120A Hmwork

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.
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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]
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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.]
S12
: 1 -- 3                     [Regions in the plane]
S14
: 1 -- 3, 5, 6, 8         [Domains of functions and mapping properties of functions]
S18:  5, 10, 11              [Limits and continuity ]
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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.]
S26:
1a, 1c, 2a, 2b, 4                             [More examples of analytic functions]
S30: 2, 6                                                [Exponential function as an analytic function]
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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.

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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]
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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.]
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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]
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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]

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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!!
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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)]

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

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