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Calculus: Early Transcendentals Single Variable
Fourth Edition   ©2019

Calculus: Early Transcendentals Single Variable

Jon Rogawski (University of California, Los Angeles) , Colin Adams (Williams College) , Robert Franzosa

  • ISBN-10: 1-319-05593-1; ISBN-13: 978-1-319-05593-6; Format: Paper Text, 800 pages

Chapter 1: Precalculus Review
1.1 Real Numbers, Functions, and Graphs
1.2 Linear and Quadratic Functions
1.3 The Basic Classes of Functions
1.4 Trigonometric Functions
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
1.7 Technology: Calculators and Computers
Chapter Review Exercises

Chapter 2: Limits
2.1 The Limit Idea: Instantaneous Velocity and Tangent Lines
2.2 Investigating Limits
2.3 Basic Limit Laws
2.4 Limits and Continuity
2.5 Indeterminate Forms
2.6 The Squeeze Theorem and Trigonometric Limits
2.7 Limits at Infinity
2.8 The Intermediate Value Theorem
2.9 The Formal Definition of a Limit
Chapter Review Exercises

Chapter 3: Differentiation
3.1 Definition of the Derivative
3.2 The Derivative as a Function
3.3 Product and Quotient Rules
3.4 Rates of Change
3.5 Higher Derivatives
3.6 Trigonometric Functions
3.7 The Chain Rule
3.8 Implicit Differentiation
3.9 Derivatives of General Exponential and Logarithmic Functions
3.10 Related Rates
Chapter Review Exercises

Chapter 4: Applications of the Derivative
4.1 Linear Approximation and Applications
4.2 Extreme Values
4.3 The Mean Value Theorem and Monotonicity
4.4 The Second Derivative and Concavity
4.5 L’Hôpital’s Rule
4.6 Analyzing and Sketching Graphs of Functions
4.7 Applied Optimization
4.8 Newton’s Method
Chapter Review Exercises

Chapter 5: Integration
5.1 Approximating and Computing Area
5.2 The Definite Integral
5.3 The Indefinite Integral
5.4 The Fundamental Theorem of Calculus, Part I
5.5 The Fundamental Theorem of Calculus, Part II
5.6 Net Change as the Integral of a Rate of Change
5.7 The Substitution Method
5.8 Further Integral Formulas
Chapter Review Exercises

Chapter 6: Applications of the Integral
6.1 Area Between Two Curves
6.2 Setting Up Integrals: Volume, Density, Average Value
6.3 Volumes of Revolution: Disks and Washers
6.4 Volumes of Revolution: Cylindrical Shells
6.5 Work and Energy
Chapter Review Exercises

Chapter 7: Techniques of Integration
7.1 Integration by Parts
7.2 Trigonometric Integrals
7.3 Trigonometric Substitution
7.4 Integrals Involving Hyperbolic and Inverse Hyperbolic Functions
7.5 The Method of Partial Fractions
7.6 Strategies for Integration
7.7 Improper Integrals
7.8 Numerical Integration
Chapter Review Exercises

Chapter 8: Further Applications of the Integral
8.1 Probability and Integration
8.2 Arc Length and Surface Area
8.3 Fluid Pressure and Force
8.4 Center of Mass
Chapter Review Exercises

Chapter 9: Introduction to Differential Equations
9.1 Solving Differential Equations
9.2 Models Involving y' 5 k(y 2 b)
9.3 Graphical and Numerical Methods
9.4 The Logistic Equation
9.5 First-Order Linear Equations
Chapter Review Exercises

Chapter 10: Infinite Series
10.1 Sequences
10.2 Summing an Infinite Series
10.3 Convergence of Series with Positive Terms
10.4 Absolute and Conditional Convergence
10.5 The Ratio and Root Tests and Strategies for Choosing Tests
10.6 Power Series
10.7 Taylor Polynomials
10.8 Taylor Series
Chapter Review Exercises

Chapter 11: Parametric Equations, Polar Coordinates, and Conic Sections
11.1 Parametric Equations
11.2 Arc Length and Speed
11.3 Polar Coordinates
11.4 Area and Arc Length in Polar Coordinates
11.5 Conic Sections
Chapter Review Exercises

Appendices A1
A. The Language of Mathematics
B. Properties of Real Numbers
C. Induction and the Binomial Theorem
D. Additional Proofs

ANSWERS TO ODD-NUMBERED EXERCISES
REFERENCES
INDEX

Additional content can be accessed online at www.macmillanlearning.com/calculuset4e:

Additional Proofs:
L’Hôpital’s Rule
Error Bounds for Numerical
Integration
Comparison Test for Improper
Integrals

Additional Content:
Second-Order Differential
Equations
Complex Numbers