120B Applied Complex Analysis
Home 120B Hmwork Announcements Test Information 120B Course Goals Extra Notes Topics Covered 

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Please re-check this page before doing each homework assignment as they may change!

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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.

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Homework #1: (Due Tuesday, April 10 in the drop box by 9:00PM.)

Section 77, Exercises 1abc, 2, 3, 7.     [Residue Calculations and Residue Theorem]
Section 79, Exercises 1ab, 2bc, 4.       [Classifying Singular Points and more residue calculations]
Section 81, Exercises 2b, 4, 6, 7a.       [Residues and Poles]
Section 83, Exercises 2,  6*, 3a, 8.      [Zeros and Poles]

(*You should look at this exercise but do not hand it in.)
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Homework #2:   (Due Tuesday, April 17 in the drop box by 9:00PM)

Section 86, Exercises  6, 7, 9                 [Integrating ratios of polynomials]
Section 88, Exercises 3, 5, 6, 8, 12.*     [Fourier Integrals]
Section 92, Exercises 1, 5, 6.                [Integrating ratios of trig. polynomials]

*Suggestion: Follow the outline, but take the real and imaginary parts at the very end.
So in part 12 a) show;

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Homework #3:  (Due Tuesday, April 24 in the drop box by 9:00PM.)
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Section 91, Exercises 1, 2, 6***. [Branch cuts and such]
Section 94, Exercises 5, 6, 8. [Argument Principal and Rouche's theorem]

*** You need not hand in problem 6 from Section 91.
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TEST #1:  Friday April 27 in class.  Covers material above.

Please bring a Blue Book and your student ID to the test.  Here is a Study Guide:
You are allowed a single two sided (of a standard 8.5''x11'' sheet of paper) "cheat" sheet.
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Homework #4:  (Due Tuesday, May 1 in the drop box by 9:00PM.)

(Short homework because of test.)

Section 59, Exercises 1, 4                [Maximum Modulus Principle]
Section 95, Exercises 1, 3                [Inverse Laplace Transforms]
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Homework #5:   (Due Tuesday, May 8  in the drop box by 9:00PM.)

Section 96, Exercises 2, 5.                   [Linear Transformations]
Section 98, Exercises 4, 9, 12*, 13.      [Mappings involving 1/z]
Section 117, Exercise 8                     [Laplacian under analytic change of variables.]

*Hint. If a (not equal to 0) is the center of the domain circle and 1/a were the center of the image circle, then show |az| would have to be constant for z in the domain circle which is false!

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Homework #6:  (Due Tuesday, May 15  in the drop box by 9:00PM.)

Section 100, Exercises 1, 2, 3, 4, 5, 7   [Fractional Linear Transformations]
Section 102, Exercises 1, 3.                 [Fractional Linear Transformations continued]
Section 114, Exercises 3, 4,**   6.        [Conformal Maps and Inverse Functions]
Section 115, Exercises 1, 2.                 [Harmonic Conjugates]

**Delay Section 114, Exercises 3, 4 until later.
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TEST #2:  Friday May 18 in class.  Covers material above.
Please bring a Blue Book and your student ID to the test.  Here is a Study Guide:
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 Tuesday, May 22 in the drop box by 9:00PM.)

Section 106, Exercises 1, 4, 8**        [Mapping Properties of functions involving ez. ]
Section 114, Exercises 3, 4               [Conformal Mapping Properties of basic analytic functions]

** Have a look at Section 106, Exercises 8 [regarding sin(z)] but do not hand it in!
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Homework #8: (Due Tuesday, May 29 in the drop box by 9:00PM.)

Section 108, Exercise 4.                       [More mapping properties of z --> z2 .]
Section 121, Exercises 4, 8, 10             [Steady state temperature problems.]
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Homework #9: (Due Tuesday, June 5 in the drop box by 9:00PM.)

Section 123, Exercises 4, 5.                 [Electrostatic potentials in 2-dimensions]
Section 126, Exercises 6, 9, 18.**         [2D-static irrotational & incompressible fluid flow]
Also turn in the two problems at
the end of the Dirichlet Problem Handout.

** Have a look at Section 126, Exercises 18 but do not hand it in!
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Final Exam:  Wednesday June 13 at 8:00am -11:00am in TBA (Probably Peterson Hall, Room 102.)  The final is cumulative.
Please bring a Blue Book and your student ID to the test.