Complex Variables

Description: This is a course on functions of a complex variable and their line integrals.

Textbook Reference:
Saff and Snider: Fundamentals of Complex Analysis with Applications to Engineering and Science

Additional References:
Michael Ward: MATH 305 course material
Jeremy Orloff: Complex Variables with Applications

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Lecture Notes:
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I. Complex numbers
[1.1-1.5]

II. Analytic functions
[1.6, 2.1, 2.3-2.5]

III. Exponential and logarithm
[3.1, 3.3]

IV. Multi-valued functions
[3.3, 3.5]

V. Line integrals
[4.1-4.3]

VI. Cauchy's integral formula
[4.4-4.5]

VII. Liouville theorem and maximum principle
[4.6]

VIII. Taylor series
[5.1-5.3]

IX. Laurent series
[5.5-5.6]

X. Residue theorem I
[6.1-6.3]

XI. Residue theorem II
[6.4-6.6]

XII. Argument principle
[6.7]

XIII. Fourier transform
[8.2]

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Midterm 1:
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Midterm 1 will cover the following lecture notes:

I. Complex numbers
II. Analytic functions
III. Exponential and logarithm
IV. Multi-valued functions

[Practice Midterm 1A] [Solutions]

[Practice Midterm 1B] [Solutions]

[Practice Midterm 1C] [Solutions]

[Practice Midterm 1D] [Solutions]

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Midterm 2:
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Midterm 2 will cover the following lecture notes:

V. Line integrals
VI. Cauchy's integral formula
VII. Liouville theorem and maximum principle
VIII. Taylor series
IX. Laurent series
X. Residue theorem I
XI. Residue theorem II

[Practice Midterm 2A] [Solutions]

[Practice Midterm 2B] [Solutions]

[Practice Midterm 2C] [Solutions]

[Practice Midterm 2D] [Solutions]

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Final exam:
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The final exam covers everything done in class except for the Fourier transform.

[Practice Final A] [Solutions]

[Practice Final B] [Solutions]

[Practice Final C] [Solutions]

[Practice Final D] [Solutions]