MTH 4150 - Partial Differential Equations

3 lecture hours 0 lab hours 3 credits

Course Description
This course introduces the quantitative and qualitative analysis of partial differential equations. Topics include classification of partial differential equations, separation of variables, eigenvalue problems, Fourier series, the wave equation, the heat equation, and Laplace equation. Models and applications such as heat diffusion and vibrating strings are discussed. Mathematical software is used.
Prereq: MTH 2130, MTH 2140 (quarter system prereq: MA 235, MA 2323)
Note: None
This course meets the following Raider Core CLO Requirement: Think Critically

Course Learning Outcomes
Upon successful completion of this course, the student will be able to:

Classify partial differential equations as linear or nonlinear, homogeneous or nonhomogeneous, and determine their order
Determine if given functions are solutions of a partial differential equation
Determine if an initial-value problem or initial-boundary-value problem is ill-posed
Use separation of variables to separate a partial differential equation into a system of ordinary differential equations and find all product solutions
Find all eigenvalues and associated eigenfunctions for a given system of ordinary differential equations
Model an applied situation with an appropriate PDE with boundary and initial conditions
Determine the coefficients of the Fourier series for a piecewise smooth periodic function
Evaluate the Fourier series at points for continuous and noncontinuous functions
Use even and odd periodic extensions to determine the cosine and sine Fourier series of a nonperiodic function
Solve the one-dimensional heat and wave equations on finite domains with initial and boundary conditions
Solve the two-dimensional Laplace's equation on finite domains with boundary conditions
Use the method of characteristics to solve first-order linear partial differential equations
Use software to visualize, interpret, and find solutions to partial differential equations

Prerequisites by Topic

Infinite series
Multivariable calculus
Ordinary differential equations

Course Topics

Interpreting partial differential equations
Interpreting initial and boundary conditions
Classifying partial differential equations
The principle of superposition
Eigenvalue problems
Periodic functions
Fourier series for periodic and nonperiodic functions
Finding solutions of the heat equation by separation of variables
Modeling and analyzing one-dimensional diffusion
Finding solutions of the wave equation by separation of variables
Modeling and analyzing vibrating string
Finding solutions of Laplace's equation by separation of variables
Characteristic curves of partial differential equations
Other topics at instructor discretion: characteristics for general second-order linear partial differential equations, Laplace and Fourier transforms, special functions, Strum-Liouville theory, partial differential equations in higher dimension, Green's functions, or numerical methods

Coordinator
Dr. Niles Armstrong

Add to Portfolio.

Close Window