Center for Recruitment and Retention of Mathematics Teachers
University of Arizona ¤
November 8, 2017
Using Mapping Diagrams to Make Sense of Functions and Calculus
Part II
Linearity, Limits, Derivatives,Differential Equations, and Integration
Martin Flashman
Professor of Mathematics
Humboldt State University
http://users.humboldt.edu/flashman/Presentations/CRR2017/MD.LINKS.II.html
Abstract:
Participants
will learn how to use mapping diagrams (MD) to make sense of functions
and relate these to materials taught in calculus and in preparing for
calculus.
A mapping diagram is an alternative to a Cartesian graph that visualizes
a function using parallel axes. Like a table, it can present finite
date, but also can be used dynamically with technology.
An overview of basic function concepts with MD’s will begin the session using worksheets and GeoGebra.
Connections of MD's to key concepts in studying calculus and preparing
to study calculus will follow showing the power of MD’s to make sense of
function concepts of measurement, rate, composition, and approximation
related to calculus.
Background and examples will be available at Mapping Diagrams from
A(lgebra) B(asics) to C(alculus) and D(ifferential) E(quation)s. A
Reference and Resource for Function Visualizations Using Mapping
Diagrams. http://users.humboldt.edu/flashman/MD/section-1.1VF.html
Outline for Workshop II ¤
- Mapping Diagrams
- What is a Mapping Diagram? Review
- Brief reports on use Workshop I
- Linear Functions
- Linear functions are the key to understanding calculus.
- Nonlinear ( 1/x, trig, exp/ln) Connect to Resource
- Limits and The Derivative (visualize rate/ratio)
- An On-line Lesson on the Derivative
- Limits with Mapping Diagrams
- The Derivative As A
- Number,
- Magnification
- Rate
- Vector
- The Chain Rule: Mapping Diagrams for Composite (Linear) Functions
- An On-line Lesson on the Chain Rule
- Continuity and Solving Equations
- The Intermediate Value Theorem
- Newton's Method.
- 1st and 2nd Derivative Analysis [Time permitting]
- Differentials, Differential Equations, and Euler's Method
- Mapping Diagrams for the Differential
- Differential Equations, Euler, Mapping Diagrams
- Integration, the Fundamental Theorem(s) of Calculus, and Applications to Area.