Office: Carver 411

Telephone: 294-7671

E-mail: swillson@iastate.edu

FAX: (515)-294-5454

The first class is Tuesday, January 13, 2015, and the last class is Thursday, April 30, 2015. There are no classes Spring Break (the week of March 16 - 20).

- three hour exams (approximately 50 points each),
- a comprehensive final exam (100 points)
- approximately 10 graded homework sets with total normalized to approximately 100 points
- a graded problem (lecture challenge) each day there is not an exam (2 points each for a total of approximately 54 points)

- Exam, Thursday, February 12.
- Exam, Thursday, March 12.
- Exam, Thursday, April 23.
- Final exam, the week of May 4-8.

- Complex numbers and the complex plane (1.1-1.5) (2 weeks)
- Complex functions and mappings (2.1-2.4) (2 weeks)
- Analytic functions (3.1-3.5) (2.5 weeks)
- Elementary functions (4.1-4.3, 4.5) (2 weeks)
- Integration in the complex plane (5.1-5.5) (3 weeks)
- Series and residues (6.1-6.6) (2.5 weeks)
- Conformal mapping (7.1-7.2) (1 week)

- Add, subtract, multiply, and divide complex numbers
- Represent points in the plane by complex numbers
- Represent complex numbers in polar form
- Find powers and roots of complex numbers
- Find sets of points in the complex plane solving simple equations

- Describe complex functions by their real and imaginary parts
- Compute images of simple sets under complex functions
- Draw parametric curves in the complex plane
- Visualize images of sets under linear mappings
- Visualize images of sets under power functions and roots
- Visualize inverse functions

- Understand limits in the complex plane
- Understand continuity in the complex plane
- Compute derivatives of complex functions
- Use the Cauchy-Riemann equations to test for analytic functions
- Recognize harmonic functions and find their harmonic conjugates

- Use the complex exponential function
- Use complex logarithm functions, especially the principal value
- Use complex powers
- Use complex trigonometric and hyperbolic functions
- Solve very simple Dirichlet problems for heat flow or electrical potential

- Understand the definition of line integrals (contour integrals) in the complex plane
- Evaluate contour integrals
- Find upper bounds for contour integrals
- Understand the Cauchy-Goursat theorem for closed contour integrals
- Use Cauchy's integral formulas to evaluate closed contour integrals
- Understand consequences of Cauchy's integral formulas

- Understand convergence of sequences and series in the complex plane
- Compute Taylor series in the complex plane
- Compute Laurent series about an isolated singularity
- Understand zeros and poles of complex functions
- Compute residues of a complex function at a pole
- Use Cauchy's Residue Theorem to compute closed contour integrals and related real improper integrals

- Understand the nature of conformal mappings
- Tell where a complex function is conformal
- Understand angle magnification at a critical point
- Use linear fractional transformations

Last updated January 13, 2015.