Math Methods of Applied Sciences I

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.

Prerequisites: 

MATH 3406 or MATH 4305, and MATH 2552

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