Calculus

Calculus II

Complex Analysis

Faculty of Applied Sci and Eng

Linear Algebra

MAT | 194 | Calculus | exam | 

MAT195_Problems_Chap_10_and_11.pdf

MAT | 292 | Faculty of Applied Sci and Eng | exam | 

Math 389 PS 8 Note: Section 2.5 covers more general Laurent series with inﬁntely many negative powers of z - z 0 . You are responsible only for the kind we did in class, with only ﬁnitely many negative powers, namely the kind that occurs at a pole. Sect. 2.5. #1-9, 10, 13, 14, 15 , 17, 25, 26, 27a,b,c. Suppose D is a simply-connected domain and f is an analytic function on D with no zeroes. Show that there is an analytic branch of log f ( z ) deﬁned on D , namely a function g ( z ) such that e g ( z ) = f ( z ) for all z ∈ D . Hint: to motivate the argument note that if such a g exists then it must satisfy g ′ ( z )= f ′ ( z ) /f ( z ) on D . Explain why f ′ ( z ) /f ( z ) in analytic on D and has a primitive on D . Let g be any such primitive. Show that e g ( z ) = Cf ( z ) by considering the function e g ( z ) /f ( z ). Now adjust g ( z ) so that the constant becomes 1. If you get stuck on this, it is covered in Sect. 2.4. 1

MAT | 389 | Complex Analysis | question bank | Math 389 PS 8 Note: Section 2.

MAT | 389 | Complex Analysis | study guides | 

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