Overview

Included in degrees & certificates

• 124

Prerequisites

• Basic physics
• multivariable calculus
• vector analysis
• Fourier series
• complex numbers
• and ordinary differential equations

Learning Outcomes

Upon successful completion of this course the student will:

·       Understand and become efficient with the application of Fourier series with all functions satisfying Dirichlet conditions.

·       Use Fourier and Laplace transforms to solve second order differential equations.

·       Solve both first order homogeneous and inhomogeneous differential equations.

·       Understand the difference between linear and non-linear differential equations.

·       Solve both homogeneous and nonhomogeneous second order differential equations including series solutions.

·       Understand Sturm Liouville theory and the concept of determining eigenfunctions and eigenvalues based on boundary conditions.

·       Solve Bessel and Legendre differential equations including the application of generating functions to both solve and apply to physical problems.

·       Solve partial differential equations in cartesian, cylindrical, and spherical coordinates.

·       Apply the method of “separation of variables” to solve partial differential equations for physical systems including time and up three coordinate variables.