Mathematics and Computer Science at Western Carolina University

Revised: November 2006 (Julie Barnes)

The complex number system, limits, continuity, derivatives, transcendental, and multi-valued functions, and integration. Prerequisite Math 256.

To provide a knowledge of basic complex variables.
To develop students' computational, analytical, and interpretive skills for solving problems using complex functions.
To expose students to real-life applications of complex variables in a variety of fields.

Zill, Dennis and Shanahan, Patrick. A First Course in Complex Analysis with Applications, Jones and Bartlett, 2003.

Grading procedures and factors influencing course grade are left to the discretion of individual instructors, subject to general university policy.

Attendance policy is left to the discretion of individual instructors, subject to general university policy.

Chapter 1: Complex Numbers and the Complex Plane (7 days)
- Complex Numbers and Their Properties
- Complex Plane
- Polar Form of Complex Numbers
- Powers and Roots
- Sets of Points in the Complex Plane
Chapter 2: Complex Functions and Mappings (9 days)
- Complex Functions
- Complex Functions as Mappings
- Linear Mappings
- Special Power Functions
- Reciprocal Function
- Limits and Continuity
Chapter 3: Analytic Functions (6 Days)
- Differentiability and Analyticity
- Cauchy-Riemann Equations
- Harmonic Functions
Chapter 4: Elementary Functions (6 days)
- Exponential and Logarithmic Functions
- Complex Powers
- Trigonometric and Hyperbolic Functions
Chapter 5: Integration in the Complex Plane (7 days)
- Real Integrals
- Complex Integrals
- Cauchy-Goursat Theorem
- Independence of Path
- Cauchy's Integral Formulas and Their Consequences
Chapter 6: Series and Residues (6 days or as time allows)
- Sequences and Series
- Taylor Series
- Laurent Series
- Zeros and Poles
- Residues and Residue Theorem