## Math Methods of Applied Sciences II

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.

Prerequisites:
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