Section 3.1 Differentiable Functions - Maple Application Center
Application Center Applications Section 3.1 Differentiable Functions

## Section 3.1 Differentiable Functions

Authors
: Dr. John Mathews
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Does the notion of a derivative of a complex function make sense? If so, how should it be defined, and what does it represent? These and other questions will be the focus of the next few sections. Using our imagination, we take our lead from elementary Calculus and define the derivate of f; at z[0];, written f '(z[0];), by f '(z[0];) = Limit((f(z)-f(z[0]))/(z-z[0]),z = z[0]); , provided that the limit exists. When this happens, we say that the function f; is differentiable at z[0];. If we write Delta*z = z-z[0];, then this definition can be expressed in the form f '(z[0];) = Limit((f(z[0]+Delta*z)-f(z[0]))/(Delta*z),Delta*z = 0) .

#### Application Details

Publish Date: October 01, 2003
Created In: Maple V
Language: English

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