Overview

Discussion of heat flow, electromagnetic waves, elastic waves, and quantum-mechanical waves; applications of orthogonal functions to electromagnetic multipoles, angular momentum in quantum mechanics, and to normal modes on acoustic and electromagnetic systems. Applications of complex analysis to Green Function in quantum mechanics and electromagnetism. Application of Fourier series and transforms to resonant systems. Applications of partial differential equation techniques to equation of physics.

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.