HSU Mathematics Department Colloquium
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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

http://flashman.neocities.org/Presentations/MD.HSU.CV.3_3_16.html

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¤.

Questions?

The End!

http://flashman.neocities.org/Presentations/MD.HSU.CV.3_3_16.html

References:¤

Mapping Diagrams from A(lgebra) B(asics) to C(alculus) and D(ifferential) E(quation)s.
A Reference and Resource Book on Function Visualizations Using Mapping Diagrams

The Sensible Calculus Program