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Calculus 11th Edition

Ron Larson | Bruce H. Edwards

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Overview

With a long history of innovation in the market, Larson/Edwards’ CALCULUS has been widely praised by a generation of students and professors for solid and effective pedagogy that addresses the needs of a broad range of teaching and learning styles and environments. Each title in the series is one component in a comprehensive calculus course program that carefully integrates and coordinates print, media, and technology products for successful teaching and learning. Two strong digital options, Enhanced WebAssign and MindTap® are also available. MindTap® Math is the digital learning solution that powers students from memorization to mastery. It gives you complete control of your course—to provide engaging content, to challenge every individual, and to build their confidence.

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 received his Ph.D. in mathematics from the University of Colorado and is considered the pioneer of using multimedia to enhance the learning of mathematics, having authored over 30 software titles since 1990. Dr. Larson conducts numerous 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 2013 Text and Academic Authors Association Award for CALCULUS, 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 bestselling 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. Professor Edwards has produced five mathematics courses for the Great Courses (The Teaching Company). He has also coauthored a wide range of award winning mathematics textbooks with Professor Ron Larson.

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.

  • LarsonCalculus.com – The authors created a free website offering many valuable resources, including 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).
  • ENHANCED WEBASSIGN: CALCULUS, Eleventh Edition, is fully supported by Enhanced WebAssign (EWA), the powerful online homework and course management system that engages students in learning the math. EWA includes new end-of-chapter exercises, animated simulations, and pre-built assignments vetted by trusted subject matter experts along with robust course, section, assignment, and question settings and online testing to help instructors foster a deeper understanding of course concepts.
  • The How Do You See It? exercise in each section presents a problem that students 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 against 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 examined to ensure they are rigorous, relevant, and cover all topics suggested by our users. Multi-step, real-life exercises reinforce problem-solving skills and mastery of concepts by giving students the opportunity to apply the concepts in real-life situations. Putnam Exam questions push the limits of students’ understanding of calculus. Graphing technology exercises allow students to make use 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.
  • 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.

Calculus

TABLE OF CONTENTS

P. PREPARATION FOR CALCULUS.
Graphs and Models. Linear Models and Rates of Change. Functions and Their Graphs. Review of Trigonometric Functions. 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: Even Fourth-Degree Polynomials. Concavity and the Second Derivative Test. Limits at Infinity. A Summary of Curve Sketching. Optimization Problems. Section Project: Minimum Time. 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. 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. Indeterminate Forms and L’Hopital’s Rule. Inverse Trigonometric Functions: Differentiation. 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 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: 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'' 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.
B. Integration Tables.
C. Precalculus Review (Web).
C.1. Real Numbers and the Real Number Line.
C.2. The Cartesian Plane.
D. Rotation and the General Second-Degree Equation (Web).
E. Complex Numbers (Web).
F. Business and Economic Applications (Web).
G. Fitting Models to Data (Web).

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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.

Student Solutions Manual

ISBN: 9781337275392
This guide offers step-by-step solutions for all odd-numbered text exercises in Multivariable Calculus 11e (Chapters 11-16 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
Need a leg up on your homework or help to prepare for an exam? The Student Solutions Manual contains worked-out solutions for all odd-numbered exercises in Multivariable Calculus 11e (Chapters 11- 16 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.