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Stay on current Cengage site**WebAssign** is a powerful digital solution designed by educators to help students learn maths and science, not just do homework. Instructors get the flexibility to define mastery thresholds and manage student learning aids down to the question level giving students the support they need to learn when they need it. **WebAssign** provides extensive content, instant assessment, and superior support.

Designed for the three-semester engineering calculus course, CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition, continues to offer instructors and students innovative teaching and learning resources. The Larson team always has two main objectives for text revisions: to develop precise, readable materials for students that clearly define and demonstrate concepts and rules of calculus; and to design comprehensive teaching resources for instructors that employ proven pedagogical techniques and save time. The Larson/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student. Every edition from the first to the sixth of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas.

1. PREPARATION FOR CALCULUS.

Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Fitting Models to Data. Inverse Functions. Exponential and Logarithmic Functions. Review Exercises. P.S. Problem Solving.

2. LIMITS AND THEIR PROPERTIES.

A Preview of Calculus. Finding Limits Graphically and Numerically. Evaluating Limits Analytically. Continuity and One-Sided Limits. Infinite Limits. Section Project: Graphs and Limits of Trigonometric Functions. Review Exercises. P.S. Problem Solving.

3. DIFFERENTIATION.

The Derivative and the Tangent Line Problem. Basic Differentiation Rules and Rates of Change. Product and Quotient Rules and Higher-Order Derivatives. The Chain Rule. Implicit Differentiation. Section Project: Optical Illusions. Derivatives of Inverse Functions, Related Rates. Newton's Method. Review Exercises. P.S. Problem Solving.

4. APPLICATIONS OF DIFFERENTIATION.

Extrema on an Interval. Rolle's Theorem and the Mean Value Theorem. Increasing and Decreasing Functions and the First Derivative Test. Section Project: Rainbows. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Section Project: Connecticut River. Differentials. Review Exercises. P.S. Problem Solving.

5. INTEGRATION.

Antiderivatives and Indefinite Integration. Area. Riemann Sums and Definite Integrals. The Fundamental Theorem of Calculus. Section Project: Demonstrating the Fundamental Theorem. Integration by Substitution. Numerical Integration. The Natural Logarithmic Function: Integration. Inverse Trigonometric Functions: Integration. Hyperbolic Functions. Section Project: St. Louis Arch. Review Exercises. P.S. Problem Solving.

6. DIFFERENTIAL EQUATIONS.

Slope Fields and Euler's Method. Differential Equations: Growth and Decay. Differential Equations: Separation of Variables. The Logistic Equation. First-Order Linear Differential Equations. Section Project: Weight Loss. Predator-Prey Differential Equations. Review Exercises. P.S. Problem Solving.

7. APPLICATIONS OF INTEGRATION.

Area of a Region Between Two Curves. Volume: The Disk Method. Volume: The Shell Method. Section Project: Saturn. Arc Length and Surfaces of Revolution. Work. Section Project: Tidal Energy. Moments, Centers of Mass, and Centroids. Fluid Pressure and Fluid Force. Review Exercises. P.S. Problem Solving.

8. INTEGRATION TECHNIQUES, L'HOPITAL'S RULE, AND IMPROPER INTEGRALS.

Basic Integration Rules. Integration by Parts. Trigonometric Integrals. Section Project: Power Lines. Trigonometric Substitution. Partial Fractions. Integration by Tables and Other Integration Techniques. Indeterminate Forms and L'Hopital's Rule. Improper Integrals. Review Exercises. P.S. Problem Solving.

9. INFINITE SERIES.

Sequences. Series and Convergence. Section Project: Cantor's Disappearing Table. The Integral Test and p-Series. Section Project: The Harmonic Series. Comparisons of Series. Section Project: Solera Method. Alternating Series. The Ratio and Root Tests. Taylor Polynomials and Approximations. Power Series. Representation of Functions by Power Series. Taylor and Maclaurin Series. Review Exercises. P.S. Problem Solving.

