MTH 303, Complex Variables
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Course Information
Oct 14- Dec 6, 1996
MWF 11-11:50 a.m.
Final Exam on Monday, Dec 9, 1995, 2:00-5:00 p.m.
215 Calloway Hall
Wake Forest University
Instructor: Elmer K. Hayashi
- Text:
- E. B. Saff and A. D. Snider,
Fundamentals of Complex Analysis
for Mathematics, Science, and Engineering
1993, second edition,
Prentice Hall
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Syllabus
The course will cover most of Chapters 1-6 in the textbook. This is
a half-semester course beginning on October 14, 1996.
- Complex Numbers
- Analytic Functions
- Complex Integration
- Cauchy's Integral Theorem and Formula
- Taylor and Laurent Series
- Cauchy's Residue Theorem
- Evaluation of Real Integrals using the Residue Theorem
- Argument Principle and Rouche's Theorem
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Grading Policy
There will be two one-hour exams tentatively scheduled for November
1st and November 20th. The final exam is scheduled for Monday, December
9th from 2:00-5:00 p.m. Your semester grade will be determined by the number
of points earned out of 400 possible points. Each hour exam will be worth
100 points, the final exam will be worth 200 points. Homework problems
will be suggested on a regular basis. It is the student's responsibility
to do the associated reading, and learn how to solve the problems. Regular
attendance as well as diligent effort are essential for achieving success
in this course. This is not a spectator course; be an active participant.
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Assignments
Monday, Oct 14, 1996
Representations of Complex Numbers.
Read sections 1.1 and 1.2.
Do page 5: 5-13, 17, 20; page 11: 4,10,12.
Wednesday, Oct 16, 1996
Polar Representation, Powers and Roots.
Read sections 1.3 and 1.4.
Do page 11: 7a-d,h-j; page 20: 7; page 31: 4-6.
Friday, Oct 18,1996
Fall Holiday
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Monday, Oct 21, 1996
Euler's equation, the Complex Exponential Function.
Read sections 2.1 and 2.2.
Do page 44-45: 1, 2, 3, 5; page 50: 19.
Wednesday, Oct 23, 1996
Analytic Functions, Cauchy-Riemann Equations, Exponential Functions.
Read sections 2.3, 2.4, and 3.1.
Do pages 56-57: 7, 9; page 62: 5.
Friday, Oct 25, 1996
Trigonometric, Hyperbolic, and Logarithmic Functions.
Read sections 3.1 and 3.2.
Do page 80: 9, 17; page 86-87: 1, 5.
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Monday, Oct 28, 1996
Complex Powers and Inverse Trigonometric Functions.
Read section 3.3.
Do page 93: 1, 3, 11
Wednesday, Oct 30, 1996
Contours and Contour Integrals.
Read sections 4.1 and 4.2.
Do page 113: 1a-c, 3; pages 122-123: 5, 14a.
Friday, Nov 1, 1996
Hour Exam on Chapters 1-3.
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Monday, Nov 4, 1996
Independence of Path, Cauchy's Integral Theorem.
Read section 4.3 and 4.4.
Do pages 128-129: 1a-g; page 150: 9,10.
Wednesday, Nov 6, 1996
Cauchy's Integral Formula. Read section 4.5. Do page 160: 3,4.
Friday, Nov 8, 1996
Taylor Series.
Read sections 5.1 and 5.2.
Do pages 195-196: 1adef, 5, 11a-c.
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Monday, Nov 11, 1996
Laurent Series.
Read sections 5.3 and 5.5.
Do page 203: 6, 8; page 218: 4-6.
Wednesday, Nov 13, 1996
Zeros and Singularities.
Read section 5.6.
Do pages 225-226: 1, 2
Friday, Nov 15, 1996
Cauchy's Residue Theorem.
Read section 6.1.
Do page 251: 1, 3. .
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Monday, Nov 18, 1996
Trig Integrals over [0,2pi].
Read section 6,1.
Do page 255: 1-4
Wednesday, Nov 20, 1996
Hour Exam on Chapters 4-5.
Friday, Nov 22, 1996
Improper Integrals, Cauchy Principal Value.
Read section 6.2.
Do page 262: 1-4.
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Monday, Nov 25, 1996
Improper Integrals, Cauchy Principal Value.
Wednesday, Nov 27, 1996
Thanksgiving Holiday
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Monday, Dec 2, 1996
Argument Principle and Rouche's Theorem.
Read section 6.3.
Do page 297: 6-9, 22.
Wednesday, Dec 4, 1996
Summary and Review
Friday, Dec 6, 1996
Summary and Review
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Monday, Dec 9, 1996
Final Exam, 2:00-5:00 p.m., CA 112.
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Created 8/20/96
ekh@mthcsc.wfu.edu