## Request for consultation

## 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! Capstone exercise: The Capstone is a new type of exercise that appears in every section. The exercise synthesizes the main concepts of the section and presents them in one exercise. They often contain computational and non-computational parts. These exercises are excellent to work through in class to present a topic for the first time or in class homework review. The Instructor’s Resource Guide offers teaching tips on how one might use the Capstone Exercises in class.
- Larson Join In Clicker can be found on the Instructor Companion Site.
- Exercises—revised based on actual usage! New exercises abound in the ninth edition of CALCULUS. Based on analyses of actual student usage data, the exercise sets have been overhauled to improve student understanding. Many exercises were added, some were revised, and some were removed. The results are exercise sets that effectively address student learning needs.
- New! Second Order Differential Equations: Added as a new chapter to the multivariable standalone portion of the book and available online, this new chapter delves into second order differential equations. This will greatly help engineering and math majors.
- New! 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.
- 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
- Instructor Resource Guide w/Solutions—The instructor’s resource contains an abundance of resources keyed to the textbook by chapter and section, including chapter summaries, teaching strategies, multiple versions of chapter tests, final exams, gateway tests, and suggested solutions to the Chapter Openers, Explorations, Section Projects, and Technology features in the text.

P.1 Graphs and Models. P.2 Linear Models and Rates of Change. P.3 Functions and Their Graphs

P.4 Fitting Models to Data.

Chapter 1: Limits and Their Properties.

1.1 A Preview of Calculus. 1.2 Finding Limits Graphically and Numerically. 1.3 Evaluating Limits Analytically. 1.4 Continuity and One-Sided Limits. 1.5 Infinite Limits. Section Project: Graphs and Limits of Trigonometric Functions.

Chapter 2: Differentiation.

2.1 The Derivative and the Tangent Line Problem. 2.2 Basic Differentiation Rules and Rates of Change. 2.3 The Product and Quotient Rules and Higher-Order Derivatives. 2.4 The Chain Rule. 2.5 Implicit Differentiation. Section Project: Optical Illusions. 2.6 Related Rates.

Chapter 3: Applications of Differentiation.

3.1 Extrema on an Interval. 3.2 Rolle''s Theorem and the Mean Value Theorem. 3.3 Increasing and Decreasing Functions and the First Derivative Test. Section Project: Rainbows. 3.4 Concavity and the Second Derivative Test. 3.5 Limits at Infinity. 3.6 A Summary of Curve Sketching. 3.7 Optimization Problems. Section Project: Connecticut River. 3.8 Newton''s Method. 3.9 Differentials.

Chapter 4: Integration.

4.1 Antiderivatives and Indefinite Integration. 4.2 Area. 4.3 Riemann Sums and Definite Integrals. 4.4 The Fundamental Theorem of Calculus. Section Project: Demonstrating the Fundamental Theorem. 4.5 Integration by Substitution. 4.6 Numerical Integration.

Chapter 5: Logarithmic, Exponential, and Other Transcendental Functions.

5.1 The Natural Logarithmic Function: Differentiation. 5.2 The Natural Logarithmic Function: Integration. 5.3 Inverse Functions. 5.4 Exponential Functions: Differentiation and Integration. 5.5 Bases Other than e and Applications. Section Project: Using Graphing Utilities to Estimate Slope. 5.6 Inverse Trigonometric Functions: Differentiation. 5.7 Inverse Trigonometric Functions: Integration. 5.8 Hyperbolic Functions. Section Project: St. Louis Arch.

Chapter 6: Differential Equations.

6.1 Slope Fields and Euler''s Method. 6.2 Differential Equations: Growth and Decay. 6.3 Separation of Variables and the Logistic Equation. 6.4 First-Order Linear Differential Equations. Section Project: Weight Loss.

Chapter 7: Applications of Integration.

7.1 Area of a Region Between Two Curves. 7.2 Volume: The Disk Method. 7.3 Volume: The Shell Method. Section Project: Saturn. 7.4 Arc Length and Surfaces of Revolution. 7.5 Work. Section Project: Tidal Energy. 7.6 Moments, Centers of Mass, and Centroids. 7.7 Fluid Pressure and Fluid Force.

Chapter 8: Integration Techniques, L''Hopital''s Rule, and Improper Integrals.

