Math 483/583 - Complex Variables - Spring 2019
Class Information
Instructor: Tuan Pham
Grader: Jhih-Jyun Zeng
Section 1
Class meetings: Covell Hall 218, MWF 9:00 - 9:50 AM
[Syllabus]
[Tentative calendar]
[Canvas site]
Office Hours
MWF 10:00 - 11:30 AM at Kidder Hall 268
Assignments
Lecture notes
Lecture 28 (Jun. 7): write different Laurent series; Calculus of Residue
Lecture 27 (Jun. 5): application of Laurent series in complex integration; Cauchy's Residue theorem
Lecture 26 (Jun. 3): analyticity and holomorphicity; Laurent series
Lecture 25 (May 31): Taylor series of complex-variabled functions
Lecture 24 (May 29): general Cauchy's Integral formula; complex series
Lecture 23 (May 24): applications of Cauchy's Integral formula
Lecture 22 (May 22): Cauchy's Integral formula
Lecture 21 (May 20): Cauchy-Goursat theorem
Lecture 20 (May 17): Fundemental Theorem of Calculus for complex functions
Lecture 19 (May 15): computing complex integrals, geometric interpretation
Lecture 18 (May 13): examples of conformal / non-conformal mappings, complex integration
Lecture 17 (May 10): antiderivatives, mapping properties of holomorphic functions
Lecture 16 (May 8): differentiation rules, constant functions
Lecture 15 (May 3): Cauchy-Riemann equations, holomorphic functions
Lecture 14 (May 1): limit at infinity, derivative of complex functions
Lecture 13 (Apr. 29): velocity along a path, region of continuity of a complex function
Lecture 12 (Apr. 26): continuity of complex functions, curves on complex plane
Lecture 11 (Apr. 24): topological properties of regions, limit of complex functions
Lecture 10 (Apr. 22): inverse sine function; topological properties of regions
Lecture 9 (Apr. 19): examples on finding domains, branch points, branch cuts
Lecture 8 (Apr. 17): define single-valued branches for multi-valued functions
Lecture 7 (Apr. 15): logarithm function, branch cuts, power function
Lecture 6 (Apr. 12): exponential, sine, cosine function
Lecture 5 (Apr. 10): quadratic formula, exponential function
Lecture 4 (Apr. 8): powers and roots of complex numbers
Lecture 3 (Apr. 5): geometric representation of complex numbers
Lecture 2 (Apr. 3): algebraic properties of complex numbers
Lecture 1 (Apr. 1): introduction
Remarks before / after class
Worksheet 6/7/2019
Evaluating complex integral by series
Complex integral via Mathematica
Mapping properties of inversion function
A good exposition on conformal mappings: for application of Complex Variables on fluid flows, see p. 20-27 and 48-53
Solution to midterm exam
Worksheet 5/3/2019
Multivalued functions via Mathematica
Mapping properties via Mathematica
More examples on branch cuts, branch points of multi-valued functions
More examples on plotting with Mathematica
A tutorial on Overleaf (an online LaTeX editor) is here. Alternatively, an offline LaTeX editor can be downloaded here.
A simple template that can be used to write homework is here.
A quick guide on installing and plotting with Mathematica
Links
Department of Mathematics
Oregon State University
 | This page was last modified on Saturday, June 8, 2019
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