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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. For use in or out of the classroom, the companion website LarsonCalculus.com offers free access to multiple tools and resources to supplement students’ learning.

## Digital Platforms

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WebAssign is a flexible and fully customizable online instructional solution that puts powerful tools in the hands of teachers, enabling you to realize your teaching goals and instantly assess individual student performance to help students learn math, not just do online homework.

## Features & Benefits

{{collapseContainerClosed['features'] ? 'Show More' : 'Show Less'}}- LarsonCalculus.com: The authors created a free website hosting valuable resources. At this website, students 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).
- HOW DO YOU SEE IT? Exercises: The How Do You See It? exercise in each section presents a problem that students will solve by visual inspection using the concepts learned in the lesson.
- Remarks: These hints and tips can be used to reinforce or expand upon concepts, help students learn how to study mathematics, caution them about common errors, address special cases, or show alternative or additional steps to a solution of an example.
- Exercise Sets: The exercise sets have been carefully and extensively reviewed to ensure they are rigorous, relevant, and thorough. Multi-step, real-life exercises reinforce problem-solving skills and mastery of concepts by letting you apply the concepts in real-life situations. Putnam Exam questions appear in selected sections 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.

### Calculus: Early Transcendental Functions

#### TABLE OF CONTENTS

Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Review of Trigonometric Functions. 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: Even Fourth-Degree Polynomials. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Section Project: Minimum Time. 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. Indeterminate Forms and L’Hopital’s Rule. The Natural Logarithmic Function: Integration. Inverse Trigonometric Functions: Integration. Hyperbolic Functions. Section Project: Mercator Map. Review Exercises. P.S. Problem Solving.

6. DIFFERENTIAL EQUATIONS.

Slope Fields and Euler''s Method. Growth and Decay. 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: Pyramid of Khufu. Moments, Centers of Mass, and Centroids. Fluid Pressure and Fluid Force. Review Exercises. P.S. Problem Solving.

8. INTEGRATION TECHNIQUES AND IMPROPER INTEGRALS.

Basic Integration Rules. Integration by Parts. Trigonometric Integrals. Section Project: The Wallis Product. Trigonometric Substitution. Partial Fractions. Numerical Integration. Integration by Tables and Other Integration Techniques. 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. 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: Cassini Oval. 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. 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: Surface Area in Polar Coordinates. 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. Section Project: Parachute Jump. Series Solutions of Differential Equations. Review Exercises. P.S. Problem Solving.

APPENDIX.

A. Proofs of Selected Theorems (Online).

B. Integration Tables.

C. Precalculus Review. (Online).

C.1 Real Numbers and the Real Number Line. C.2 The Cartesian Plane.

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

E. Complex Numbers. (Online).

F. Business and Economic Applications. (Online).

G. Fitting Models to Data. (Online).

### Training and Support

At Cengage, our top priority is taking care of you and your students and making sure that you have a successful experience with our products. Your personalized support team will consult with you to help you find the best solution to address your specific course goals, and once you’ve found that solution, will work with you to build your course and design a customized training and development program to ensure you and your students are ready to hit the ground running.

### Higher Ed Faculty Community

The Higher Ed Faculty Community is a collaborative space designed to inspire innovation and advance teaching excellence in higher education. Here, we’ll celebrate and support great teaching, across the country and across disciplines, ultimately advancing the richness of education and the lifelong confidence and success of college students. Plus, you will find ample resources, teaching wisdom and expert advice from your peers, from us, and from Cengage Faculty Partners so that you can spend more time doing what you do best.

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

#### Online Test Bank

ISBN: 9781337552677

Organize your course and capture your students' attention with the resources found in the Test Bank.

#### Instructor Companion Website

ISBN: 9781337552981

#### Instructor's Resource Guide

ISBN: 9781337553018

Contains a variety of resources to help you prepare and present text material in a manner that meets your personal preferences and course needs. It provides suggested homework assignments, teaching tips, worked out examples, and chapter projects.

ISBN: 9781337275422

This manual contains worked-out solutions to all exercises in Chapters 11-16 of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, Seventh Edition.

#### Complete Solutions Manual, Volume 1

ISBN: 9781337552646

This manual contains worked-out solutions to all exercises in Chapters 1-6 of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th Edition.

#### Complete Solutions Manual, Volume 2

ISBN: 9781337552653

This manual contains worked-out solutions to all exercises in Chapters 7-10 of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th Edition.

### FOR STUDENTS

#### Student Solutions Manual

ISBN: 9781337552561

This manual contains worked-out solutions for all odd-numbered exercises in Larson/Edwards' CALCULUS OF A SINGLE VARIABLE: EARLY TRANSCENDENTAL FUNCTIONS, 7th Edition (Chapters 1-10 of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th Edition).