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Department:

MATH

Course Number:

6701

Hours - Lecture:

3

Hours - Lab:

0

Hours - Recitation:

0

Hours - Total Credit:

3

Typical Scheduling:

Every summer and fall semesters

Review of linear algebra and ordinary differential equations, brief introduction to functions of a complex variable.

Course Text:

No text

Topic Outline:

- Linear Algebra
- Finite dimensional vector spaces, norms and inner products
- Linear independence, bases, orthogonality
- Linear operators and their matrix representations
- Eigenvalues and eigenvectors of symmetric and nonsymmetric matrices

- Ordinary Differential Equations
- Review of calculus based integration methods for differential equations
- Existence and uniqueness of solutions of initial value problems for first order equations
- Fundamental solutions and particular integrals for linear equations
- Application to boundary value problems and elementary regular and singular perturbation problems

- Introduction to Functions of a Complex Variable
- Complex numbers, analytic functions, Cauchy's integral theorem
- Taylor and Laurent expansions, residue theorem, introduction to conformal transformations