With contributions from Fabio Milner

A Work in Progress (Original posting: July, 2015. Latest revision: August, 2019)

Cite as:

Thompson, Patrick W., Ashbrook, Mark, & Milner, Fabio. (2019) *Calculus: Newton, Leibniz, and Robinson meet technology.* Retrieved from http://patthompson.net/ThompsonCalc/.

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Click here for license information.Chapter 1: Infinitely Small and Infinitely Large Quantities

Chapter 2: Trigonometric Functions

- 2.0 From Trigonometry for High School to Trigonometry for Calculus
- 2.1 A Graph You've Surely Seen
- 2.2 The Meaning of
*x*in*y*= sin(*x*) - 2.3 Positive and Negative Angle Measures
- 2.4 Angle Measures Greater than 2π or less than -2π
- 2.5 The Meaning of
*y*in*y*= sin(*x*) - 2.6 The Tangent Function in Trigonometry
- 2.7 The Meaning of
*x*and*y*in*y*= tan(*x*) - 2.8 Properties of Trigonometric Functions

Chapter 3: Functions, Variables, and Graphs

- 3.1 Variables, Constants, and Parameters
- 3.2 Graphing Calculator (GC)
- 3.3 Using Graphing Calculator
- 3.4 Typing Mathematical Statements in GC
- 3.5 What is a Graph?
- 3.6 How GC Draws Graphs
- 3.7 Understanding GC's DNA
- 3.8 (To Be Rewritten)
- 3.9 Coordinate Systems
- 3.10 Functions
- 3.11 Function Notation
- 3.12 Using Function Notation
- 3.13 Function Notation and Mathematical Models
- 3.14 Independent Variable vs. Argument of Function
- 3.15 Constant Rate of Change & Linear Functions
- 3.16 Operations on Functions
- 3.17 Properties of Functions
- 3.18 Inverse of a Function
- 3.19 Transformations of Graphs: An Application of Inverse Functions

- 4.1 Constant Rate of Change
- 4.2 Differentials as Linear Functions
- 4.3 Differentials in Action
- 4.4 Rate of Change at a Moment
- 4.5 How Small is "Small Enough"?
- 4.6 Functions Having a Value At Which There Is No Rate of Change at a Moment
- 4.7 Wrinkly Functions
- 4.8 Infinitely Wrinkly Functions Having No Rate of Change at Any Moment
- 4.9 Exact Rate of Change Functions

Chapter 5: Accumulation from Rate of Change

Chapter 6: Rate of Change from Accumulation

Chapter 8: More on Integrals

Chapter 9:Integration Techniques

Chapter 10: Approximating Functions' Values

- 10.0 Approximating Rate of Change and Accumulation Function's Values
- 10.1 New Perspectives on Approximating Accumulation Functions from Rate of Change Functions
- 10.2 Polynomial Approximations, Taylor Series, and Convergence at a Moment
- 10.2-old Sequences, Series, and Convergence at a Point (traditional)
- 10.3 Sequences, Series, and Convergence Over an Interval

Chapter 11: Polar Coordinates

Chapter 12: Parametric Relationships and Functions

Calculus: Newton Meets Technology is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.

Based on a work at http://patthompson.net/ThompsonCalc.

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