This is a list of all courses offered by the Math Department.  Not all courses are offered each year.  What is provided is a general description of the courses and the prerequisites.  The actual content may vary.

<- Return to Course List

Description

This course is an introduction to complex variables accessible to juniors and seniors in engineering, physics and mathematics. The algebra of complex numbers, analytic functions, Cauchy Integral Formula, theory of residues and application to the evaluation of real integrals, conformal mapping and applications to physical problems.

Prerequisites

MATH 241 or MATH 340

Topics

Complex Numbers

Complex arithmetic
Geometric representation
Polar form
Powers
Roots
Elementary plane topology

Analytic Functions

Continuity
Differentiability
Cauchy-Riemann equations
Analytic functions
Harmonic functions and harmonic conjugates

Contour Integrals

Upper bound estimates
Anti-derivatives
Cauchy-Goursat theorem
Cauchy integral formulas
Liouville's theorem
Fundamental theorem of algebra
Maximum modulus theorem

Elementary functions

Exponential function
Logarithmic function
Trigonometric functions
Hyperbolic functions
The functions zc and cz

Infinite sequences and series

Sequences and series of constants
Sequence and series of functions
Geometric series
Power series and Taylor series
Laurent series

Residues

Isolated singularities
Resides and the residue theorem
Evaluation of real integrals by residues

Boundary value problems and applications

Conformal mappings
Mapping properties of some elementary functions
Application to the steady state heat flow and electrostatic potential