Outline
BCME E20:Visualizing Complex Analysis with Mapping Diagrams
E20 - Making Sense of Complex Analysis with Mapping Diagrams: A New Visualization Tool Enhanced by Technology (GeoGebra)
Links: http://users.humboldt.edu/flashman/Presentations/BCME/BCME.LINKS.html
Understanding functions is an important challenge in studying complex numbers and complex analysis.
Mapping diagrams, frequently coupled with tables, are a valuable alternative to graphs for visualizing real variable functions and without a comparable alternative for complex variables. The session will start with basics of mapping diagrams to visualise real and complex linear and linear fractional functions. Participants will take a hands on mapping diagram tour using GeoGebra through visualisations of complex functions and integration theory and practice, concluding with visualisations to make sense of numerical methods for estimating integrals, Cauchy's Theorem and the Cauchy Integral Formula.
Check for Complex Analysis 2nd Ed, Ian Stewart and David Tall
http://www.cambridge.org/gb/academic/subjects/mathematics/real-and-complex-analysis/complex-analysis-2nd-edition#tO6bwJtRzAdRMS7V.99, to appear in August 2018.
Table of Contents
Introduction: Linear & Linear Fractional Functions
- Mapping Diagram, Spreadsheet, Graph, Realign, Focus
- Complex Plane
- Table and Mapping Diagram for A Complex Linear Function
- Complex Linear Mapping Diagram II: f(z) = Az
- Complex Linear Mapping Diagrams I (Circles)
- Mapping diagram for Moebius Function
- Mapping diagram for Moebius Transformation: roots and poles, lines and circles
- Moebius Transformation: MD circle with spherical projection
Mapping Diagrams to Visualize Elementary Functions
Limits and Continuity for Complex Functions
Mapping Diagrams to Visualize Differentiation and Applications
Mapping Diagrams to Visualize Integration