Single Variable Calculus: Early Transcendentals, Fourth Edition

• Each exercise set is clearly partitioned into groups of problems using headings such as Fundamentals, Applications, Mathematical Models, Projects, Calculator/CAS Problems, etc
• Each chapter opens with its own table of contents and an introduction to the material covered in the chapter.
• The text ends with Resource Pages, which is a compact review of basic concepts from algebra, geometry, trigonometry, and calculus. Many of the topics cover in the Resources Page are discussed in greater depth in the Student Resources Guide.
• The Test Yourself section is a self-test consisting of 56 questions on four broad areas of precalculus, and encourages students to review the more essential prerequisite subjects that are used throughout the text.
• Notes from the Classroomsections are informal discussions that are aimed at the student and discuss common algebraic, procedural, and notational errors, as well as provide advice and questions asking students to think about and extend upon the ideas just presented.
• Instructor's resources include a complete solutions manual and test items.
• Introduces calculus concepts and topics in a clear concise manner for maximum student retention.
• Straightforward exposition at a level accessible to today’s college students.
• Includes examples and applications ideal for science and engineering students.
• Concise reasoning behind every calculus concept is presented.

Chapter 1  Functions 

1.1   Functions and Graphs
1.2   Combining Functions
1.3   Polynomial and Rational Functions
1.4   Transcendental Functions
1.5   Inverse Functions
1.6   Exponential and Logarithmic Functions
1.7   From Words to Functions
 Chapter 1 in Review

Chapter 2  Limit of a Function

2.1   Limits—An Informal Approach
2.2   Limit Theorems
2.3   Continuity
2.4 Trigonometric Limits
2.5   Limits That Involve Infinity
2.6 Limits—A Formal Approach
2.7 The Tangent Line Problem
 Chapter 2 in Review

Chapter 3  The Derivative

3.1   The Derivative
3.2   Power and Sum Rules
3.3   Product and Quotient Rules
3.4   Trigonometric Functions
3.5   Chain Rule
3.6   Implicit Differentiation
3.7   Derivatives of Inverse Functions
3.8   Exponential Functions
3.9   Logarithmic Functions
3.10  Hyperbolic Functions
 Chapter 3 in Review

Chapter 4    Applications of the Derivative

4.1   Rectilinear Motion
4.2 Related Rates
4.3   Extrema of Functions
4.4   Mean Value Theorem
4.5   Limits Revisited—L’Hôpital’s Rule
4.6   Graphing and the First Derivative
4.7   Graphing and the Second Derivative
4.8   Optimization
4.9   Linearization and Differentials
4.10  Newton’s Method
 Chapter 4 in Review 

Chapter 5    Integrals

5.1   The Indefinite Integral
5.2   Integration by the u-Substitution
5.3   The Area Problem   
5.4   The Definite Integral
5.5   Fundamental Theorem of Calculus
 Chapter 5 in Review

Chapter 6  Applications of the Integral

6.1   Rectilinear Motion Revisited
6.2   Area Revisited
6.3   Volumes of Solids: Slicing Method
6.4   Volumes of Solids: Shell Method
6.5   Length of a Graph
6.6   Area of a Surface of Revolution
6.7 Average Value of a Function
6.8   Work
6.9   Liquid Pressure and Force
6.10  Centers of Mass and Centroids
 Chapter 6 in Review

Chapter 7  Techniques of Integration

7.1 Integration—Three Resources
7.2   Integration by Substitution
7.3   Integration by Parts
7.4   Powers of Trigonometric Functions    
7.5   Trigonometric Substitutions
7.6   Partial Fractions
7.7   Improper Integrals
7.8 Approximate Integration
 Chapter 7 in Review
 

Chapter 8  First-Order Differential Equations

8.1   Separable Equations
8.2   Linear Equations
8.3   Mathematical Models
8.4  Solution Curves without a Solution    
8.5   Euler’s Method
        Chapter 8 in Review

Chapter 9  Sequences and Series

9.1 Sequences
9.2   Monotonic Sequences
9.3   Series
9.4   Integral Test
9.5  Comparison Tests
9.6   Ratio and Root Tests
9.7   Alternating Series
9.8   Power Series
9.9   Representing Functions by Power Series
9.10  Taylor Series
9.11  Binomial Series
 Chapter 9 in Review

Chapter 10  Conics and Polar Coordinates

10.1  Conic Sections
10.2    Parametric Equations
10.3    Calculus and Parametric Equations
10.4  Polar Coordinate System
10.5   Graphs of Polar Equations 
10.6   Calculus in Polar Coordinates
10.7   Conic Sections in Polar Coordinates
  Chapter 10 in Review  

Appendix
Proofs of Selected Theorems
Answers to Test Yourself
Answers to Selected Odd-Numbered Problems
Index

Resource Pages:
Review of Algebra
Formulas from Geometry
Graphs and Functions
Review of Trigonometry
Exponential and Logarithmic Functions
Differentiation
Integration Formulas

Appropriate for the first two terms in a three-term college calculus sequence.

• Chapter 2
  Chapter 2