Math 313 - Complex Variables, Fall 2016

Time: Tue & Thur 11 a.m. - 12:15 p.m., SMLC 356, Syllabus
Instructor Info: Anna Skripka, skripka [at] math [dot] unm [dot] edu
 
Prerequisite: Math 264 (required), other 300- or 400-level math courses (recommended)
Sample Math 313 goals (slight deviation is possible)
 
Textbook: Fundamentals of complex analysis with applications, by E.B. Saff and A.D. Snider, Prentice Hall, 3rd ed., 2003, ISBN 0139078746;
Extra examples and exercises: Schaum's outlines. Complex variables, by M. Spiegel, S. Lipschutz, J. Schiller, D. Spellman, McGraw-Hill, 2nd ed., 2009, ISBN 0071615695
 
Solutions and grades are to be posted on UNM Learn.
 
Video lectures by one of the textbook authors.
 
Assignments will be graded only if they are submitted by the deadline. A student is allowed to submit homework by email in a SINGLE PDF file. All assigned problems are to be submitted, but only selected problems will be graded. To help the grader, please write your solutions neatly and clearly and staple the sheets. Grades will depend on both clarity and correctness.
In addition to the specified topics, quizzes may also contain questions on old as well as prerequisite material.
 
Attendance: Students with excessive absences will be dropped from the course according to the university attendance rules. This also applies to students in the wait list.
 
Want a regrade? Check the solution key and state precisely in your claim which step of your solution seems to have been overlooked by the grader. This should be done within a week since the assignments were distributed in class.
 
Office hours in SMLC 212: Tue and Thur 10:25 - 10:50 a.m., 1 - 1:30 pm, and also by appointment
CAPS tutoring sessions: Tue 6 - 9 pm, Wed 12 - 2 pm.
 
Handouts: Analytic and harmonic functions,   Complex integration
 
TENTATIVE Schedule (will be updated at the end of each week)
Week
Important Dates
Sections
Topics
Homework
1
Aug 23 (Pretest), 25
1.1-1.3
(Schaum p. 9-32)
Complex numbers. Polar form.
section 1.1: #7,9,11,13-16,20,22-24; section 1.2: #4,7(except (f)), 9,10; section 1.3: #2,5,7,9,10,12,13
2
Aug 30, Sep 1 (Q 1 & HW 1 on 1.1-1.3)
1.4, 1.5
home reading: 1.6
Complex exponential. Roots. Planar sets.
section 1.4: #1,2,4,5,7-11,16,17; section 1.5: #4-8; section 1.6: #2-8
3
Sep 6, 8 (Q 2 & HW 2 on 1.4, 1.5, 1.6)
Drop with no grade: Sep 9
2.1, 2.2
(Schaum p. 62-67)
Functions of complex variables. Limits and continuity.
section 2.1: #1-5,6(a,b),7-9,11,13; section 2.2: #7,11,19-21,25
4
Sep 13, 15 (Q 3 & HW 3 on 2.1, 2.2)
2.3, 2.4,
home reading: 3.1
(Schaum p. 85-96)
Analytic functions. Cauchy-Riemann equations. Polynomials and rational functions.
section 2.3: #4,7,11,13,15; section 2.4: #1,3,5,7,8,10,11,13 (apply 10,12), 15; section 3.1: #1,3(a,b),7,11,13 (using (21) is not required)
5
Sep 20, 22 (Q 4 on 2.3, 2.4, 3.1)
2.5, 3.2, 3.3
Harmonic functions. Exponential, trigonometric, and logarithmic functions.
section 2.5: #1-4,7,16,18; section 3.2: #1,2,4,5(a,b,c,d),7,9(a,b,c,d),10,11,15,17-20; section 3.3: #1-6,9-15
Practice Test 1
6
Sep 27, 29 (Exam 1 on 1.1-3.3; HW 4 on 2.3-2.5, 3.1-3.3)
3.4
Application: boundary value problems.
section 3.4: #1*-6 (*there is a typo in the book answer)
7
Oct 4, 6
3.5, 4.1-4.3
Complex powers & inverse trigonometric functions. Complex integration.
section 3.5: #1-9*,11 (*instead of deriving (11), may derive -i(z^2-1)^(-1/2)); section 4.1: #1-5,7,8,10,11; section 4.2: #3,5-14; section 4.3: #1,2,4,5,7
8
Oct 11 (HW 5 on 3.4, 3.5, 4.1-4.3)
4.4
Cauchy's integral theorem.
section 4.4: #1,3,9-13,15-17
9
Oct 18, 20 (Q 5 on 3.4, 3.5, 4.1-4.3)
4.5, 4.6,
home reading: 5.1
(Schaum p. 184-186)
Cauchy's integral formula. Bounds for analytic functions. Review of series.
section 4.5: #1,3,4,5,7,8,11,14; section 4.6: #4,5,6,8,10,11,13,14; section 5.1: # 1(a,b,c),2(b,c),7,11,14(b,c),21
10
Oct 25, 27 (Q 6 & HW 6 on 4.4-4.6, 5.1)
5.2, 5.3, 5.5
(Schaum p. 188-190)
Power, Taylor, and Laurent Series.
section 5.2: #5(a,b,c,d,g),7,8,13,14; section 5.3: #4,5(a,b,c),6; section 5.5: #1-6,9
Practice Test 2
11
Nov 1, 3 (Exam 2 on 3.4-5.5; HW 7 on 5.2, 5.3, 5.5)
5.6
home reading: 5.7
Laurent Series. Classification of singularities.
section 5.6: #1(a,b,c,d,g),3,5; section 5.7: #1,3(b,c)
12
Nov 8, 10 (HW 8 on 5.6, 5.7)
Withdrawal deadline: Nov 11
6.7, 7.1, 7.2, 7.3
Argument principle and Rouche's theorem. Conformal mappings and their applications.
section 6.7: #1,3(see Theorem 3),6-9,13,18; section 7.1: #1; section 7.2: #3,5,10,11(a,c,d,e)
13
Nov 15, 17 (Q 7 on 5.6, 6.7, 7.1, 7.2; HW 9 on 6.7, 7.1, 7.2)
7.3, 7.4, 7.6
Möbius transformations and boundary value problems.
section 7.3: #2-9; section 7.4: #2,6,9; section 7.6: #1,2,3,6
14
Nov 22 (HW 10 on 7.3, 7.4, 7.6)
6.1, 6.2
(Schaum p. 214-226)
Residue theorem and its applications. Trigonometric integrals.
section 6.1: #3,7; section 6.2: #1,2&3(see Example 2),4,5
15
Nov 29, Dec 1 (Q 8 on 7.3, 7.4, 7.6, 6.1, 6.2)
6.3, 6.4, 6.5
Improper integrals. Indented contours.
section 6.3: #1,2,3(use Example 2 in 6.1),4-7; section 6.4: #4-9; section 6.5: #2-7
16
Dec 6 (HW 11 on 6.1-6.5), 8
6.6
Integrals involving multiple-valued functions. Review.
section 6.6: #1-4
Practice Test 3
17
Dec 13 (Tuesday), 12:30-2:30 p.m.: Final Exam