture slides :
Fixed Point  (pdfhtml)
Codes written or demonstrated in class :
fixedpoint.m
Thursday --  Fixed point iteration (continued)

Week #3 (Sept. 9)
Tuesday --  Order and rates of convergence
Lecture slides :
Order and rates of convergence  (pdfhtml)
Thursday --  Order and rates of convergence (continued)

Week #4 (Sept. 16)
Tuesday --  Newton's Method
Thursday --  Secant Method

Week #5 (Sept. 23)
Tuesday --  Linear Systems
Lecture slides :
Intro to linear systems  (pdfhtml)
Gaussian Elimination  (pdfhtml)
Thursday --  Gaussian elimination using matrices; matrix inverses; LU Decomposition
Lecture slides :
Elimination matrices  (pdfhtml)
Matrix Inverses  (pdfhtml)
LU Decomposition  (pdfhtml)

Week #6 (Sept. 30)
Tuesday --  Review of homework #1
Thursday --  LU Decomposition code
Codes written or demonstrated in class :
solve.m

Week #7 (Oct. 7)
Tuesday --  Partial Pivoting
Codes written or demonstrated in class :
lu_no_pp_round.m
lu_with_pp_round.m
lu_no_pp.m
lu_with_pp.m
sd_round.m
matrices.m
Thursday --  Error Analysis with partial pivoting

Week #8 (Oct. 14)
Tuesday --  Error analysis of Gaussian Elimination
Thursday --  Midterm #1

Week #9 (Oct. 21)
Tuesday --  Work on Midterm exam
Thursday --  Work on Midterm exam

Week #10 (Oct. 28)
Tuesday --  Introduction to iterative methods
Lecture slides :
Introduction to Iterative methods  (pdfhtml)
Codes written or demonstrated in class :
simple_iteration.m
set_matrix.m
Thursday --  Convergence of Splitting Methods
Codes written or demonstrated in class :
splitting.m
set_matrix.m
Other resources :
SIREV95.pdf  -- Convergence of the Gauss-Seidel and Jacobi methods

Week #11 (Nov. 4)
Tuesday --  Splitting Methods (cont)
Lecture slides :
Matrix Splitting Methods  (pdfhtml)
Codes written or demonstrated in class :
test_splitting.m
Thursday --  Conjugate Gradient Method
Codes written or demonstrated in class :
steepest_descent.m
cj.m

Week #12 (Nov. 11)
Tuesday --  Polynomial interpolation
Lecture slides :
Solving the Vandermonde Matrix System  (pdfhtml)
Thursday --  Lagrange Polynomials
Lecture slides :
Lagrange Interpolation Formula  (pdfhtml)
Codes written or demonstrated in class :
plot_lagrange.m
lagrange_coeffs.m
ell_j.m
Other items of interest :
CramersRule.pdf

Week #13 (Nov. 18)
Tuesday --  Barycentric Formula, Interpolation Error
Lecture slides :
Barycentric Formula  (pdfhtml)
Thursday --  Chebyshev Polynomials

Week #14 (Dec. 2)
Tuesday --  Chebyshev and Legendre Polynomials
Other items of interest :
SixMyths.pdf
Thursday --  Numerical Integration
Codes written or demonstrated in class :
error_poly.m
heat_flow.m

Week #15 (Dec. 9)
Tuesday --  Quadrature rules - convergence theory
Thursday --  In class practice exam

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Homework Assignments

Homework projects are designed to enforce mathematical concepts and to build and improve Matlab programming skills. Homeworks will be due roughly every two weeks.

Homework #1

Due Sept. 12

Assignment :
hmwk1.pdf

Homework #2

Due Oct. 1

Assignment :
hmwk2.pdf

Homework #3

Due Oct. 15

Assignment :
hmwk3.pdf

Homework #4

Due Nov. 7

Assignment :
hmwk4.pdf

Homework #5

Due Dec. 5

Assignment :
hmwk5.pdf

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Exams

We will have one midterm and one final

Midterm Exam Date October 17

This exam will be open notes and open book



Final Exam Date Tuesday December 17th, 9:30-11:30

The final exam will be comprehensive


You can find the Final Exam calendar here.

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Matlab tutorials

Below are a series of tutorials that should help you become familar with Matlab syntax

  1. Using Matlab as a Graphing Calculator, Part I
  2. Using Matlab as a Graphing Calculator, Part II
  3. Using Matlab as a Graphing Calculator, Part III
  4. Loops and one dimensional arrays
  5. Two dimensional arrays and introduction to matrices
  6. Vandermonde matrix systems
  7. Lagrange polynomials

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Grading policy

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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