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Nov 21, 2024
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MA 387 - Partial Differential Equations3 lecture hours 0 lab hours 3 credits
Course Description
This course provides a smooth transition from a course in elementary ordinary differential equations to more advanced topics in a first course in partial differential equations, with heavier emphasis on Fourier series and boundary value problems. Topics covered includes separation of variables, classification of second order equations and canonical form, Fourier series, the one-dimensional and two-dimensional wave equation and heat equation, and Laplace’s equation. It also covers some applications, such as vibrating string, vibrating membrane, vibration of beams, heat conduction in bars and rectangular regions, etc. (not for credit to students that have taken MA 703). (prereq: MA 235 , MA 232 or MA 2323 )
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
- Infinite series
- Ordinary differential equations
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
- The two-dimensional wave and two-dimensional heat equations
- Laplace’s equation in rectangular coordinates
- The Poisson’s Equation: The method of eigenfunction expansion
- Neumann and Robin conditions
- Laplacian in various coordinate systems
- Two-dimensional wave equation in polar coordinates: Vibration of a circular membrane
- Two-dimensional Laplace’s equation in polar coordinates
Coordinator
Dr. Yvonne Yaz
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