Introduction to Complex Variables
(MATH 407, Department page)
Offered Fall only
FALL 2009
Time and Place: TR 5:00-6:15 pm, Room 337 Flarsheim Hall
Professor: Richard Delaware
Office Hours: See Current Semester Office Hours
Office: Room 306 A, Manheim Hall
Mailbox: Room 206, Haag Hall, Dept. of Mathematics and Statistics
Phone: 816.235.2850
Email: delawarer@umkc.edu
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Dated Announcements (Most recent at the top)
-
- T 6 October 2009
- Homework 3: DUE T 13 Oct. (7 exercises)
3.2, p.115: 16, 18a, 22.
3.3, p.123: 6.
3.5, p.136: 8.
4.1, p.159: 8, 10ab.
- R 10 September 2009
- Homework 2: DUE R 17 Sept. (11 exercises)
1.6, p.42: 10, 18.
2.1, p.56: 4abc(Read the note before the exercises), 10abcd(Show all graphical steps, show each component map).
2.2, p.63: 4, 22.
2.3, p.70: 4abc, 12[Relabel P(z) as P_n(z)], 16.
2.4, p.77: 6(ignore the hint?), 12(Write f(z) = u + iv).
- T 1 September 2009
- See Weekly Schedule - Exam 1 and 2 date changes
- R 27 August 2009
- Homework 1: DUE R 3 Sept. (12 exercises)
1.1, p.4: 4, 10, 20abcd.
1.2, p.12: 4abc, 8, 16.
1.3, p.22: 12abcd, 20.
1.4, p.31: 4abc, 18ab, 22.
1.5, p.37: 6b.
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Syllabus, Texts, Grading
PREREQUISITES:
TEXTS:
- Required: FUNDAMENTALS OF COMPLEX ANALYSIS, with Applications to Engineering and Science, by E. B. Saff and A. D. Snider.
- In the text, we will cover most of Chapters 1-6, and part of 7.
EXAMS:
- There will be three 75 min. Exams (100 points each) during the semester, each given a letter grade for your convenience.
- There will be some announced 25 min. Quizzes.
- The FINAL EXAM (150 points) will be held in our usual classroom, 3:30 - 5:30 pm, on Friday Dec. 18, 2009.
HOMEWORK:
- A list of suggested homework problems will be posted here. Selected problems will be collected and graded.
- For homework use only one side of standard 8½ x 11 paper. When due, put it on my desk at the start of class.
- Late assignments of any kind are NOT accepted, except by prior arrangement.
GRADES:
- 70% -- 3 Exams (100 pts each) and Final Exam (150 pts)
- 30% -- Homework and Quizzes
- I use grading software to provide grade reports. At the end of the semester before the Final Exam is recorded, I will drop your "most damaging" score. However, the Final Exam cannot be dropped.
NOTES:
- You will be proving some theorems in this course. So, you must discuss proofs with your classmates and me if you are to do well.
- You will not be able to do every suggested problem. But to succeed, you must try a good number.
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Complex Function Graphers, Internet Sites
- The following possibly useful programs are FREE (!) from Peanut Software:
- Winplot: A general-purpose plotting utility, which can draw (and animate) curves and surfaces presented in a variety of formats.
- Winfeed: A fractal exploration program. It allows the user to explore functional iteration, including Mandelbrot and Julia sets, ferns and
snowflakes, web and bifurcation diagrams, and more.
- Graphics for Complex Analysis,
Douglas N. Arnold, Professor of Mathematics at the University of Minnesota
Director of the Institute for Mathematics and its Applications in Minneapolis
http://www.ima.umn.edu/~arnold/complex.html
- Complex Function Grapher
Andy Bennett, Professor of Mathematics, Kansas State University
http://www.math.ksu.edu/~bennett/jomacg/
- Visualizing Complex-valued Functions in the Plane
Frank A. Farris, Professor of Mathematics, Santa Clara University
http://www.maa.org/pubs/amm_complements/complex.html
- f(z), the Complex Variables program
http://www.lascauxsoftware.com/
- Nice Mobius Transformation Video
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Suggested Homework Problems [Subject to change]
Chapter 1
- 1.1, p.4: 3-25, 27, 28(Classic); Grad. Students: 30.
- 1.2, p.12: 3-14, 16, 17; Grad. Students: 20, 21.
- 1.3, p.22: 1, 3-5, 7-13, 15, 17-20, 22, 23, 25, 26.
- 1.4, p.31: 1-5, 7-13, 15-18, 22.
- 1.5, p.37: 1-16; Grad. Students: 17, 18.
- 1.6, p.42: 1-22; Grad. Students: 23.
- 1.7, p.50: 1, 5.
Chapter 2
- 2.1, p.56: 2-11; Grad. Students: 13.
- 2.2, p.63: 3-7, 9, 11-15, 17, 20-22, 25; Grad. Students: 23.
- 2.3, p.70: 1-4, 7, 9, 11-13, 16; Grad. Students: 8, 14.
- 2.4, p.77: 1-2, 4-15; Grad. Students: 16.
- 2.5, p.84: 1, 3-7, 11, 12, 14, 16; Grad. Students: 20, 21.
- 2.6, SKIP
- 2.7, SKIP
Chapter 3
- 3.1, p.108: 1-7, 9, 11-19; Grad. Students: 20, 21.
- 3.2, p.115: 1-7, 9-11, 14-23.
- 3.3, p.123: 1-14, 17, 18.
- 3.4, p.129: 1-5.
- 3.5, p.136: 1-8, 10, 11, 15, 16.
- 3.6, SKIP
Chapter 4
- 4.1, p.159: 1, 2, 5-11, 14.
- 4.2, p.170: 3, 6, 8-18.
- 4.3, p.178: 1-11.
- 4.4, p.199: 1-4, 9, 10, 12-19.
- 4.5, p.212: 1-10; Grad. Students: 16, 17.
- 4.6, p.219: 1-11, 13, 15-18.
- 4.7, SKIP
Chapter 5
- 5.1, p.239: 1-4, 7, 10-12, 17-21.
- 5.2, p.249: 1adef, 2adef, 4-8, 13, 15, 16.
- 5.3, p.258: 2, 3, 5, 6, 8, 9, 11, 12, 15, 16, 18.
- 5.4, SKIP
- 5.5, p.276: 1-7, 9, 11-13.
- 5.6, p.285: 1-3, 5-8, 10-13, 15-18.
- 5.7, p.290: 1-7.
- 5.8, SKIP
Chapter 6
- 6.1, p.313: 1-7.
- 6.2, p.317: 1-7.
Chapter 7
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Exam Outlines [Posted here as available]
Exam 1 (Ch. 1-3.2)
- Possibilities [Subject to change]
Exam 1 Outline
Exam 2 (Ch. 3.3-4.2)
- Possibilities [Subject to change]
Exam 2 Outline
Exam 3 (Ch. 4.3-4.6, Ch. 5)
- Possibilities [Subject to change]
Final Exam (Chapters 1 - 5, 6.1-6.2, 7.3, with some omissions) - Possibilities [Subject to change]
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