Week 1
- Complex Arithmetic,
Chapter 1
Week 2
- Analytic Functions,
Sections 2.1 - 2.3
- The Cauchy-Riemann Equations, Harmonic Functions,
Sections 2.4, 2.5
Week 3
- Elementary Functions: Exponential, Trigonometric, and Hyperbolic
Functions,
Sections 3.1, 3.2
- The Logarithm, Elementary Harmonic Functions, Complex Powers,
Inverse Trigonometric and Hyperbolic Functions,
Sections 3.3 - 3.5
Week 4
- Contours in the Complex Plane,
Section 4.1
- Contour Integrals, Independence of Path,
Sections 4.2, 4.3
Week 5
- Cauchy's Theorem, Cauchy's Integral Formula,
Sections 4.4b, 4.5
- Consequences of Cauchy's Integral Formula,
Section 4.5
- Takehome Midterm
Week 6
- Bounds for Analytic Functions,
Section 4.6
- Sequences and Series, Taylor Series
Sections 5.1, 5.2
Week 7
- Taylor Series, Power Series,
Sections 5.2, 5.3
- Power Series, Laurent Series,
Sections 5.3, 5.5
Week 8
- Fall Break (Monday and Tuesday)
- Laurent Series, Zeroes and Singularities,
Sections 5.5, 5.6
Week 9
- Zeroes and Singularities, The Residue Theorem,
Sections 5.6, 6.1
- Residues, Certain Real Improper Integrals,
Sections 6.1, 6.3
Week 10
- Real Improper Integrals, Trigonometic Integrals over [0, 2Pi],
Sections 6.3, 6.1
- Trigonometric Integrals over (-infinity, infinity), Indented Contours,
Sections 6.4, 6.5
- Takehome Midterm
Week 11
- Integration of Multiple-Valued Functions, Conformal Mapping,
Sections 6.6, 7.1
- Conformal Mapping, Laplace's Equation,
Sections 7.1, 7.2
Week 12
- Moebius Transformations,
Sections 7.3, 7.4
- The Schwarz-Christoffel Transformation,
Section 7.5
Week 13
- 2-D Fluid Flow,
Sections 7.6, 7.7
- 2-D Fluid Flow, Electrostatics, Heat Flow,
Sections 7.6, 7.7
- Thanksgiving (Thursday and Friday)
Week 14
- The Fourier Transform,
Section 8.2
- The Fourier Transform: Applications to PDEs,
Section 8.2
Week 15
- The Laplace Transform,
Section 8.3
- The Laplace Transform: Applications to ODEs,
Section 8.3
- Takehome Final
Last modified August 2003, by ward at hmc.edu
|