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Department:

MATH

Course Number:

6702

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

0

Hours - Total Credit:

3

Typical Scheduling:

Every spring semester

Review of vector calculus and and its application to partial differential equations.

Course Text:

No text

Topic Outline:

- Multidimensional Calculus
- Curves and surfaces, gradients, divergence and curl
- Taylor expansions in IR3
- Divergence and Stokes theorem
- Classification of partial differential equations
- The concept of well-posed problems

- Potential Problems
- Derivation of Laplace's equation; Dirichlet and Neumann problems
- The maximum principle and uniqueness of solutions
- Green's identities and Green's functions for selected domains
- Connections to variational problems and complex variables

- Parabolic Problems
- Derivation of the heat equation in IR3; discussion of boundary and initial conditions; the maximum principle for the heat equation and uniqueness of solutions; fundamental solution for pure initial value problems; Duhamel's principle for inhomogeneous equations

- Hyperbolic Problems
- The concept of characteristics for a single first order equation
- Solution of initial value problems; the concept of a shock
- D'Alembert solution of the wave equation; Huyghen's principle and the solution of the wave equation in IR3