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 $. ¤
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
M. Flashman GeoGebra Book [in development]: Mapping Diagrams to Visualize Complex Analysis http://ggbtu.be/bNi69jyKs
AMATYC Webinar Martin Flashman - Using Mapping Diagrams to Understand Functions (YouTube)
AMATYC Webinar M Flashman Using Mapping Diagrams to Understand Trig Functions (YouTube)
Martin Flashman ...Solving Linear Equations Visualized with Mapping Diagrams (YouTube)
Martin Flashman ...Partial Derivatives: An Introduction Using Mapping Diagrams (You Tube)
AMATYC Webinar Martin Flashman - Using Mapping Diagrams to Understand Functions (YouTube) AMATYC Webinar M Flashman Using Mapping Diagrams to Understand Trig Functions (YouTube)Martin Flashman ...Solving Linear Equations Visualized with Mapping Diagrams (YouTube)Martin Flashman ...Partial Derivatives: An Introduction Using Mapping Diagrams (You Tube)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