Outline
BCME 9 - A20 Visualizing Equation Solutions
A20 - Visualizing Quadratic, Cubic, and Quartic Equation Solutions: An Introduction to Complex Numbers, Functions, and Mapping Diagrams -
Links: http://users.humboldt.edu/flashman/Presentations/BCME/BCME.LINKS.html
Understanding a quadratic, cubic or quartic equation and finding its solutions (roots) is a challenging part of the curriculum where students encounter a rich domain of mathematics - including geometry, numbers (real and complex), and functions. Visualising the solution of these equations is a valuable tool for meeting this challenge at any level. Starting with the representation of linear and quadratic equations, participants will take a hands on tour through visualisations including connections to the complex plane and 3D mapping diagrams for linear and quadratic complex functions, and concluding with recent work on visualising solutions to equations.
Table of Contents
What is a (real) mapping diagram (MD)?
Some Historical Uses of Mapping Diagrams
MD to visualize solving linear and quadratic equations.
- Using Mapping Diagrams to Make Sense of Functions and Equations
- Table and Mapping Diagram for A Complex Linear Function
- Complex Linear Mapping Diagram II: f(z) = Az
- Complex Variable Function Mapping Diagrams and Solving Real and Complex Quadratic Equations
- Mapping Diagram Solving A Quadratic Equation(Real and Complex)
MD to visualize complex solutions to cubic functions and equations.
Mapping Diagrams for Quartic Equations
Bibliography/References