Fall 2013 Math 238: Advanced Complex Variables
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San Jos´ e State University Department of Mathematics Fall 2013 Math 238: Advanced Complex Variables Instructor: Slobodan Simi´ c, [email protected] Time and place: MW 12:00-1:15 in MH 234 Prerequisite: Math 138 or instructor consent Textbook: David C. Ullrich, Complex Made Simple, American Math. Society, Graduate Studies in Mathematics, vol. 97, 2008 What this course is about: Complex analysis is a classical branch of math- ematics which studies complex functions of a complex variable. It is both intrinsically beautiful and useful not only in mathematics but also in electrical engineering, physics and elsewhere. Unlike in real analysis, in complex analysis one gets many things for “free”: for instance, if a complex function is differentiable once, it is differentiable infinitely many times (it is, in fact, analytic!). After reviewing the basics, in Math 238 we will focus on some beautiful advanced results and concepts such as the Riemann Mapping Theorem, analytic continuation, Riemann surfaces (depicted above), the Picard theorems, and so on. The text I chose is full of careful explanations of why the theorems work the way they do. It is aimed directly at students and assumes minimal prerequisites. Web page: Go to http://www.math.sjsu.edu/˜ simic/ and click on Math 238.
Transcript of Fall 2013 Math 238: Advanced Complex Variables
San Jose State University Department of Mathematics
Fall 2013
Math 238: Advanced Complex Variables
Instructor: Slobodan Simic, [email protected]
Time and place: MW 12:00-1:15 in MH 234
Prerequisite: Math 138 or instructor consent
Textbook: David C. Ullrich, Complex Made Simple, American Math. Society,Graduate Studies in Mathematics, vol. 97, 2008
What this course is about: Complex analysis is a classical branch of math-ematics which studies complex functions of a complex variable. It isboth intrinsically beautiful and useful not only in mathematics but alsoin electrical engineering, physics and elsewhere. Unlike in real analysis,in complex analysis one gets many things for “free”: for instance, if acomplex function is differentiable once, it is differentiable infinitely manytimes (it is, in fact, analytic!). After reviewing the basics, in Math 238we will focus on some beautiful advanced results and concepts such asthe Riemann Mapping Theorem, analytic continuation, Riemann surfaces(depicted above), the Picard theorems, and so on. The text I chose is fullof careful explanations of why the theorems work the way they do. It isaimed directly at students and assumes minimal prerequisites.
Web page: Go to http://www.math.sjsu.edu/ simic/ and click on Math 238.
