MA 387 - Partial Differential Equations

• 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.

• Infinite series
• Linear differential equations

• What is a partial differential equation and interpreting a given partial differential equation (2 classes)
• Periodic functions (1 class)
• Fourier series (2 classes)
• Fourier series of functions with arbitrary periods (2 classes)
• Half-range expansions: Fourier sine and cosine series ( 1 class)
• Complex form of Fourier series (1 class)
• Forced oscillations (1 class)
• Modeling: Vibrating string and one-dimensional wave equation (1 class)
• Solution of one-dimensional wave equation using method of separation of variables (2 classes)
• D’Lambert’s method of solving one-dimensional wave equation (1 class)
• Solution of one-dimensional heat equation using method of separation of variables (2 classes)
• Heat conduction in bars: Varying the boundary conditions (1 class)
• The two-dimensional wave and two-dimensional heat equations (1 class)
• Laplace’s equation in rectangular coordinates (2 classes)
• The Poisson’s Equation: The method of eigenfunction expansion (1 class)
• Neumann and Robin conditions (2 classes)
• Laplacian in various coordinate systems (1 class)
• Two-dimensional wave equation in polar coordinates: Vibration of a circular membrane (1 class)
• Two-dimensional Laplace’s equation in polar coordinates (1 class)
• Review for exams and exams (4 classes)