120A Hmwork
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Please observe the following neatness guidelines for homework that you turn in to be graded; homework not conforming to these guidelines will not receive full credit and may not be graded at all.

  1. Use clean, white paper (preferably ruled) that is not torn from a spiral notebook.

  2. Write your name clearly on the front page of your completed assignment.

  3. Write clearly and legibly.

  4. Clearly number each solution and present them in numerical order.

bulletProblems are from Brown and Churchill, "Complex Variables and Applications,"  9th edition unless otherwise indicated.
If I write
S2:  3, 4, 10 : it means do problems 3, 4 and 10 at the end of Section 2 of the 9th ed. of the book.

horizontal rule

Homework #0: ("Due" Thursday, October 1.)

S2:  3, 4, 10          [Algebraic properties of C]
S3:  1                    [Basic arrithematic]
S5:  1ab, 3, 4, 5.    [Euclidean geometry and triangle inequality]

These problems on basic properties of complex numbers  will not be collected but they will be covered in sections.
This material will be covered on the tests.

Homework #1: (Due Thursday, October 1 in the drop box by 7:00PM.)

S6: 2, 8, 14                     [complex conjugation]
S9: 1, 4, 5cd, 6, 9, 10      [Polar form of complex numbers and properties.]
S11: 1, 2, 6, 7                 [roots of complex numbers]
S42: 2, 3, 4                    [complex functions of a real variable, differentiation and integration]

Homework #2:   (Due Thursday, October 8 in the drop box by 7:00PM)

Problems 6.1 and 6.2 in the following file: Taylor Exercises.pdf.  [Looking at e^z another way.]
: 1 -- 3                     [Regions in the plane]
: 1 -- 3, 5, 6, 8         [Domains of functions and mapping properties of functions]
S18:  5, 10, 11              [Limits and continuity ]

Homework #3:  (Due Thursday, October 15 in the drop box by 7:00PM.)

S20:  1, 2, 3, 4,  9 (Do not hand in #9.)    [Complex Differentiation]
S24: 1b, 1c, 3b                                       [Cauchy Riemann Equations.]
1a, 1c, 2a, 2b, 4                             [More examples of analytic functions]
S30: 2, 6                                                [Exponential function as an analytic function]

TEST #1:  Monday, October 19 in class : Covers material above.

Please bring a Blue Book to the test. Here is a Test 1 Study Guide.


Homework #4:   (Due Thursday, October 22 in the drop box by 7:00PM.)

S38: 2, 3, 7, 11, 15                                [Trig. functions and their properties]
S39: 1,  7a,b, 10, 15                              [Hyperbolic functions and their properties]  
S33: 1, 2c, 3, 8 [8 should read, find all z such that iπ/2 is in log(z).]    [Logarithms]

Homework #5:   (Due Thursday, October 29 in the drop box by 7:00PM.)

S34: 1, 5                                               [Logarithms continued.]
S36: 1, 2, 6, 8a                                      [Power functions]

S40: 1a, 1b, 4                                        [Inverse Trig. and Hyperbolic functions]
S43: 1                                                   [Contours and properties of integrals of t.]

Homework #6:  (Due Thursday, November 5 in the drop box by 7:00PM.)

S46: 1, 3, 6, 10                                    [Contour integrals.]
S47: 1, 2, 7                                          [Estimating contour integrals]
S49: 2, 4, 5                                          [Anti-derivatives and the fundamental theorem of calculus]
S53: 1a-c, 2, 3, 4                                 [The Cauchy - Goursat theorem]

Homework #7:  (Due Thursday, November 12 in the drop box by 7:00PM.)
Wednesday, November 11 is a holiday this year.

S57: 1a)-d), 3,  4, 7 10 (10 is not to be handed in.)   [Cauchy integral formula and its consequences]
S59: 4                                                                    [Maximum modulus principle]
S61: 2, 4, 6                                                            [Series of complex numbers]             


Test #2 is Monday, November 16 in class: Covers material above.

Second Midterm is Monday, November 16 at 10:00AM in class.
Please bring a Blue Book and your student ID to the test.  Here is a Study Guide: F15_Study_Guides.pdf
You are allowed a single one sided (of a standard 8.5''x11'' sheet of paper) "cheat" sheet.
Please see the correction in the last line of the study sheet!!

Homework #8: (Due Thursday,  November 19 in the drop box by 7:00PM.)

S65: 1-3, 4,  9, 10a.      [Maclaurin Series = Taylor Series centered at 0.]
S68:  1-3.                     [Laurent Series]
S72:  1-3.                     [
Manipulating Power Series (substitutions, differentiation, integration)]


Happy Thanksgiving Holiday, Thursday and Friday, November 26-27.

Homework #9: (Due Thursday, December 3 in the drop box by 7:00PM.)

S73:  1, 4, 5     [Multiplication and Division of Power Series]
S771, 2         [Computing Residues]

(For the remaining problems, use the residue theorem method from class.)

S86: 2, 4, 9      [Evaluating integrals Involving Rational Functions]                                       
S88: 4, 6 (do the integral with sin(x) replaced by e^(ix).)     [Evaluation integrals involving exponential / trig. functions.]

Also compute the following integral


where a>0 and b>0 and  a  is not equal to  b.


The following problems will not be collected!
S79:  1a-c        [Singular point classifications]
S811, 3         [Classifying poles]

Final Exam:  Friday, December 11, 2015 at 8:00am -11:00am in TBA.  Please bring a Blue Book. No calculators or books are allowed. You may have one 8.5 x 11 inch sheet of notes (one sided) if you like.  See Final_Review_Sheet.pdf for a study guide.