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## Overview

The Larson CALCULUS program has a long history of innovation in the calculus market. It has been widely praised by a generation of students and professors for its solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title is just one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning.

- NEW Chapter Openers - Each Chapter Opener highlights five real-life applications of calculus found throughout the chapter. The applications reference the examples or exercises featured. You can find a full listing of the applications in the Index of Applications.
- NEW HOW DO YOU SEE IT? Exercise - The How Do You See It? exercise in each section presents a problem that you will solve by visual inspection using the concepts learned in the lesson.
- NEW LarsonCalculus.com - We’ve created a free website hosting valuable resources. At this website, you can access the following: Proof Videos – Watch co-author Bruce Edwards present theorems and explain their proofs. Calculus Videos – Watch Dana Mosely explain concepts of calculus. Interactive Examples – Explore examples using Wolfram’s free CDF player (plug-in required). Rotatable Graphs – View and rotate three-dimensional graphs using Wolfram’s free CDF player (plug-in required). Biographies – Read biographies of men and women who were instrumental in creating calculus. Web Appendices – Read the web-only appendices that accompany the text. Data Downloads – Use real data to solve problems.
- Table of Contents Changes - We moved Appendix A (Proofs of Selected Theorems) to the website www.LarsonCalculus.com, which also includes videos of co-author Bruce Edwards explaining these proofs.

- CAS Investigation: Many examples throughout the book are accompanied by CAS Investigations. These are collaborative investigations using a computer algebra system (e.g., Maple) to further explore the related example. CAS Investigations are located online and in the Multimedia eBook
- REVISED Remarks - To eliminate any possible confusion, all Study Tips and Notes have been combined into one feature, Remarks. These hints and tips can be used to reinforce or expand upon concepts, help you learn how to study mathematics, caution you about common errors, address special cases, or show alternative or additional steps to a solution of an example.
- REVISED Exercise Sets - The exercise sets have been carefully and extensively examined to ensure they are rigorous, relevant, and cover all topics suggested by our users. The exercises have been reorganized and titled so you can better see the connections between examples and exercises. Multi-step, real-life exercises reinforce problem-solving skills and mastery of concepts by giving you the opportunity to apply the concepts in real-life situations. Putnam Exam questions to push the limits of students’ understanding of calculus. Graphing technology exercises for students to make us of a graphing utility to help find solutions.
- Second Order Differential Equations: Available online, this chapter delves into second order differential equations. This will greatly help engineering and math majors.
- Enhanced WebAssign Course: The Larson EWA course has over 3,900 textbook questions which have been drawn from the book, and offer more coverage of problems and topics than most online homework programs for Calculus. The EWA course for Larson CALCULUS will present numerous section-level video lessons by Dana Mosely and animated tutorials. In addition to these assets, the course includes exercise-level features: Read It, Watch It, Master It, and Chat About It links. These tools benefit students with varied learning styles to ensure they get the most out of their online learning experience.
- Graded Homework Exercises: Online homework and tests are evaluated using powerful Maple software to ensure mathematical accuracy. Instructors control point values, weighting grades, and whether of not an item is graded. An electronic gradebook helps instructors manage course information easily and can be exported to other files, such as Excel.

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

1. 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.

2. 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. Related Rates. Review Exercises. P.S. Problem Solving.

3. 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. Newton''s Method. Differentials. Review Exercises. P.S. Problem Solving.

4. 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. Review Exercises.

P.S. Problem Solving.

5. LOGARITHMIC, EXPONENTIAL, AND OTHER TRANSCENDENTAL FUNCTIONS.

The Natural Logarithmic Function: Differentiation. The Natural Logarithmic Function: Integration. Inverse Functions. Exponential Functions: Differentiation and Integration. Bases Other than e and Applications. Section Project: Using Graphing Utilities to Estimate Slope. Inverse Trigonometric Functions: Differentiation. 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. Separation of Variables and the Logistic Equation. First-Order Linear Differential Equations. Section Project: Weight Loss. 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.

10.6 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. SECOND ORDER DIFFERENTIAL EQUATIONS* ONLINE.

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.

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).

F. Business and Economic Applications (Web).

Cengage provides a range of supplements that are updated in coordination with the main title selection. For more information about these supplements, contact your Learning Consultant.

### FOR INSTRUCTORS

#### Instructor's Resource Guide

ISBN: 9781337275453

The robust Instructor’s Resource Guide contains an abundance of resources to aid instructors in preparing and presenting text material in a manner that meets their personal preferences and course needs. It provides a variety of tools keyed to the textbook at the section and chapter level, including section objectives, teaching tips, and chapter projects. An electronic version of the Instructor Guide is available on the PowerLecture DVD.

#### Cengage Learning Testing, powered by Cognero® Instant Access

ISBN: 9781337275613

Cengage Learning Testing Powered by Cognero® is a flexible, online system that allows you to author, edit, and manipulate content from the text's test bank or elsewhere, including your own favorite test questions; create multiple test versions in an instant; and deliver tests from your LMS, your classroom, or wherever you want. This is available online via www.cengage.com/login.

#### Student Solutions Manual

ISBN: 9781337275385

This guide offers step-by-step solutions for all odd-numbered text exercises in Calculus of a Single Variable 11e (Chapters P-11 of Calculus 11e). The worked-out solutions give students a way to check their answers, ensure that they took the correct steps to arrive at an answer, and help them understand how to solve even the toughest problems.

#### Instructor's Website

ISBN: 9781337275439

Microsoft® PowerPoint® slides and image library for the entire book, posted on the Instructor Companion Website, let you incorporate images from the book right into your lectures. Also posted on the Instructor Companion site, is the Complete Solutions Manual for Larson/Edwards, Calculus, 11th manual provides complete solutions to all the exercises from the text.

### FOR STUDENTS

#### Student Solutions Manual

ISBN: 9781337275385

Need a leg up on your homework or help to prepare for an exam? The Student Solutions Manual contains step-by-step, worked-out solutions for all odd-numbered exercises in Calculus of a Single Variable 11e (Chapters P-11 of Calculus 11e). This gives you a quick and easy way to check your answers, make sure you took the right steps to arrive at an answer, and help you understand how to solve those tough problems.

#### Student Solutions Manual

ISBN: 9781337275392

This manual contains worked-out solutions for all odd-numbered exercises for Chapters 11-16 in Larson/Edwards' CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th Edition.