| |
May 13, 2024
|
|
|
|
|
MA 703 - Partial Differential Equations3 lecture hours 0 lab hours 3 credits
Course Description
This course presents partial differential equations that arise in some topics of vibrations, heat transfer and fluid dynamics and long transmission line problems. Topics covered include Fourier series; half-range expansions: Fourier sine and cosine series; one-dimensional wave equation; two-dimensional wave equation; one-dimensional heat equation; two-dimensional heat equation; Laplace’s equation; Poisson’s equation; Dirichlet, Neumann and Robin conditions. All of these partial differential equations will be studied in rectangular coordinates and very briefly in polar, cylindrical and spherical coordinates. (prereq: MA 235, and MA 232, MA 2323, or equivalent)
Course Learning Outcomes
Upon successful completion of this course, the student will be able to:
- Write Fourier series of functions with period 2p
- Write Fourier series of functions with arbitrary periods
- Be able to write Fourier series of non-periodic functions using half-range expansions
- Write the complex form of Fourier series
- Solve one-dimensional wave equation using method of separation of variables and apply it to vibrating strings
- Solve one-dimensional heat equation using method of separation of variables and apply it to heat conduction in bars
- Solve two-dimensional wave and heat equations using method of separation of variables
- Solve two-dimensional Laplace’s equation in rectangular coordinates
- Solve two-dimensional wave equation in polar coordinates and apply it to vibrating membranes
- Solve two-dimensional Laplace’s equation in polar coordinates and use it in applications
Prerequisites by Topic
- Ordinary differential equations
- Infinite series
Course Topics
- What is a partial differential equation and interpreting a given partial differential equation
- Periodic functions
- Fourier series
- Fourier series of functions with arbitrary periods
- Half-range expansions: Fourier sine and cosine series
- Complex form of Fourier series
- Forced oscillations
- Modeling: Vibrating string and one-dimensional wave equation
- Solution of one-dimensional wave equation using method of separation of variables
- D’Lambert’s method of solving one-dimensional wave equation
- Solution of one-dimensional heat equation using method of separation of variables
- Heat conduction in bars: Varying the boundary conditions
- Two-dimensional wave and heat equations
- Laplace’s equation
- Neumann and Robin conditions
- Vibrations of a circular membrane
Coordinator
Dr. Yvonne Yaz
Add to Portfolio (opens a new window)
|
|
Skip to Main Content
