Lecture Notes, Problems, etc., Math 4426

The instructor's classroom notes are made available to students here.
These notes have equal standing with the text as a basis for the course.
Suggested exercises, where shown, are based on the text.

These notes are, for the most part, provided in the form of .pdf files
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A notation (Information) following the hyperlink indicates that the material
is for the student's information only and will not be explicitly tested on exams, etc.

The posting date shown indicates the most recent date of posting; thus a lecture
might be posted originally on one date and then corrected, and posted again, at a later date.
The lecture date indicates the first day a particular set of notes was used in class.

Lecture of Tuesday, January 15, 2008.

Eigenvalues and Eigenvectors
Posted January 15, 2008.

Lecture of Thursday, January 17, 2008.

Differential Operators and their Adjoints
Posted January 18, 2008.

Lecture of Tuesday, January 22, 2008.

Self-Adjoint Differential Operators
Posted January 24, 2008.

Lectures of Thursday, January 24 and Tuesday, January 29, 2008.

The Nonuniform String
Posted January 24, 2008; additional pages added January 28.

Hints for suggested exercises.
Posted January 30, 2008.

Lectures of Thursday, January 31 and Tuesday, February 5, 2008.

The Sturm - Liouville Theorem
Posted February 5, 2008.

Lecture of Thursday, February 7, 2008.

Numerical treatment of Sturm - Liouville Problems
Posted February 12, 2008.

Lectures of Tuesday, February 12, and Thursday, February 14, 2008.

Vibrations of an Elastic Beam
Posted February 12, 2008.

Lectures of Tuesday, February 19, and Thursday, February 21, 2008.

The Laplace and Poisson Equations
Posted February 20, 2008.

Lectures of Tuesday, February 26, and Thursday, February 28, 2008.

Axisymmetric Vibrations in a Disk
Posted February 28, 2008. Note suggested exercises at end of file.

Lectures of Tuesday, March 11 through Tuesday, March 18, 2008.

General Vibrations in a Disk
Posted March 13, 2008.

Lectures of Thursday, March 20 through Thursday, March 27, 2008.

The Laplacian in R^3; Part I
Posted March 27, 2008.

Lecture of Tuesday, April 1, 2008.

The Laplacian in R^3; Spherical Harmonics
Posted April 1, 2008.

Lecture of Thursday, April 3, 2008.

The Helmholtz, and Related, Equations
Posted April 3, 2008.

Lecture of Tuesday, April 8, 2008.

The Galerkin Method
Posted April 10, 2008.

Lecture of Thursday, April 10 and Tuesday, April 15, 2008.

Spline Functions, Page 1.
Spline Functions, Page 2.
Spline Functions, Page 3.
Spline Functions, Page 4.
Spline Functions, Page 5.
Spline Functions, Page 6.
Spline Functions, Page 7.
Spline Functions, Page 8.
Spline Functions, Page 9.
Spline Functions, Page 10.
Spline Functions, Page 11.
Posted April 13, 2008.

Lecture of Thursday, April 17, 2008.

The Collocation Method
Posted April 17, 2008.

Lecture of Thursday, April 24, 2008.

The Finite Difference Method in R^2
Posted April 24, 2008.

Lecture of Tuesday, April 29, 2008.

The Linear Finite Element Method in R^2
Posted April 24, 2008.