{"id":765,"date":"2013-11-13T15:08:17","date_gmt":"2013-11-13T20:08:17","guid":{"rendered":"https:\/\/people.clas.ufl.edu\/avince\/?page_id=765"},"modified":"2026-03-19T08:15:15","modified_gmt":"2026-03-19T12:15:15","slug":"complex-variable","status":"publish","type":"page","link":"https:\/\/people.clas.ufl.edu\/avince\/complex-variable\/","title":{"rendered":"Complex Variable"},"content":{"rendered":"\r\n
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Complex Variable<\/h1>\n\n\n\n
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MAA 4402\u00a0 and\u00a0 MAA 5404<\/span><\/p>\n\n\n\n\n\n

Spring 2025<\/span><\/p>\n\n\n\n\n\n\n\n\n\n

______________________________________________________<\/p>\n\n\n\n\n\n

Time:<\/span><\/b>\u00a0 MWF period 7\u00a0<\/span><\/p>\n\n\n\n\n\n

Room<\/strong>:\u00a0 FLI 113<\/span><\/p>\n\n\n\n\n\n

Email<\/b>:\u00a0 avince@ufl.edu<\/span><\/p>\n\n\n\n\n\n

Office<\/strong>:\u00a0 438 Little Hall <\/span><\/p>\n\n\n\n\n\n

Office hours<\/strong>:\u00a0 MWF period 5 and by appointment<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n

Textbook:<\/b>\u00a0 Complex Variable and Applications\u00a0 \u00a09th edition<\/span><\/p>\n\n\n\n\n\n

\u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0 \u00a0Brown and Churchill<\/span><\/p>\n\n\n\n\n\n\n\n\n\n\n\n

Complex analysis<\/strong>\u00a0is not only of use in other branches of mathematics, but also in various fields of engineering. The course, like calculus, concerns functions of a single variable and covers limits, derivatives, integrals, and series. However, because the variable is a complex number, rather than a real number, the subject has a completely different flavor than calculus – in my opinion simpler and more elegant.<\/p>\n\n\n\n\n\n\n\n\n\n

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<\/a>Homework<\/span><\/h3>\n\n\n\n\n\n\n\n\n\n

