• Eugenia Brin, Longtime Supporter of Science and Performing Arts at UMD, Dies

    Eugenia Brin, a Russian immigrant and retired NASA scientist who, with her family of accomplished Terps, became an important benefactor of the University of Maryland, died on Dec. 3, 2024. She was 76 years old. The rest of the article can be read here: https://cmns.umd.edu/news-events/news/eugenia-brin-1948-2024 Read More

  • 2024 Michael Brin Dynamical Systems Prize for Young Mathematicians Awardees

    Math is excited to announce that Francisco Arana-Herrera has been awarded the 5th Michael Brin Dynamical Systems Prize for Young Mathematicians.  The prize was shared between Francisco and Rohil Prasad. Details about eh prize and previous winners can be found at  https://science.psu.edu/math/research/dynsys/dynamical-systems-prize-young-mathematicians Read More

  • UMD Launches Award to Recognize Dual Majors in Computer Science and Mathematics

    Starting Spring 2025, the Grant Family Outstanding Achievement Undergraduate Student Award will recognize graduating seniors excelling in both fields. Link to the article can be read here: https://www.cs.umd.edu/article/2024/11/umd-launches-award-recognize-dual-majors-computer-science-and-mathematics Read More

  • Jonathan Poterjoy and Kayo Ide join new $6.6 million NOAA consortium

    Congratulations to AOSC's Jonathan Poterjoy and Kayo Ide (also of math and IPST) on joining a new NOAA consortium to improve the accuracy of weather forecasts.  Called CADRE, the $6.6 million initiative will focus on data assimilation, which uses observations to improve model predictions of natural systems, like Earth's atmosphere, over time.… Read More

  • Alfio Quarteroni receives the Blaise Pascal Medal in Mathematics

    Congratulations to Alfio Quarteroni for winning the 2024 Blaise Pascal Medal in Mathematics The message from the European Academy of Sciences reads: We are excited to announce that Professor Alfio Quarteroni has been awarded the esteemed 2024 Blaise Pascal Medal in Mathematics for his outstanding contributions to the field, particularly in… 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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