120A Hmwork
 This is a very tentative list and the later assignments will almost certainly change!  Please re-check this page before doing each homework assignment! 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. Use clean, white paper (preferably ruled) that is not torn from a spiral notebook. Write your name clearly on the front page of your completed assignment. Write clearly and legibly. Clearly number each solution and present them in numerical order. Problems 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.

Homework #0: ("Due" Friday, January 12)

S2:  3, 4, 10          [Algebraic properties of C]
S3:  1                    [Basic arithmetic]
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 Friday, January 19 in the drop box by 9:00PM.)

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 Friday, January 26 in the drop box by 9:00PM)

Problems 6.1 and 6.2 in the following file: Taylor Exercises.pdf.  [Looking at e^z another way.]
S43: 1                           [Change of variables in complex integrals.]
S12
: 1 -- 3                     [Regions in the plane]
S14
: 1 -- 3                     [Domains of functions]
S18:  5, 9, 10, 11           [Limits and continuity ]
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TEST #1:  Wednesday January 31 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 #3:  (Due Friday, February 2 in the drop box by 9:00PM.)

S14:  5, 6, 8                                            [mapping properties of functions]
S20:  1, 2, 3, 4,  9 (Do not hand in #9.)    [Complex Differentiation]

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Homework #4:  (Due Friday, February 9 in the drop box by 9:00PM.)

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]
S38: 2, 3, 7, 11, 15                                [Trig. functions and their properties]
S39: 1,  7a,b, 10, 15                              [Hyperbolic functions and their properties]

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Homework #5:   (Due Friday, February 16 in the drop box by 9:00PM.)

S33: 1, 2c, 3, 8*                                    [Logarithms]
S34: 1, 5                                               [Logarithms continued.]
S36: 1, 2, 6, 8a                                      [Power functions]

S40: 1a, 1b, 4                                        [Inverse Trig. and Hyperbolic functions]

*S33 #8 should have been written as follows. Find all z such that iπ/2 is in log(z).

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Homework #6:  (Due Friday, February 23 in the drop box by 9:00PM.)

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] Moved to next week's assignment.

* Look at S53 #4 but do not hand in!
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TEST #2:  Wednesday February 28 in class.  Covers material above.
Please bring a Blue Book and your student ID to the test.  Here is a Study Guide: Test2_Study_Guide.pdf
You are allowed a single one sided (of a standard 8.5''x11'' sheet of paper) "cheat" sheet.
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Homework #7:  (Due Friday, March 2 in the drop box by 9:00PM.)
S53: 1a-c, 2, 3, 4*                                 [The Cauchy - Goursat theorem]
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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Homework #8: (Due Friday,  March 9 in the drop box by 9:00PM.)

1. Let 0<a<b<oo. Evaluate* the following integral

*Hint: use the same sort of method done in class to compute Fourier transform of 1/(1+x^2).

Also do the following problems from the book.

S61: 2, 4, 6                   [Series of complex numbers]
S65: 1-3, 4,  9, 10a.      [Maclaurin Series = Taylor Series centered at 0.]
S68:  1-3.                     [Laurent Series]

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Homework #9: (Due Friday, March 16 in the drop box by 9:00PM.)

S72:  1-3.         [Manipulating Power Series (substitutions, differentiation, integration)]
S73:  1, 4, 5     [Multiplication and Division of Power Series]
S86: 3, 4, 9      [Evaluating integrals Involving Rational Functions]
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Final Exam: Wednesday March 21 at 8:00am -11:00am in TBA. The final is cumulative.
Please bring a Blue Book and your student ID to the test.  Here is a Study Guide for the course: 120A_W2018_Summary_Sheet.pdf