Welcome to Math 417! This course is an introduction to Complex Analysis. Complex Analysis is one of the great subjects of modern mathematics and an invaluable tool in physics and engineering. In this course we will explore the basic properties of complex analytic functions and derivatives and integrals of complex valued functions.
Lecturer: David Cabrera, dcabrera@uic.edu
Office hours: by appointment in SEO 619
Classroom: LH 210
Textbook: Complex Analysis by J. Bak and D. J. Newman, 1997, Second Edition. Another textbook that is recommended is Complex Variables and Applications by J. W. Brown and R. V. Churchill, 2004, Seventh Edition.
Prerequisites: A grade of C or better in Math 210 (multivariable calculus).
Homework: Homework will be due every other lecture starting on Friday, June 18. Late homework will not be accepted without prior permission from the instructor. You are allowed to discuss problems with each other. However, the write-up must be your own and should reflect your own understanding of the problem.
Grading: There will be a midterm exam and a final exam. The homework, midterm exam, and final exam will each count equally toward your final grade.
Lecture Schedule:
| Week | Date | Topics | Problems | HW, Due Date |
| 1 | Mon 6/14 | Complex Numbers (1.1-1.2) Exponential Form |
HW 1 Sol |
Fri 6/18 |
| Wed 6/16 | Roots Functions of a Complex Variable |
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| Fri 6/18 | Limits | HW 2 Sol |
Fri 6/25 | |
| 2 | Mon 6/21 | Derivative (2.1) Cauchy-Riemann Eqns. (2.1) |
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| Wed 6/23 | Analytic Functions (3.1) Harmonic Functions |
HW 3 Sol |
Wed 6/30 | |
| Fri 6/25 | Exponentials (3.2) Logarithms |
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| 3 | Mon 6/28 | Trigonometric Functions (3.2) | HW 4 Sol |
Wed 7/7 |
| Wed 6/30 | Inverse Trig. Functions Contour Integrals (4.1) |
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| Fri 7/2 | Contour Integrals (4.1), ML-Bound Antiderivatives |
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| 4 | Mon 7/5 | No Class | ||
| Wed 7/7 | Cauchy-Goursat Theorem (4.2) Path Independence, Path Deformation |
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| Fri 7/9 | Midterm Exam -- Sol | Summer 08 Midterm Sol |
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| 5 | Mon 7/12 | Cauchy Integral Formula (5.1) | HW 5 Sol |
Fri 7/16 |
| Wed 7/14 | Sequences, Series (6.1) Taylor Series |
HW 6 Sol |
Wed 7/21 | |
| Fri 7/16 | Laurent Series (9.2) | |||
| 6 | Mon 7/19 | Classification of Singularities (9.1) Residues (10.1) |
HW 7 Sol |
Wed 7/28 |
| Wed 7/21 | Residues of Poles Improper Integrals (11.1) |
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| Fri 7/23 | Improper Integrals | |||
| 7 | Mon 7/26 | Improper Integrals | HW 8 Sol |
Wed 8/4 |
| Wed 7/28 | Trigonometric Integrals Inverse Laplace Transform |
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| Fri 7/30 | Argument Principle (10.2) Rouche's Theorem |
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| 7 | Mon 8/2 | Mobius Transformations (13.2) | ||
| Wed 8/4 | Mobius Transformations Review |
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| Fri 8/6 | Final Exam | Summer 08 Final Partial Sol More Practice Problems |