HSU Mathematics Department Colloquium
March 3, 2016
Complex Variables: Mapping Diagrams for 
Visualizing Complex Arithmetic and Functions
Dynamically with GeoGebra

Part I
Mapping Diagrams for Real Functions
Complex Arithmetic
Part II
Complex Functions
 Part III
Calculus for Complex Functions

Martin Flashman
Professor of Mathematics
Humboldt State University


5.1 Limits and  Continuity   ¤
Definition:  $\lim_{z \rightarrow z_0} f(z) = L$ means:
Given any $\epsilon>0 $ there is a $\delta> 0$ so
that if $0 <|z-z_0|<\delta$, then $|f(z)- L|<\epsilon$.

Example: $\lim_{z \rightarrow i} z^2 + 2z = -1+2i$ means:
Given any $\epsilon>0 $ there is a $\delta> 0$ so
that if $0 <|z-i|<\delta$, then $|z^2 +2z +1-2i|<\epsilon$.

5.2 The Derivative for Complex Functions    ¤
5.2.1 The Derivative for Powers of z: $f(z) = z^n$.
$$f'(z_0)= \lim_{\Delta z \to 0} \frac{f(z)-f(z_0)}{z-z_0}$$

$$f'(z_0)= \lim_{\Delta z \to 0} \frac{z^n-z_0^n}{z-z_0}$$

6.1 Visualizing the integral $∮_C \frac1z dz $. ¤

Thanks for attending¤.


The End!



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A Reference and Resource Book on Function Visualizations Using Mapping Diagrams

The Sensible Calculus Program