10. CONICS, PARAMETRIC EQUATIONS, AND POLAR COORDINATES.

Conics and Calculus. Plane Curves and Parametric Equations. Section Project: Cycloids. Parametric Equations and Calculus. Polar Coordinates and Polar Graphs. Section Project: Anamorphic Art. Area and Arc Length in Polar Coordinates. Polar Equations of Conics and Kepler's Laws. Review Exercises. P.S. Problem Solving.

11. VECTORS AND THE GEOMETRY OF SPACE.

Vectors in the Plane. Space Coordinates and Vectors in Space. The Dot Product of Two Vectors. The Cross Product of Two Vectors in Space. Lines and Planes in Space. Section Project: Distances in Space. Surfaces in Space. Cylindrical and Spherical Coordinates. Review Exercises. P.S. Problem Solving.

12. VECTOR-VALUED FUNCTIONS.

Vector-Valued Functions. Section Project: Witch of Agnesi. Differentiation and Integration of Vector-Valued Functions. Velocity and Acceleration. Tangent Vectors and Normal Vectors. Arc Length and Curvature. Review Exercises. P.S. Problem Solving.

13. FUNCTIONS OF SEVERAL VARIABLES.

Introduction to Functions of Several Variables. Limits and Continuity. Partial Derivatives. Section Project: Moiré Fringes. Differentials. Chain Rules for Functions of Several Variables. Directional Derivatives and Gradients. Tangent Planes and Normal Lines. Section Project: Wildflowers. Extrema of Functions of Two Variables. Applications of Extrema of Functions of Two Variables. Section Project: Building a Pipeline. Lagrange Multipliers. Review Exercises. P.S. Problem Solving.

14. MULTIPLE INTEGRATION.

Iterated Integrals and Area in the Plane. Double Integrals and Volume. Change of Variables: Polar Coordinates. Center of Mass and Moments of Inertia. Section Project: Center of Pressure on a Sail. Surface Area. Section Project: Capillary Action. Triple Integrals and Applications. Triple Integrals in Cylindrical and Spherical Coordinates. Section Project: Wrinkled and Bumpy Spheres. Change of Variables: Jacobians. Review Exercises. P.S. Problem Solving.

15. VECTOR ANALYSIS.

Vector Fields. Line Integrals. Conservative Vector Fields and Independence of Path. Green's Theorem. Section Project: Hyperbolic and Trigonometric Functions. Parametric Surfaces. Surface Integrals. Section Project: Hyperboloid of One Sheet. Divergence Theorem. Stokes's Theorem. Review Exercises. Section Project: The Planimeter. P.S. Problem Solving.

16. ADDITIONAL TOPICS IN DIFFERENTIAL EQUATIONS (Web).

Exact First-Order Equations. Second-Order Homogeneous Linear Equations. Second-Order Nonhomogeneous Linear Equations. Series Solutions of Differential Equations. Review Exercises. P.S. Problem Solving.

APPENDIX.

A. Proofs of Selected Theorems (Web).

B. Integration Tables.

C. Precalculus Review. (Web).

C.1 Real Numbers and the Real Number Line. C.2 The Cartesian Plane. C.3 Review of Trigonometric Functions.

D. Rotation and the General Second-Degree Equation (Web).

E. Complex Numbers. (Web).

- How Do You See It?--The "How Do You See It?" feature in each section presents a real-life problem that students solve by visual inspection using the concepts learned in the lesson. This exercise is excellent for classroom discussion or test preparation.
- LarsonCalulus.com--This robust companion website offers multiple tools and resources. Access to these features is free. Students can watch videos explaining concepts or proofs from the book, explore examples, view three-dimensional graphs, download articles from math journals, and much more!
- Interactive Examples--Examples throughout the book are accompanied by interactive examples at LarsonCalculus.com. These interactive examples use Wolfram's free CDF Player and allow students to explore calculus by manipulating functions or graphs, and observing the results.
- Proof Videos--Students can watch videos of co-author Bruce Edwards as he explains the proofs of the theorems in CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Sixth Edition, at LarsonCalculus.com.
- Remark--These hints and tips reinforce or expand on concepts, help students learn how to study mathematics, caution students about common errors, address special cases, or show alternative or additional steps to a solution of an example.

