Homework #0: ("Due" Thursday,
September 27)
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 on Thursday,
September 27.
This material will be covered on the tests.
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Homework #1: (Due Thursday, October 4 in
the drop box by 5:00PM.)
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 11 in the drop box by 5:00PM)
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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Homework #3:
(Due Thursday, October 18 in the drop box by 5:00PM.)
S14: 5, 6, 8
[mapping properties of functions]
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 22 at
12:00noon in Class.
Covers material above.
Please bring a Blue Book to the test.
Here is a study guide:
120A-Test1-Study-Guide.pdf
. There will be no cheat sheet for the first midterm.
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Homework #4:
(Due Thursday, October 25 in the drop box by 5:00PM.)
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 Thursday, November 1 in the drop box by 5:00PM.)
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 Thursday, November 8 in the drop box by 5:00PM.)
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]
* Look at S53 #4 but do not hand in!
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TEST #2: Friday, November 9 at 12:00
Noon in Class. The focus of the
test is on the
material in Homeworks 4-6.
Please bring a Blue Book and your
student ID to the test.
You are allowed a single one sided
(of a standard 8.5''x11''
sheet of paper) "cheat" sheet.
Here is a study guide for the second test:
120A-Test2-Study-Guide.pdf.
Veterans Day in the following Monday, November
12 so only one lecture day for next homework!
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Homework #7:
(Due Thursday, November 15 in the drop box by 5:00PM.)
S57: 1a)-d), 3, 4, 7 10 (10 is not to be
handed in.) [Cauchy integral formula and its consequences]
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No homework due on November 22 because of
Thanksgiving.
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Homework #8:
(Due Thursday, November 29 in the drop box by
5:00PM.)
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.
S59: 4 [Maximum modulus principle]
This problem is no longer due.
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 Thursday, November 7 in the drop box by 5:00PM.)
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:
Thursday December 13, 11:30am - 2:30pm in
Peterson Hall, Room 102.
