Calculus: Single Variable, 7th Edition

Calculus: Single Variable, Enhanced eText

Author(s): Deborah Hughes-Hallett; William G. McCallum; Andrew M. Gleason; Eric Connally; Daniel E. Flath; Sel
Publisher: Wiley
Copyright year: © 2017
Edition: 7th
ISBN: 9781119139317, 1119139317
Description

Calculus: Single Variable, 7e continues the effort to promote courses in which understanding and computation reinforce each other. The 7th Edition reflects the many voices of users at research universities, four-year colleges, community colleges, and secondary schools. This new edition has been streamlined to create a flexible approach to both theory and modeling. The program includes a variety of problems and examples from the physical, health, and biological sciences, engineering and economics; emphasizing the connection between calculus and other fields. Calculus: Single Variable, 7e will include Wiley's seamlessly integrated adaptive WileyPLUS ORION program, covering content from refresher Algebra and Trigonometry through Multi-Variable Calculus. Calculus: Single Variable, 7e is the first adaptive calculus program in the market.

Cover
Dedication
Title Page
Copyright
Preface
Acknowledgments
Chapter 1: Foundation for Calculus: Functions and Limits
1.1 Functions and Change
1.2 Exponential Functions
1.3 New Functions from Old
1.4 Logarithmic Functions
1.5 Trigonometric Functions
1.6 Powers, Polynomials, and Rational Functions
1.7 Introduction to Limits and Continuity
1.8 Extending the Idea of a Limit
1.9 Further Limit Calculations Using Algebra
1.10 Optional Preview of the Formal Definition of a Limit
Chapter 2: Key Concept: The Derivative
2.1 How Do We Measure Speed?
2.2 The Derivative at a Point
2.3 The Derivative function
2.4 Interpretations of the Derivative
2.5 The Second Derivative
2.6 Differentiability
Chapter 3: Short-Cuts to Differentiation
3.1 Powers and Polynomials
3.2 The Exponential Function
3.3 The Product and Quotient Rules
3.4 The Chain Rule
3.5 The Trigonometric Functions
3.6 The Chain Rule and Inverse Functions
3.7 Implicit Functions
3.8 Hyperbolic Functions
3.9 Linear Approximation and the Derivative
3.10 Theorems about Differentiable Functions
Chapter 4: Using the Derivative
4.1 Using First and Second Derivatives
4.2 Optimization
4.3 Optimization and Modeling
4.4 Families of Functions and Modeling
4.5 Applications to Marginality
4.6 Rates and Related Rates
4.7 L'Hopital's Rule, Growth, and Dominance
4.8 Parametric Equations
Chapter 5: Key Concept: The Definite Integral
5.1 How Do We Measure Distance Traveled?
5.2 The Definite Integral
5.3 The Fundamental Theorem and Interpretations
5.4 Theorems about Definite Integrals
Chapter 6: Constructing Antiderivatives
6.1 Antiderivatives Graphically and Numerically
6.2 Constructing Antiderivatives Analytically
6.3 Differential Equations and Motion
6.4 Second Fundamental Theorem of Calculus
Chapter 7: Integration
7.1 Integration by Substitution
7.2 Integration by Parts
7.3 Tables of Integrals
7.4 Algebraic Identities and Trigonometric Substitutions
7.5 Numerical Methods for Definite Integrals
7.6 Improper Integrals
7.7 Comparison of Improper Integrals
Chapter 8: Using the Definite Integral
8.1 Areas and Volumes
8.2 Applications to Geometry
8.3 Area and ARC length in Polar Coordinates
8.4 Density and Center of Mass
8.5 Applications to Physics
8.6 Applications to Economics
8.7 Distribution Functions
8.8 Probability, Mean, and Median
Chapter 9: Sequences and Series
9.1 Sequences
9.2 Geometric Series
9.3 Convergence of Series
9.4 Tests for Convergence
9.5 Power Series and Interval of Convergence
Chapter 10: Approximating Functions Using Series
10.1 Taylor Polynomials
10.2 Taylor Series
10.3 Finding and Using Taylor Series
10.4 The Error in Taylor Polynomial Approximations
10.5 Fourier Series
Chapter 11: Differential Equations
11.1 What is a Differential Equation?
11.2 Slope Fields
11.3 Euler's Method
11.4 Separation of Variables
11.5 Growth and Decay
11.6 Applications and Modeling
11.7 The Logistic Model
11.8 Systems of Differential Equations
11.9 Analyzing the Phase Plane
11.10 Second-Order Differential Equations: Oscillations
11.11 Linear Second-Order Differential equations
Appendices
A Roots, Accuracy, and Bounds
B Complex Numbers
C Newton’s Method
D Vectors in the Plane
Ready Reference, Formulas and Tables
Index
EULA
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