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Finney, Demana, Waits, Kennedy Calculus: Graphing, Numerical, Algebraic 4th Edition

Contents

Chapter 1 Prerequisites for Calculus

1.1 Lines
1.2 Functions and Graphs
1.3 Exponential Functions
1.4 Parametric Equations
1.5 Functions and Logarithms
1.6 Trigonometric Functions

 

Chapter 2 Limits and Continuity

2.1 Rates of Change and Limits
2.2 Limits Involving Infinity
2.3 Continuity
2.4 Rates of Change and Tangent Lines

 

Chapter 3 Derivatives

3.1 Derivative of a Function
3.2 Differentiability
3.3 Rules for Differentiation
3.4 Velocity and Other Rates of Change
3.5 Derivatives of Trigonometric Functions

 

Chapter 4 More Derivatives

4.1 Chain Rule
4.2 Implicit Differentiation
4.3 Derivatives of Inverse Trigonometric Functions
4.4 Derivatives of Exponential and Logarithmic Functions

 

Chapter 5 Applications of Derivatives

5.1 Extreme Values of Functions
5.2 Mean Value Theorem
5.3 Connecting ƒ’ and ƒ’’ with the Graph of ƒ
5.4 Modeling and Optimization
5.5 Linearization and Differentials
5.6 Related Rates

 

Chapter 6 The Definite Integral

6.1 Estimating with Finite Sums
6.2 Definite Integrals
6.3 Definite Integrals and Antiderivatives
6.4 Fundamental Theorem of Calculus
6.5 Trapezoidal Rule

 

Chapter 7 Differential Equations and Mathematical Modeling

7.1 Slope Fields and Euler’s Method
7.2 Antidifferentiation by Substitution
7.3 Antidifferentiation by Parts
7.4 Exponential Growth and Decay
7.5 Logistic Growth

 

Chapter 8 Applications of Definite Integrals

8.1 Integral As Net Change
8.2 Areas in the Plane
8.3 Volumes
8.4 Lengths of Curves
8.5 Applications from Science and Statistics

 

Chapter 9 Sequences, L’Hôpital’s Rule, and Improper Integrals

9.1 Sequences
9.2 L’Hôpital’s Rule
9.3 Relative Rates of Growth
9.4 Improper Integrals

 

Chapter 10 Infinite Series

10.1 Power Series
10.2 Taylor Series
10.3 Taylor’s Theorem
10.4 Radius of Convergence
10.5 Testing Convergence at Endpoints

 

Chapter 11 Parametric, Vector, and Polar Functions

11.1 Parametric Functions
11.2 Vectors in the Plane
11.3 Polar Functions

 

Appendixes

A1 Formulas from Precalculus Mathematics
A2 Mathematical Induction
A3 Using the Limit Definition
A4 Proof of the Chain Rule
A5 Conic Sections
A6 Hyperbolic Functions
A7 A Brief Table of Integrals

 

Glossary

Selected Answers
Applications Index
Index