# Classes

#### Spring 2021 Teaching:

**Math 221 - Honors Applied Differential Equations**

#### Previously Taught:

**Math 121 - Calculus I**

**Course Description:**

This is a first course in differentiation and integration of algebraic and
trigonometric functions with applications to physical sciences and engineering.

__Prerequisites:__ Math 121 is open only for two credits to students with credit in Math 115.
Students in Math 121 are expected to have completed one of the following: Math 103 or
Math 104; three years of college preparatory mathematics, including trigonometry, and a
score of 28 or more on Enhanced ACT Mathematics; or a qualifying score on the mathematics placement test.

**Math 221 - Honors Applied Differential Equations**

**Course Description:**

Topics include first and second order ordinary differential equations and models, higher order equations, Laplace transforms, and systems of linear equations.

__Prerequisites:__ Math 126 or Math 146 with grade of C- or higher, and invitation from the Department of Mathematics. It is helpful, but not required, to take Math 290 or 291 concurrently. Not open to students with credit in Math 320 or Math 220.

**Math 647 - Applied Partial Differential Equations**

**Course Description:**

Boundary value problems; topics on partial differentiation; theory of characteristic curves; partial differential equations of mathematical physics.

__Prerequisite:__ Math 127 or Math 147 and Math 220 or Math 221 or Math 320.

**Math 648 - Calculus of Variations and Integral Equations**

**Course Description:**

Topics in the calculus of variations, integral equations and applications.

__Prerequisite:__ Math 220 or Math 221 and Math 290 or Math 320.

**Math 765 - Mathematical Analysis I**

**Course Description:**

Math 765 and Math 766 are theoretical courses on the fundamental concepts of analysis and the methods of proof. These two courses include the concept of a real number; limits, continuity, and uniform convergence; and derivatives and integrals of functions of one and of several real variables.

__Prerequisite:__ Math 290, or equivalent.

**Math 800 - Complex Analysis I**

**Course Description:**

Complex numbers and functions; complex differential operators;
Cauchy-Riemann equations; analytic and harmonic functions; Cauchy formula; Power series representation of analytic functions; Liouville's theorem;
zeros of analytic functions; Laurent series and meromorphic functions; argument principle, the residue theorem and applications; counting zeros and
poles of meromorphic functions; maximum modulus principle and Schwartz
lemma; Riemann mapping theorem.

__Prerequisite:__ Math 766 or concurrently with Math 766.

**Math 850 - Differential Equations and Dynamical Systems**

**Course Description:**

Discrete and differentiable dynamical systems with an emphasis on the qualitative theory. Topics to be covered include review of linear systems, existence and uniqueness theorems, flows and discrete dynamical systems, linearization (Hartman-Grobman theorem), stable and unstable manifolds, Poincare sections, normal forms, Hamiltonian systems, and an introduction to bifurcation theory and chaos.

__Prerequisite:__ Math 320 and Math 766, or permission of instructor.

**Math 950 - Partial Differential Equations**

**Course Description:**

Introduction; equations of mathematical physics; classification of linear equations and systems. Existence and uniqueness problems for elliptic, parabolic, and hyperbolic equations. Eigenvalue problems for elliptic operators; numerical methods.

__Prerequisite:__ Math 766.