MATH 120A COMPLEX VARIABLES NOTES: REVISED …
MATH 120a complex variables notes : REVISEDDecember 3, 2003BRUCE K. 120A Lecture notes , Fall : REVISED : december 3, (9/26/03) our purposes the definition of COMPLEX VARIABLES is thecalculus ofanalytic functions, where a functionF(x, y)=(u(x, y),v(x, y))fromR2to itself is analytic iffit satisfies the Cauchy Riemann equations:ux= vyandvx= , the associated calculus has some verybeautiful and useful properties which will be explained in this class. The followingfact makes the subject useful in of the common elementary functions, likexn,ex,sinx,tanx,lnx,etc. haveunique extensions to analytic functions. Moreover, the solutions tomany ordinary differential equations extend to analytic functions.
MATH 120A COMPLEX VARIABLES NOTES: REVISED December 3, 2003 3 Remark 1.4 (Not Done in Class). Here is a way to understand some of the basic properties of C …
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