• 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

  • Archana Receives the Donna B. Hamilton Award

    Archana Khurana has been selected to receive the Donna B. Hamilton Award for Excellence in Undergraduate Teaching in a General Education Course.  Awards are based solely on student nominations and are solicited from across campus.  From the many nominations received, the selection committee was very impressed by the student experience… Read More

  • Yanir Receives a Do Good Campus Fund Grant

    Yanir’s proposal on “Incorporating outreach into the curriculum via experiential learning” is one of the only 27 projects out of 140 submissions that were funded by the UMD Do Good Campus Fund. Read More

  • Congrats to 3 CMNS Students Named Goldwater Scholars

    Congratulations to UMD’s 3 Goldwater Scholars this year, all from CMNS: Junior physics and mathematics double-degree student Yash Anand Sophomore atmospheric and oceanic science and physics double-degree student Malcolm Maas Junior biological sciences and mathematics double-degree student Jerry Shen Over the last 15 years, UMD’s nominations yielded 49 scholarships—No. 2… Read More

  • 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
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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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