Course Objective: To provide the necessary mathematical tools required for undergraduate studies as well as advanced study in engineering or the physical sciences.

 Instructor: Dr. Daniel K. Marble

Office: 324A Science Building, Tarleton State University

Office Hours: 10:00 - 10:30 and 4:00 - 5:00

Phone: 254-968-9880

Fax: 254-968-9534

E-Mail: Marble@tarleton.edu

Text: Mathematical Methods for Physicists 4th Ed. by Arfken and Weber

 Grading: A student's course grade will be determined by their performance on three exams and their average on assigned problem sets. The weight for each of these graded exercises is shown below:

Test 1 25%

Test 2 25%

Test 3 25%

Problem sets 25%

 Graduate Students: Since graduate school is intended to allow superior students to study material in greater depth than possible at the undergraduate level, students wishing to obtain graduate credit for this course will be required to do additional work. This includes a computer project and a series of additional reading assignments with problem sets to broaden the student's knowledge of topics that are omitted or only briefly covered in undergraduate physics courses. These include

 1. Chapter 2 - Tensor Analysis

2. Chapter 4 - Group Theory

3. Chapter 12 - Bessel Functions

4. Chapter 13 - Special Functions including Hermite, and Laguerre Functions as well as

5. Chapter 18 - Nonlinear Methods and Chaos

Students with Disabilities: Any student with a disability needing special assistance should contact the Mathematics and Physics Departmental Disability Coordinator (Dr. Dwayne Snider) at 254-968-9536.

 Internet Resources: A web page for this course is presently under construction. Eventually, the site will contain course material including copies of class notes, homework assignments and solutions, etc.

 I. Vector Analysis and Matrix Mathematics

Chapter 1 - Vector Analysis

1. Definition of Vectors and Properties (1.1-1.2)

2. Scalar, Cross and Triple Products (1.3-1.5)

3. Gradient, Divergence, and Curl (1.6-1.9)

4. Vector Integration, Gauss's Theorem and Stokes's Theorem (1.10-1.12)

  Chapter 2 - Vector Analysis in Curved Coordinates and Tensors

1. Orthogonal Coordinates - (2.1)

2. Vector Operations - (2.2)

3. Coordinate Systems - (2.3-2.5)

  Chapter 3 - Determinants and Matrices

1. Matrices (Trace, Inversion, etc) - (3.2)

2. Types of Matrices (Orthogonal, Unitary, Hermitian, Normal, etc) - (3.3-3.4, 3.6)

3. Eigenvalue Problems - (3.5)

II. Infinite Series

Chapter 5 - Infinite Series

1. Fundamental Concepts and Convergence - (5.1-5.5)

2. Taylor Expansion, Laurent Expansion, and Power Series - (5.6-5.7)

  Chapter 14 - Fourier Series

1. General Properties and Applications - (14.1-14.4)

 III. Transforms

Chapter 15 - Integral Transforms

1. Fourier Transforms - (15.1-15.7)

2. Laplace Transforms - (15.8-15.10)

IV. Differential Equations and Orthogonal Functions

Chapter 8 - Differential Equation

1. General Information - (8.1-8.2)

2. Separation of Variables - (8.3)

3. Series Solution Methods - (8.5-8.6)

4. Green Function Solution Methods - (8.7)

5. Fourier and Laplace Methods

Chapter 9 - Sturm-Liouville Theory & Orthogonal Functions

1. Self-Adjoint, Eigenvalue, Eigenfunctions, Orthogonality - (9.1-9.4)

V. Legendre Functions

Chapter 12 - Legendre Functions

1. Physics Examples and Special Properties -(12.1-12.2)

2. Orthogonality - (12.3)

3. Associated Legendre Functions and Spherical Harmonics - (12.5-12.6)

4. Orbital Angular Momentum and Addition of Spherical Harmonics - (12.7-12.9)

 VI. Complex Variables

Chapter 6 - Functions of a Complex Variable I

1. Complex Algebra - (6.1)

2. Cauchy-Riemann Conditions - (6.2)

3. Cauchy's Integral Theorem - (6.3-6.4)

4. Laurent Expansion Revisited - (6.5)

  Chapter 7 - Functions of a Complex Variable II

1. Singularities and Calculus of Residues - (7.1-7.2)

2. Dispersion Relations and Causality - (7.3)

 VII. Calculus of Variations

Chapter 17 - Calculus of Variations

1. Concept of Variation - (17.1)

2. Euler Equation - (17.2)

3. Several Independent Variables - (17.4)

4. Lagrangian Multipliers - (17.6)