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## Overview

Designed for the three-semester engineering calculus course, CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th 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 seventh 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.

- Stepped-out solution videos with instruction are available at CalcView.com for selected exercises throughout the text. The selected textbook exercises will have a QR code next to the exercise number for easy access via a smart phone.
- The Section Projects have been carefully and extensively examined to ensure they are rigorous and relevant. The authors have added and revised a number of these projects.
- More conceptual exercises have been added to help students better understand the concepts being taught in each section.
- The Section Projects have been carefully and extensively examined to ensure they are rigorous and relevant. The authors have added and revised a number of these projects

- 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 or not an item is graded. An electronic gradebook helps instructors manage course information easily and can be exported to other files, such as Excel.
- 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.
- WebAssign Course: The Larson WebAssign course has over 3,900 textbook questions drawn from the book, that offer more coverage of problems and topics than most online homework programs for Calculus. The WebAssign 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 Talk to a Tutor links. These tools benefit students with varied learning styles to ensure they get the most out of their online learning experience.

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).

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.

#### Complete Solutions Manual, Volume 3

ISBN: 9781337275422

This manual contains worked-out solutions to all exercises in Chapters 11-16 of CALCULUS: EARLY TRANSCENDENTAL FUNCTIONS, 7th 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.

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