Math 532 — Functions of a Complex Variable — Syllabus

Analytic functions, Cauchy-Riemann equations, theorem of Cauchy, Laurent series, calculus of residues, and applications.

Complex Numbers: operations, algebraic properties, moduli, exponential forms, arguments, roots of complex numbers, regions in the complex plane. Analytic functions: functions of complex variables, mappings, limits, continuity, derivatives, differentiation rules, Cauchy-Riemann equation, harmonic functions. Elementary functions: exponential functions, logarithmic functions, identities for logarithmic functions, complex exponents, trigonometric functions, hyperbolic functions, inverse trigonometric functions. Integrals: integrals of complex valued functions, contour integrals, Cauchy-Goursat theorem, Cauchy integral formula, Liouville’s theorem, fundamental theorem of algebra, maximum modulus theorem. Series: convergence of sequences & series, Taylor series, Laurent series. Residues and poles: Cauchy residue theorem, residues at poles, three types of isolated singular points. Applications of residues: Argument principle, improper integrals, Rouches theorem. Conformal mappings, bilinear transforms.

• Represent complex numbers algebraically and geometrically.
• Define and analyze limits and continuity for complex functions as well as consequences of continuity.
• Apply the concept and consequences of analyticity and the Cauchy-Riemann equations and of results on harmonic and entire functions including the fundamental theorem of algebra.
• Analyze sequences and series of analytic functions and types of convergence.
• Evaluate complex contour integrals directly and by the fundamental theorem, apply the Cauchy integral theorem in its various versions, and the Cauchy integral formula.
• Represent functions as Taylor and Laurent series, classify singularities and poles, find residues and evaluate complex integrals using the residue theorem.
• Construct conformal mappings between specific domains.

If you are a student with a disability and believe you will need accommodations for this class, it is your responsibility to contact the Student Ability Success Center at (619) 594-6473. To avoid any delay in the receipt of your accommodations, you should contact Student Ability Success Center as soon as possible. Please note that accommodations are not retroactive, and that I cannot provide accommodations based upon disability until I have received an accommodation letter from Student Ability Success Center. Your cooperation is appreciated.

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The SDSU Math & Stat Learning Center is in the Love Library, Room LL-328. "The Math and Stats Learning Center is open to support students in all lower division math courses at SDSU. We have tutors available for walk-in help during all open hours. TAs for Math 141, 150, 151, and 252 also hold their office hours there. Please see the schedule of when the TAs for your class will be in the center by going to our website: mlc.sdsu.edu. The MLC is supported by your student success fee. We strongly encourage you to use this wonderful, free resource. Some students believe that they should not need to ask for help. But, research has shown that the average grade for students who attend the MLC is one half grade higher than those who don’t seek such support."

If you are enrolled in a class which does not have targeted support, the MLC can still serve as a great math study/meeting place; and if you are interested in becoming a tutor in the center, keep an eye on the center's webpage for hiring announcements.

Students are generally encouraged to study together, and to work together to solve exercises. Finals, Midterms, Quizzes, Project, and other designated "individual work" activities must be completed without assistance. All violations will be reported to the Center for Student Rights and Responsibilities and will also result in score/grade reductions at the professor's discretion. Please review SDSU's full policy on academic honesty.

Examples of academic dishonesty include but are not limited to

• copying, in part or in whole, from another's test or other examination
• obtaining copies of a test, an examination, or other course material without the permission of the instructor
• collaborating with another or others in work to be presented without the permission of the instructor
• falsifying records, laboratory work, or other course data
• submitting work previously presented in another course, if contrary to the rules of the course
• altering or interfering with grading procedures
• assisting another student in any of the above
• using sources verbatim or paraphrasing without giving proper attribution (this can include phrases, sentences, paragraphs and/or pages of work)
• copying and pasting work from an online or offline source directly and calling it your own
• using information you find from an online or offline source without giving the author credit
• replacing words or phrases from another source and inserting your own words or phrases

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Students are instructed to contact their professor/instructor in the event they need to miss class, etc. due to an illness, injury or emergency. All decisions about the impact of an absence, as well as any arrangements for making up work, rest with the instructors. Student Health Services (SHS) does not provide medical excuses for short-term absences due to illness or injury. When a medical-related absence persists beyond five days, SHS will work with students to provide appropriate documentation. When a student is hospitalized or has a serious, ongoing illness or injury, SHS will, at the student's request and with the student’s consent, communicate with the student’s instructors via the Vice President for Student Affairs and may communicate with the student’s Assistant Dean and/or the Student Ability Success Center

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