• Maria Cameron Receives the 2024 MURI Award

    Congratulations to Maria Cameron for her MURI award. MURI are multidisciplinary university research initiative grants that are awarded by the department of defense. Cameron’s grant is sponsored by the office of naval research. Her team includes Balakumar Balachandran (ME) and Miao Yu (ME). This is a project on “disorder-influenced collective Read More
  • A $27.2M Gift to the Math Department by the Brin Family

    The university announced today a big gift to the Math Department. The very generous gift of $27.2M was made by Michael & Eugenia Brin. The gift will endow the Brin Mathematics Research Center, establish an endowed chair, and launch a summer camp for high school students. The official university’s press Read More
  • 2023 Putnam Competition Result

    We very excited to report that our Putnam team ranked 8th, honorable mention, among 471 institutions in the 2023 Putnam math competition.Our team members this year were Vincent Trang, Daniel Yuan, Omar Habibullah, and Andrew Parker.Vincent Trang ranked 43rd and Daniel Yuan ranked 64th among 3,857 participants. Read More
  • Simons Fellows - Darvas, Kanigowski, Rubinstein

    Congratulations to Tamas Darvas, Adam Kanigowski, and Yanir Rubinstein for being named Simons Fellows. Read More
  • Doron Levy is elected 2024 Class of Fellows of the AMS

    Congratulations to Dr. Doron Levy, as Fellow of the American Mathematical Society, Class of 2024 (https://www.ams.org/cgi-bin/fellows/fellows_by_year.cgi)!  Dr. Levy was elected  ``For his contributions to Mathematical Oncology and Mathematical Biology".  Read More
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Description

This course is an introduction to complex variables, accessible to juniors and seniors in engineering, physics and mathematics. It covers:  algebra of complex numbers, analytic functions, Cauchy Integral Formula, Taylor and Laurent series, theory of residues (and  application to the evaluation of real integrals), conformal mapping and applications to physical problems.

Prerequisites

1 course with a minimum grade of C- from (MATH241, MATH340).


Level of Rigor

Standard


Sample Textbooks

Complex Variables and Applications, by Churchill/Brown.

Fund. of Complex Analysis for Math. Science & Engineering, by Saff and Snider


Applications

Engineering, physics, astronomy, mathematics


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Additional Notes

Students interested in grad school in MATH should strongly consider this course

Recommended as a foundational course for all math majors.


Topics

Algebra of complex numbers 

Elementary functions of a complex variable (exponential, logarithmic and trigonometric functions)

Analytic functions, Cauchy-Riemann equations

Harmonic functions and harmonic conjugates

Contour Integrals

Cauchy-Goursat theorem

Cauchy integral formulas and application (Liouville's theorem, Fundamental theorem of algebra)

Power series and Taylor series

Laurent series

Residues and applications (evaluation of real integrals)

Mapping properties of some elementary functions

Conformal mappings

Application to the steady state heat flow and electrostatic potential

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