- JMM2018: Mapping Diagrams: Functions and Equation Solutions
- What is a (real) mapping diagram (MD)?
- Some Historical Uses of Mapping Diagrams
- I. MD to visualize general functions and equations before "calculus"
- II. A. MD to visualize Differential Calculus
- II.B. MD to visualize Differential Equations and Integral Calculus
- II.C. MD to visualize Multi-variable Calculus
- III. MD to visualize Complex Analysis
- Bibliography/References
JMM2018: Mapping Diagrams: Functions and Equation Solutions
- Author:
- Martin Flashman
AMS Special Session on Visualization in Mathematics:
Perspectives of Mathematicians and Mathematics Educators
Links: http://users.humboldt.edu/flashman/Presentations/JMM.AMS.MD.LINKS.html
A mapping diagram is an alternative to a Cartesian graph that visualizes a function using parallel axes.
Like a table, it can present finite data, but it also can work continuously and dynamically with technology.
Using GeoGebra as the primary technology, this presentation will cover topics from visualizing the algebra in solving simple linear equations
to understanding the functions of real analysis for differentiation and integration.
The conclusion will focus on complex analysis with new dynamic 3 dimensional mapping diagrams for visualizing complex polynomial functions and solutions to
cubic equations.
Table of Contents
What is a (real) mapping diagram (MD)?
Some Historical Uses of Mapping Diagrams
- Examples from the past: Napiers Logarithm
- Examples from the Past: I. Newton
- Example from the 20th Century- M Spivak (1967)
- Examples from the recent past: 20th Century- E.McSquared
- Example from the 20th Century: H. Picciotto
- Example from the 21st Century : L. Gonick (2012)
- Mapping diagrams with adjustable output centre
I. MD to visualize general functions and equations before "calculus"
II. A. MD to visualize Differential Calculus
II.B. MD to visualize Differential Equations and Integral Calculus
II.C. MD to visualize Multi-variable Calculus
III. MD to visualize Complex Analysis
- Table and Mapping Diagram for A Complex Linear Function
- Complex Variable Function Mapping Diagrams and Solving Real and Complex Quadratic Equations
- Complex Variable Function Mapping Diagrams and Solving Real Cubic Equations
- 9:40 AM Room 31B: Session on Revitalizing Complex Analysis: Making Sense of Complex Integration
- Complex Linear Mapping Diagram II: f(z) = Az
- Integral Examples from List
- Complex Line Integral: Definition and F.T. Examples
Bibliography/References