Skip to main content
\(\newcommand{\N}{\mathbb{N}} \newcommand{\Z}{\mathbb{Z}} \newcommand{\R}{\mathbb{R}} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)
A Modeling Approach to Calculus
D. Brian Walton
Contents
Prev
Up
Next
Annotations
Contents
Prev
Up
Next
Front Matter
Preface
1
Overview to the Course
Learning Mathematics
Numbers and Measurements
Variables, Expressions, and Equations
Graphs and Relations between Variables
Models and Dynamics
2
Sequences as Models
Introduction to Sequences
Recursive Sequences and Projection Functions
Computing Sequence Values
Exponents, Inverses and Logarithms
Logarithms and Their Properties
Dynamic Models Using Sequences
3
Discrete Calculus
Introduction to Discrete Calculus
Increments of Sequences
Accumulation Sequences
Summation Formulas
Limits of Sequences
Calculating Sequence Limits
4
Functions as Continuous Models
An Introduction to Functions
Constructing Functions
Transformations of Functions
Functions Defined on Intervals
Limits of Functions
Continuity of Functions
Describing the Behavior of Functions
5
Continuous Accumulation and Integration
An Overview of Calculus
Accumulation of Change
Riemann Sums
Properties of Definite Integrals
Functions Defined by Accumulation
6
Modeling Rates of Change by Differentiation
Rate of Accumulation and the Derivative
Extreme Values
Introduction to Optimization
Functions Defined by Their Rates
Rates of Change
The Derivative
Differentiation
Derivatives Take Practice
The Chain Rule
The Derivative of Exponential Functions
Implicit Differentiation and Derivatives of Inverse Functions
Applications Involving Densities
7
Calculus for Trigonometry
Limits Involving Infinity
Continuous Functions
The Derivatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
8
Applications of Derivatives
Differentiable Functions
Consequences of the Mean Value Theorem
Extreme Values and Optimization
L'HÃ´pital's Rule
Antiderivatives
The Fundamental Theorem of Calculus
Integrals and the Method of Substitution
A
Mathematics Foundations
Numbers, Sets and Arithmetic
Algebra Review
B
Trigonometry Basics
Right Triangles and Trigonometry
Measuring Arbitrary Angles
Unit Circle Trigonometry
Inverse Trigonometric Functions
Reference material
Notation
Feedback
Authored in PreTeXt
A Modeling Approach to Calculus
D. Brian Walton
Department of Mathematics and Statistics
James Madison University
Harrisonburg, Virginia, USA
waltondb@jmu.edu
September 11, 2018
Preface