- Applications - Carefully chosen applied exercises and examples are included throughout to address the question, “When will I use this?” These applications are pulled from diverse sources, such as current events, world data, industry trends, and more, and relate to a wide range of interests.
- Writing About Concepts - Writing exercises at the end of each section are designed to test students' understanding of basic concepts in each section, encouraging them to verbalize and write answers and promote technical skills that will be invaluable in their future careers.
- Theorems - Theorems provide the conceptual framework for calculus. Theorems are clearly stated and separated from the rest of the text by boxes for quick visual reference. Key proofs often follow the theorem and can be found on LarsonCalculus.com.
- Definitions - As with theorems, definitions are clearly stated using precise, formal wording and are separated from the text by boxes for quick visual reference.
- Explorations - Explorations provide unique challenges to study concepts that have not yet been formally covered in the text. They allow students to learn by discovery and introduce topics related to ones presently being studied. Exploring topics in this way encourages students to think outside the box.
- Historical Notes and Biographies - Historical notes provide students with background information on the foundations of calculus. The Biographies introduce students to the people who created and contributed to calculus.
- Technology - Throughout the book, technology boxes show students how to use technology to solve problems and explore concepts of calculus. These tips also point out some of the pitfalls of using technology.
- Section Projects - Projects appear in selected sections and encourage students to explore applications related to the topics they are studying. They provide an interesting and engaging way for students to work and investigate ideas collaboratively.
- Putnam Exam Challenges - Putnam Exam Questions appear in selected sections. These actual Putnam Exam questions will challenge students and push them to the limits of their understanding of calculus.

**Ron Larson**

The Pennsylvania State University, The Behrend College

Dr. Ron Larson is a professor of Mathematics at The Pennsylvania State University, where he has taught since 1970. He is considered the pioneer of using multimedia to enhance the learning of Mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts seminars and in-service workshops for math educators around the country about using computer technology as an instructional tool and motivational aid. He is the recipient of the 2014 William Holmes McGuffey Longevity Award for CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, the 2014 Text and Academic Authors Association TEXTY Award for PRECALCULUS, the 2012 William Holmes McGuffey Longevity Award for CALCULUS: AN APPLIED APPROACH, and the 1996 Text and Academic Authors Association TEXTY Award for INTERACTIVE CALCULUS--a complete text on CD-ROM that was the first mainstream college textbook to be offered on the internet. Dr. Larson authors numerous textbooks including the best-selling Calculus series published by Cengage.

**Bruce H. Edwards**

University of Florida

Dr. Bruce H. Edwards is Professor of Mathematics at the University of Florida. Professor Edwards received his B.S. in Mathematics from Stanford University and his Ph.D. in Mathematics from Dartmouth College. He taught mathematics at a university near Bogotá, Colombia, as a Peace Corps volunteer. While teaching at the University of Florida, Professor Edwards has won many teaching awards, including Teacher of the Year in the College of Liberal Arts and Sciences, Liberal Arts and Sciences Student Council Teacher of the Year, and the University of Florida Honors Program Teacher of the Year. He was selected by the Office of Alumni Affairs to be the Distinguished Alumni Professor for 1991–1993. Professor Edwards has taught a variety of mathematics courses at the University of Florida, from first-year calculus to graduate-level classes in algebra and numerical analysis. He has been a frequent speaker at research conferences and meetings of the National Council of Teachers of Mathematics. He has also coauthored a wide range of award winning mathematics textbooks with Professor Ron Larson.

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