Spring
2010 Course Syllabus: Math 332-H02
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Course Title: |
Introduction
to Functions of a Complex Variable |
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Textbook: |
Fundamentals
of Complex Analysis, by E.B. Saff
and A.D. Snider, 3rd Edition, Pearson Education, 2003, ISBN:
0-13-907874-6. |
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Prerequisites: |
Math 222
with a grade of C or better. |
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Website: |
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Course
Outline |
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Date |
Lecture |
Sections |
Topic |
Assignments |
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Jan 20 |
1 |
1.1-1.2 |
Algebra
of Complex Numbers; Point/Vector Representation |
pp. 4,
12 |
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Jan 22 |
2 |
1.3-1.4 |
Polar Representation; Complex
Exponential |
pp. 22, 31 |
|
Jan 27 |
3 |
1.5 |
Powers and Roots |
p. 37 |
|
Jan 29 |
4 |
1.6-1.7 |
Planar
Sets; Stereographic Projection |
pp. 43,
50 |
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Feb 3 |
5 |
2.1-2.2 |
Functions
of Complex Variable; Limits and Continuity |
pp. 56,
63 |
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Feb 5 |
6 |
2.3-2.4 |
Analyticity;
The Cauchy-Riemann Equations |
pp. 70,
77 |
|
Feb 10 |
7 |
2.5-2.6 |
Harmonic
Functions; Steady-State Temperature |
p. 84 |
|
Feb 12 |
8 |
3.1-3.2 |
Polynomials and Rational
Functions; Exponential Function |
p. 108 |
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Feb 17 |
9 |
3.2-3.3 |
Trigonometric and Hyperbolic
Functions; Logarithm |
pp. 115,
123 |
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Feb 19 |
10 |
3.4 |
Washers
Wedges Walls |
p. 129 |
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Feb 24 |
11 |
3.5 |
Complex
Powers; Inverse Trig |
p. 136 |
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Feb 26 |
12 |
4.1-4.2 |
Contours
and Contour Integrals |
pp. 159,
170 |
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Mar 3 |
13 |
4.3-4.4 |
Independence
of Path and Cauchy’s Integral Theorem |
pp. 178,
199 |
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Mar 5 |
14 |
4.5 |
Cauchy’s Integral Formula and its
Consequences |
p. 212 |
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Mar 10 |
15 |
Review for the
Midterm Exam |
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Mar 12 |
16 |
Midterm Exam |
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Mar 24 |
17 |
4.6 |
Bounds for Analytic Functions |
p. 219 |
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Mar 26 |
18 |
5.1-5.2 |
Sequences and Series; Taylor
Series |
pp. 239,
249 |
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Mar 31 |
19 |
5.3 |
Power Series |
p. 258 |
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Apr 7 |
20 |
5.5 |
Laurent Series |
p. 276 |
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Apr 9 |
21 |
5.6-5.7 |
Zeros
and Singularities; The Point at Infinity |
pp. 285,
290 |
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Apr 14 |
22 |
6.1 |
Residue Theorem |
p. 313 |
|
Apr 16 |
23 |
6.2 |
Trigonometric
Integrals over [0, 2π] |
p. 317 |
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Apr 21 |
24 |
6.3 |
Improper Integrals over (-∞ ; ∞) |
p. 325 |
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Apr 23 |
25 |
6.4 |
Improper Integrals involving
Trigonometric Functions |
p. 336 |
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Apr 28 |
26 |
6.5 |
Indented
Contours |
p. 344 |
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Apr 30 |
27 |
6.6 |
Integrals
Involving Multiple-Valued Functions |
p. 354 |
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May 4 |
28 |
Review for
Final Exam |
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IMPORTANT
DATES |
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First Day of Semester |
January 19, 2010 |
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Midterm Exam |
March 12, 2010 |
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Last Day to Withdraw |
March 29, 2010 |
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Last Day of Classes |
May 4, 2010 (Friday Schedule) |
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Final Exam Period |
May 6 – 12, 2010 |
Grading Policy
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Assignment Weighting |
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Tentative Grading Scale |
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Homework & Quizzes |
28 % |
A |
87 -- 100 |
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Attendance |
4% |
B+ |
81 -- 86 |
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Common Exam I |
30 % |
B |
74 -- 80 |
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Final Exam |
38 % |
C+ |
67 – 73 |
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C |
60 – 66 |
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D |
54 -- 59 |
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F |
0 -- 53 |
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Course Policies
Homework problem sets will
be assigned after each class based on the material covered, and will be due the
following class. Late homework will not be accepted. A short quiz based on the
homework problems will be given once each week
Important Departmental and
University Policies
Prepared by Prof. Victor Matveev, December 23, 2008