Department of Applied Science

Course Syllabus

4360/5360 Potential Theory

I. Instructor: Dr. Haydar Al-Shukri

II. Catalog Description:

Solution to Laplace equation using different boundary and initial conditions. One-, Two-, and three-dimensional equations will be analyzed. Various coordinate systems (rectangular, cylindrical, and spherical) will be used in the solution of Laplace equation. Bessel function and orthogonality of Bessel function. Legendre functgion, Associate Legendre function, and orthogonality of Legendre function. Three lectures per week. (3 hrs)

III. Prerequisites: Calculus I, II, III, and differential equation.

IV. Course Objectives:

A. Introduce the students of applied science to Laplace equation and procedures of solving partial differential equations.

B. Solve the Laplace equation in various coordinate system using different boundary and initial conditions.

C. Utilization of Laplace equation in studying geophysical observations such as the earth’s gravitational and magnetic field.

V. Expectation of Students:

A. Students will participate in all class meetings and will complete assigned readings and other preparation for discussion of the subject matters.

B. Students will achieve satisfactory grades on a midterm and a final examination.

VI. Course Content:

A. Review of partial differential equation and coordinate systems

1. Various types of partial differential equations

2. One-, two-, and three-dimension system

3. Procedures of solving partial differential equations

4. Separation of variables

B. Potential functions

1. Distributed mass and field intensity

2. Field equations and continuity of potential

3. Dirichlet, Neumann, Churchill, and Mixed problems

4. Existence and uniqueness of solution

5. Physical problem in which Laplace equation appears

C. Laplace equation

1. Separation of variables

2. Method of superposition

3. Laplace equation in plane polar coordinates

4. Curvilinear coordinates

5. Differential vector operation

a. Gradient

b. Divergence

c. Curle

6. Spherical polar coordinate

7. Circular cylindrical coordinate

D. Midterm examination

E. Bessel equation

1. Integral representation

2. Orthogonality of Bessel function

3. Laplace equation in cylindrical coordinate

4. Potential produce by a point electric charge

5. Legendre function and orthogonality of Legendre function

6. Associate Legendre function

F. Mathematical considerations

1. Integral transform

2. Element of partial differential equations

3. Function of complex variables

4. Mapping

5. Introduction to Spherical Harmonics

F. Final examination and oral presentation of term paper.

VII. Basis for student evaluation:

A. Graduate Students:

1. Midterm Examination 25%

2. Assignments 25%

3. Term paper and presentation 25%

4. Final Examination 25%

B. Undergraduate Students:

1. Midterm examination 33%

2. Assignments 33%

3. Final examination 34%