8.1 Basic Integration Rules. 8.2 Integration by Parts. 8.3 Trigonometric Integrals. Section Project: Power Lines. 8.4 Trigonometric Substitution. 8.5 Partial Fractions. 8.6 Integration by Tables and Other Integration Techniques. 8.7 Indeterminate Forms and L''Hopital''s Rule.

Chapter 9: Infinite Series.

9.1 Sequences. 9.2 Series and Convergence. Section Project: Cantor''s Disappearing Table. 9.3 The Integral Test and p-Series. Section Project: The Harmonic Series. 9.4 Comparisons of Series. Section Project: Solera Method. 9.5 Alternating Series. 9.6 The Ratio and Root Tests. 9.7 Taylor Polynomials and Approximations. 9.8 Power Series. 9.9 Representation of Functions by Power Series. 9.10 Taylor and Maclaurin Series.

Chapter 10: Conics, Parametric Equations, and Polar Coordinates.

10.1 Conics and Calculus. 10.2 Plane Curves and Parametric Equations. Section Project: Cycloids. 10.3 Parametric Equations and Calculus. 10.4 Polar Coordinates and Polar Graphs. Section Project: Anamorphic Art. 10.5 Area and Arc Length in Polar Coordinates. 10.6 Polar Equations of Conics and Kepler''s Laws.

Chapter 11: Vectors and the Geometry of Space.

11.1 Vectors in the Plane. 11.2 Space Coordinates and Vectors in Space. 11.3 The Dot Product of Two Vectors. 11.4 The Cross Product of Two Vectors in Space. 11.5 Lines and Planes in Space. Section Project: Distances in Space. 11.6 Surfaces in Space. 11.7 Cylindrical and Spherical Coordinates.

Chapter 12: Vector-Valued Functions.

12.1 Vector-Valued Functions. Section Project: Witch of Agnesi. 12.2 Differentiation and Integration of Vector-Valued Functions. 12.3 Velocity and Acceleration. 12.4 Tangent Vectors and Normal Vectors. 12.5 Arc Length and Curvature.

Chapter 13: Functions of Several Variables.

13.1 Introduction to Functions of Several Variables. 13.2 Limits and Continuity. 13.3 Partial Derivatives. Section Project: Moiré Fringes. 13.4 Differentials. 13.5 Chain Rules for Functions of Several Variables. 13.6 Directional Derivatives and Gradients. 13.7 Tangent Planes and Normal Lines. Section Project: Wildflowers. 13.8 Extrema of Functions of Two Variables. 13.9 Applications of Extrema of Functions of Two Variables. Section Project: Building a Pipeline. 13.10 Lagrange Multipliers.

Chapter 14: Multiple Integration.

14.1 Iterated Integrals and Area in the Plane. 14.2 Double Integrals and Volume. 14.3 Change of Variables: Polar Coordinates. 14.4 Center of Mass and Moments of Inertia. Section Project: Center of Pressure on a Sail. 14.5 Surface Area. Section Project: Capillary Action. 14.6 Triple Integrals and Applications. 14.7 Triple Integrals in Cylindrical and Spherical Coordinates. Section Project: Wrinkled and Bumpy Spheres. 14.8 Change of Variables: Jacobians.

Chapter 15: Vector Analysis.

15.1 Vector Fields. 15.2 Line Integrals. 15.3 Conservative Vector Fields and Independence of Path. 15.4 Green''s Theorem. Section Project: Hyperbolic and Trigonometric Functions. 15.5 Parametric Surfaces. 15.6 Surface Integrals. Section Project: Hyperboloid of One Sheet. 15.7 Divergence Theorem. 15.8 Stokes''s Theorem. Section Project: The Planimeter.

Bonus Online Material.

Chapter 16: Additional Topics in Differential Equations (please visit URL to come).

16.1 Exact First-Order Equations. 16.2 Second-Order Homogeneous Linear Equations. 16.3 Second-Order Nonhomogeneous Linear Equations. Section Project: Parachute Jump. 16.4 Series Solutions of Differential Equations.

Book Appendices.

A. Proofs of Selected Theorems. B. Integration Tables.

Online Appendices.

C. Precalculus Review (please visit URL to come). 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 (please visit URL to come). E. Complex Numbers (please visit URL to come). F Business and Economic Applications (please visit URL to come).

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.