See canvas<\/p>\n\n\n\n\n\n

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<\/a>Topics<\/span><\/h3>\n\n\n\n
     Complex numbers\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 \r\n\u00a0\u00a0\u00a0\u00a0 rectangular and polar form\r\n     Analytic functions\u00a0\u00a0 \r\n\u00a0\u00a0\u00a0\u00a0 limits and the derivative\u00a0 \r\n\u00a0\u00a0\u00a0\u00a0 Cauchy-Riemann equations\r\n\u00a0\u00a0\u00a0\u00a0 harmonic functions\r\n     Examples\u00a0\u00a0 \r\n\u00a0\u00a0\u00a0\u00a0 exponential and log functions\u00a0\u00a0 \r\n\u00a0\u00a0\u00a0\u00a0 complex exponents\r\n\u00a0\u00a0\u00a0\u00a0 trig functions\r\n\u00a0\u00a0\u00a0\u00a0 linear fractional transformations    \r\n     Integrals\r\n\u00a0\u00a0\u00a0\u00a0 contour integral\r\n\u00a0\u00a0\u00a0\u00a0 antiderivatives\r\n\u00a0\u00a0\u00a0\u00a0 Cauchy-Goursat Theorem (and Morera's Theorem)\r\n\u00a0\u00a0\u00a0\u00a0 Cauchy Integral Formula\u00a0\u00a0\u00a0\u00a0 \r\n\u00a0\u00a0\u00a0\u00a0 Liouville's theorem and the Fundamental Theorem of Algebra\r\n\u00a0\u00a0\u00a0\u00a0 maximum modulus principal \r\n     Series \r\n\u00a0\u00a0\u00a0\u00a0 geometric series\r\n\u00a0\u00a0\u00a0\u00a0 power series\r\n\u00a0\u00a0\u00a0\u00a0 Taylor series\r\n\u00a0\u00a0\u00a0\u00a0 Laurent series\r\n\u00a0\u00a0\u00a0\u00a0 Residues and poles\r\n\u00a0\u00a0\u00a0\u00a0 isolated singularities\r\n\u00a0\u00a0\u00a0\u00a0 residue theorem\r\n\u00a0\u00a0\u00a0\u00a0 residues at poles\r\n\u00a0\u00a0\u00a0\u00a0 behavior of a function near a singularity\r\n     Evaluating real integrals<\/span><\/pre>\n\n\n\n
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<\/a>Grades<\/span><\/h3>\n\n\n\n\n\n\n\n\n\n
Four exams, a few questions on each exam.\u00a0 The lowest grade is dropped if all four exams are taken.\u00a0 Each exam has equal weight.<\/span><\/p>\n\n\n\n\n\n
Exam 1.\u00a0 February 3<\/p>\n\n\n\n\n\n
Exam 2.\u00a0 February 26<\/p>\n\n\n\n\n\n
Exam 3.\u00a0 March 26<\/p>\n\n\n\n\n\n
Exam 4.\u00a0 April 21<\/p>\n\n\n\n\n\n
There will be four homework assignments, each due the class before the corresponding exam.\u00a0 Students will have a chance to present their solutions.\u00a0 The homework itself will count toward the final grade.<\/span><\/p>\n\n\n\n\n\n
The exams will be graded on a sliding scale, the harder the exam, the more lenient the\u00a0 grading.\u00a0 Out of 100, it will never be stricter than 90A, 80B, 70C, 60D.<\/span><\/p>\n\n\n\n\n\n
Exam and homework grades will be posted on the canvas Grades section within a week, but usually sooner.<\/span><\/p>\n\n\n\n
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<\/a>Campus Resources<\/span><\/h3>\n\n\n\n
The course will be conducted in accordance with the\u00a0<\/span>Academic Honesty Policy <\/a><\/span>\u00a0and policy regarding the use of copyrighted material.<\/span><\/span><\/p>\n\n\n\n\n\n
Students with disabilities requesting accommodations should first register with the  Disability Resource Center<\/a><\/span>\u00a0by providing appropriate documentation. Once registered, students will receive an accommodation letter which must be presented to the instructor when requesting accommodation. Students with disabilities should follow this procedure as early as possible in the semester. <\/span><\/p>\n\n\n\n\n\n
Academic advise <\/span><\/a>and tutoring<\/a><\/span>, as well as <\/span>health advise<\/span><\/a><\/span>\u00a0(physical and mental) is available to students.<\/span><\/span><\/p>\n\n\n\n\n\n
Requirements for class attendance and make-up exams, assignments, and other work in this course are consistent with university policies that can be found at:<\/span> Attendance Policies <\/a><\/span><\/p>\n\n\n\n\n\n
Information on current UF grading policies for assigning grade points may be found at: Grades<\/span><\/a><\/span><\/p>\n\n\n\n\n\n
Students are expected to provide feedback on the quality of instruction in this course by completing a course evaluation online via GatorEvals<\/span><\/span><\/a>. Students will be notified when the evaluation period opens and can complete evaluations through the email they receive from GatorEvals or in their Canvas course menu under GatorEvals.<\/span><\/span><\/p>\n\n\n\n
\n\n\n\r\n\t\t\t<\/div>\r\n\t\t<\/div>\r\n\t<\/div>\r\n<\/section>\r\n","protected":false},"excerpt":{"rendered":"","protected":false},"author":289,"featured_media":0,"parent":0,"menu_order":0,"comment_status":"closed","ping_status":"closed","template":"","meta":{"_acf_changed":false,"featured_post":"","footnotes":"","_links_to":"","_links_to_target":""},"class_list":["post-765","page","type-page","status-publish","hentry"],"acf":[],"_links":{"self":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/765","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages"}],"about":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/types\/page"}],"author":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/users\/289"}],"replies":[{"embeddable":true,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/comments?post=765"}],"version-history":[{"count":10,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/765\/revisions"}],"predecessor-version":[{"id":2995,"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/pages\/765\/revisions\/2995"}],"wp:attachment":[{"href":"https:\/\/people.clas.ufl.edu\/avince\/wp-json\/wp\/v2\/media?parent=765"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}