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2.4 Use the definition of the derivative of complex function to show that f(z) is not dif- ferentiable at z = 0 where { E, if z + 0; 0, if z = 0. f(z) =

2.4 Use the definition of the derivative of complex function to show that f(z) is not dif- ferentiable at z = 0 where { E, if z + 0; 0, if z = 0. f(z) =

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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help 2.4

2.3 Give the condition which ensure that le| <1 where z e C. 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif- ferentiable at z = 0 where {, E, if z + 0; if z = 0. f(2) 0,
Transcribed Image Text:2.3 Give the condition which ensure that le| <1 where z e C. 2.4 Use the definition of the derivative of complex function to show that f(z) is not dif- ferentiable at z = 0 where {, E, if z + 0; if z = 0. f(2) 0,
Expert Solution
Step 1

The Complex Derivative

Definition: Let f be a function defined on a neighborhood of z0 ∈ ℂ. If

           limz→z0fz-fz0z-z0
exists, then we denote it by f'z0 and we say f is differentiable at z0 with complex derivative f'z0.
If f is defined and differentiable at every point of an open set U, then we say that f is analytic on U.

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