Grades 1112
Developed by: Brenda Batten
Concepts of Calculus was written to help students gain an understanding of the most important concepts in Calculus AB and to introduce students to the power of the TI89 in exploring these concepts graphically, numerically, and analytically.
Twentyeight activities organized across five chapters cover the following topics: Introductions; Limits; Derivatives; Integrals; Connections.
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This workbook views the calculator as more than just an "answer box." It is a tool that can help students come to their own understanding of concepts. Memorizing steps to a solution is insufficient. Students must be able to answer the question, "Why?"
The activities include: (click for an example of each) Explanations; Historical Notes; Tech Tips; Worked Examples; Questions to Test Understanding; Suggested Journal Entries.
Each activity contains a section for keeping a journal to give students the chance to summarize the main points in the activity and to note important definitions and theorems. This journal can serve as a review for the AP Exam.


Contents:
Evaluation Lessons are available below as PDF files, which require Adobe Acrobat Reader to view.
Letter from the Author (pdf)
Chapter 1 Introductions Introduction to the TI89 (pdf)
Introduction to Limits
Introduction to Text Scripts
Introduction to Graphing Techniques
Chapter 2 Limits Informal Definition of the Limit (pdf)
Limits of Polynomial Functions
Limits of Rational Functions: Up Close and Personal
Limits of Rational Functions: Like an Astronaut
Formal Definition of the Limit
Applications of Limits
Chapter 3 Derivatives Average Rate and Instantaneous Rate (pdf)
The Derivative Function
Derivatives and Continuity
Using Derivatives Graphically
The Mean Value Theorem for Derivatives
Chapter 4 Integrals Patterns and Accumulation: Sequences and Series (pdf)
Definite Integral as the Limit of a Riemann Sum
Definite Integral as an Accumulator
The Fundamental Theorem of Calculus: Part A
The Average Value of a Function over an Interval
The Average Value of a Function: Geometrical Interpretation
Chapter 5 Connections THE Mean Value Theorem (pdf)
Upper Limits of Integration that Vary
Lower Limits of Integration that Vary
The Fundamental Theorem of Calculus: Part B
Indefinite Integrals and Slope Fields
Differential Equations and Initial Conditions
Solving Differential Equations
