Math 465/565
Numerical Methods I
Fall 2017

Basic Information

Time and Place:  TuTh 10:30-11:45am, Mathematics Building 139
Instructor:  Dr. Grady Wright, MG-140, 426-4674, Email:
Office Hours:  Wednesday: 1:00-3:00pm, or by appointment (please e-mail to set it up).

Text Books

Software: MATLAB

MATLAB is available in most computing labs around the university, including the mathematics computing lab. A student version can be purchased at a big discount from the bookstore. Alternatively, students can obtain a free copy from OIT.

Lectures


 
Day Topics Material
22-Aug
Introduction to numerical analysis
Ch. 1
24-Aug
Round-off errors
Ch. 2
29-Aug
Round-off errors
Solving non-linear equations
Ch. 2
Ch. 3.1
31-Aug
Bisection
Fixed point
Newton's method
Ch. 3.2
Ch. 3.3
Ch. 3.4
05-Sep
Newton's method
Secant Method
Ch. 3.4
07-Sep Secant Method
Linear algebra review
Ch. 3.4
Ch. 4
12-Sep Linear algebra review
Gaussian elimination (slides)
Ch. 4
Ch. 5.1
14-Sep LU Decomposition (slides)
Partial pivoting, scaled pivoting, and complete pivoting
Ch. 5.2
Ch. 5.3
19-Sep Symmetric positive definite matrices and Cholesky decomposition
Sparse matrices and the Thomas algorithm
Ch. 5.5
Ch. 5.6
21-Sep Sparse matrices and the Thomas algorithm
Efficient implementations of Gaussian elimination: handout
Code: lupp_loop.m, lupp.m, forsub.m, backsub.m, test_lupp.m
Ch. 5.6
Ch. 5.4
26-Sep Conditioning of linear systems Ch. 5.8
28-Sep Polynomial interpolation Ch. 10.1-10.2
3-Oct Lagrange interpolation
Error in polynomial interpolation
Ch. 10.3
Ch. 10.5
5-Oct Interpolation using Newton's divided differences Ch. 10.4
10-Oct Interpolation at Chebyshev points Ch. 10.6
12-Oct Hermite interpolation
Piecewise polynomial interpolation: linear and cubic Hermite
Ch. 10.6
Ch. 11.1-11.2
17-Oct Cubic splines Ch. 11.3
19-Oct Midterm review
Spline basis functions - B-splines
Parametric curves
Ch. 11.4
Ch. 11.5
24-Oct Interpolation in two and higher dimensions
(Radial basis functions)
Ch. 11.6
 
26-Oct Best approximation: continuous least squares Ch. 12.1-12.2
31-Oct Orthogonal polynomials and least squares
Weighted least squares
Ch. 12.2
Ch. 12.3
02-Nov Weighted least squares
Chebyshev polynomials
Ch. 12.3
Ch. 12.4
07-Nov Near mini-max approximation
Numerical integration: midpoint, trapezoidal, Simpsons rules
Ch. 12.4
Ch. 15.1
09-Nov Error analysis of trapezoidal and Simpsons rules Ch. 15.1-15.2
14-Nov Error analysis of trapezoidal and Simpsons rules
Gaussian quadrature
Ch. 15.1-15.2
Ch. 15.3
16-Nov Gaussian quadrature Ch. 15.3
28-Nov Romberg integration
Adaptive quadrature
Ch. 15.5
Ch. 15.4
30-Nov Integration in two and more dimensions
Numerical differentiation
Ch. 15.5 Ch. 14.1
5-Dec Numerical differentiation
Ch. 15.5 Ch. 14.1-14.3

Homework problem sets

See "How to Present your Work" for instructions on writing up your homework assignments, and basic mathematical symbols for a description of some symbols that can greatly simplify your mathematical writing.
 
Due date Problem set Notes
07-SEPT-2017 HW01
21-SEPT-2017 HW02 solutions,
06-OCT-2017 HW03
20-OCT-2017 HW04 polyinterp.m
03-NOV-2017 HW05 splineinterp.m, DotToDot.txt, rbffit.m, rbfval.m, topodata.mat
17-NOV-2017 HW06
08-DEC-2017 HW07 Brute Force Gaussian Quadrature: Mathematica, Maple

Miscellaneous


Please e-mail me regarding any problems with the links on this page.