1. Functions

1.1    Functions and Their Graphs

1.2    Combining Functions; Shifting and Scaling Graphs

1.3    Trigonometric Functions

1.4    Graphing with Software

1.5    Exponential Functions

1.6    Inverse Functions and Logarithms

2.    Limits and Continuity 

2.1    Rates of Change and Tangent Lines to Curves

2.2    Limit of a Function and Limit Laws

2.3    The Precise Definition of a Limit

2.4    One-Sided Limits

2.5    Continuity

2.6    Limits Involving Infinity; Asymptotes of Graphs

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

3.    Derivatives

3.1    Tangent Lines and the Derivative at a Point

3.2    The Derivative as a Function

3.3    Differentiation Rules

3.4    The Derivative as a Rate of Change

3.5    Derivatives of Trigonometric Functions

3.6    The Chain Rule

3.7    Implicit Differentiation

3.8    Derivatives of Inverse Functions and Logarithms

3.9    Inverse Trigonometric Functions

3.10 Related Rates

3.11 Linearization and Differentials

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

4.    Applications of Derivatives

4.1    Extreme Values of Functions on Closed Intervals

4.2    The Mean Value Theorem

4.3    Monotonic Functions and the First Derivative Test

4.4    Concavity and Curve Sketching

4.5    Indeterminate Forms and L’Hôpital’s Rule

4.6    Applied Optimization

4.7    Newton’s Method

4.8    Antiderivatives

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

5.    Integrals

5.1    Area and Estimating with Finite Sums

5.2    Sigma Notation and Limits of Finite Sums

5.3    The Definite Integral

5.4    The Fundamental Theorem of Calculus

5.5    Indefinite Integrals and the Substitution Method

5.6   Definite Integral Substitutions and the Area Between Curves

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

6.    Applications of Definite Integrals

6.1    Volumes Using Cross-Sections

6.2    Volumes Using Cylindrical Shells

6.3    Arc Length

6.4    Areas of Surfaces of Revolution

6.5    Work

6.6    Moments and Centers of Mass

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

7.    Integrals and Transcendental Functions

7.1    The Logarithm Defined as an Integral

7.2    Exponential Change and Separable Differential Equations

7.3    Hyperbolic Functions

Questions to Guide Your Review

Practice Exercises

Additional and Advanced Exercises

8.    Techniques of Integration  

8.1    Integration by Parts

8.2    Trigonometric Integrals

8.3    Trigonometric Substitutions

8.4    Integration of Rational Functions by Partial Fractions

Teach calculus the way you want to teach it, and at a level that prepares students for their STEM majors

· New co-author Chris Heil and co-author Joel Hass aim to develop students’ mathematical maturity and proficiency by going beyond memorization of formulas and routine procedures and showing how to generalize key concepts once they are introduced.

· Key topics are presented both formally and informally. The distinction between the two is clearly stated as each is developed, including an explanation as to why a formal definition is needed. Ideas are introduced with examples and intuitive explanations that are then generalized so that students are not overwhelmed by abstraction.

· Results are both carefully stated and proved throughout the book, and proofs are clearly explained and motivated. Students and instructors who proceed through the formal material will find it as carefully presented and explained as the informal development. If the instructor decides to downplay formality at any stage, it will not cause problems with later developments in the text.

· Expanded - PowerPoint^® lecture slides now include examples as well as key theorems, definitions, and figures. The files are fully editable making them a robust and flexible teaching tool.

Assess student understanding of key concepts and skills through a wide range of time-tested exercises

· Updated - Strong exercise sets feature a great breadth of problems — progressing from skills problems to applied and theoretical problems — to encourage students to think about and practice the concepts until they achieve mastery. In the 4th SI Edition, the authors added new exercises and exercise types throughout, many of which are geometric in nature.

· Writing exercises throughout the text ask students to explore and explain a variety of calculus concepts and applications.

· Technology exercises (marked with a “T”) are included in each section, requiring students to use a graphing calculator or computer when solving. In addition, Computer Explorations give the option of assigning exercises that require a computer algebra system (CAS, such as Maple or Mathematica).

Support a complete understanding of calculus for students at varying levels

· Each major topic is developed with both simple and more advanced examples to give the basic ideas and illustrate deeper concepts.

· Updated - Figures are conceived and rendered to provide insight for students and support conceptual reasoning. In the 4^th SI Edition, new figures are added to enhance understanding and graphics are revised throughout to emphasize clear visualization.

· Enhanced - Annotations within examples (shown in blue type) guide students through the problem solution and emphasize that each step in a mathematical argument is rigorously justified. For the 4th SI Edition, many more annotations were added.

· End-of-chapter materials include review questions, practice exercises covering the entire chapter, and a series of Additional and Advanced Exercises with more challenging or synthesizing problems.

Pearson MyLabTM Math is not included. Students, if Pearson MyLab Math is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. Pearson MyLab Math should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

· New co-author Chris Heil and co-author Joel Hass aim to develop students’ mathematical maturity and proficiency by going beyond memorization of formulas and routine procedures and showing how to generalize key concepts once they are introduced.

· PowerPoint^® lecture slides now include examples as well as key theorems, definitions, and figures. The files are fully editable making them a robust and flexible teaching tool.

· Strong exercise sets feature a great breadth of problems — progressing from skills problems to applied and theoretical problems — to encourage students to think about and practice the concepts until they achieve mastery. In the 4th SI Edition, the authors added new exercises and exercise types throughout, many of which are geometric in nature.

· Figures are conceived and rendered to provide insight for students and support conceptual reasoning. In the 4th SI Edition, new figures are added to enhance understanding and graphics are revised throughout to emphasize clear visualization.

· Annotations within examples (shown in blue type) guide students through the problem solution and emphasize that each step in a mathematical argument is rigorously justified. For the 4^th SI Edition, many more annotations were added.

Pearson MyLabTM Math is not included. Students, if Pearson MyLab Math is a recommended/mandatory component of the course, please ask your instructor for the correct ISBN. Pearson MyLab Math should only be purchased when required by an instructor. Instructors, contact your Pearson representative for more information.

· Assignable Exercises: New co-author Przemyslaw Bogacki analyzed aggregated student usage and performance data from MyLabTM Math for the previous edition of this text. The results of this analysis helped improve the quality and quantity of text and MyLab exercises and learning aids that matter the most to instructors and students.

· Setup & Solve Exercises: These exercises require students to show how they set up a problem as well as the solution, better mirroring what is required on tests. This new exercise type was widely praised by users of the 3rd edition, so more were added to the 4th edition. Each Setup & Solve Exercise is also now available as a regular question where just the final answer is scored.

· Additional Conceptual Questions focus on deeper, theoretical understanding of the key concepts in calculus. These questions were written by faculty at Cornell University under an NSF grant and are also assignable through Learning CatalyticsTM.

· A full suite of Interactive Figures has been added to support teaching and learning. The figures are designed to be used in lecture as well as by students independently. The figures are editable using the freely available GeoGebra software. Videos that use the Interactive Figures to explain key concepts are also included. The figures were created by Marc Renault (Shippensburg University), Steve Phelps (University of Cincinnati), Kevin Hopkins (Southwest Baptist University), and Tim Brzezinski (Berlin High School, CT).

· Instructional videos: Numerous instructional videos augment the already robust collection within the course. These videos support the overall approach of the text by going beyond routine procedures to show students how to generalize and connect key concepts. The Guide to Video-Based Assignments makes it easy to assign videos for homework by showing which Pearson MyLab Math exercises correspond to each video.