## Math 483/583 - Complex Variables - Spring 2019

### Class Information

Instructor: Tuan Pham
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

 Homework Solution (from grader) Homework 1 Solution Homework 2 Solution Homework 3 Solution Homework 4 Solution Midterm review To selected problems Homework 5 Solution Homework 6 Solution Homework 7 Solution Homework 8 Solution Final review To selected problems

### 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