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A Modeling Approach to Calculus:
MA2C
D. Brian Walton
Contents
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Contents
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Front Matter
Preface
I
1
Foundational Principles
Learning Mathematics
Numbers, Measurements and Relations
Graphs and Relations between Variables
Formulas as Models of Relations
Algebra and Equivalence
Factoring
Exponents, Roots, and Logarithms
Logarithms and Their Properties
Applications of Logarithms
2
Functions to Model Relationships
An Introduction to Functions
Constructing Functions
Chains and Function Composition
Inverse Functions
Transformations of Functions
3
Accumulation and Rates of Change
Describing the Behavior of Functions
Rate of Accumulation and the Derivative
Accumulation of Change
Functions Defined by Accumulation
4
Sequences and Accumulation
Introduction to Sequences
Increments of Sequences
Accumulation Sequences
Summation Formulas
Limits of Sequences
Calculating Sequence Limits
5
Limits and Differentiability
An Overview of Calculus
Functions Defined on Intervals
Limits of Functions
Continuity of Functions
Instantaneous Rate of Change
The Fundamental Theorem of Calculus, Part One
II
6
Accumulation and Integrals
Accumulation Functions and the Definite Integral
Properties of Definite Integrals
Calculating Integrals Using Accumulations
Riemann Sums
7
Other Stuff Not Yet Placed
III
8
Modeling Rates of Change
Extreme Values
The Derivative
9
Rules of Differentiation
Derivative Rules
Differentiation and Related Rates
The Chain Rule
The Derivative of Exponential Functions
Implicit Differentiation and Derivatives of Inverse Functions
Logarithmic Differentiation
10
Derivatives and Integrals
Antiderivatives
Differentiable Functions
Definite Integrals and Antiderivatives
L'Hôpital's Rule
11
Calculus for Trigonometry
The Derivatives of Trigonometric Functions
Derivatives of Inverse Trigonometric Functions
12
Other Stuff
Introduction to Optimization
Extreme Values and Optimization
Integrals and the Method of Substitution
Limits Involving Infinity
Continuous Functions
Applications Involving Densities
Functions Defined by Their Rates
13
Sequences as Models
Introduction to Discrete Calculus
Recursive Sequences and Projection Functions
Computing Sequence Values
Dynamic Models Using Sequences
Back Matter
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
Feedback
Authored in PreTeXt
Chapter
10
Derivatives and Integrals
10.1
Antiderivatives
PDF version of Section 10.1
10.2
Differentiable Functions
PDF version of Section 10.2
10.3
Definite Integrals and Antiderivatives
PDF version of Section 10.3
10.4
L'Hôpital's Rule
PDF version of Section 10.4
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