Higher Education

Essential Calculus: Early Transcendental Functions, 1st Edition

  • Ron Larson The Pennsylvania State University, The Behrend College
  • Robert P. Hostetler The Pennsylvania State University, The Behrend College
  • Bruce H. Edwards University of Florida
  • ISBN-10: 0618879188  |  ISBN-13: 9780618879182
  • 1008 Pages
  • © 2008 | Published
  • College Bookstore Wholesale Price = $215.00
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About

Overview

Essential Calculus: Early Transcendental Functions responds to the growing demand for a more streamlined and faster paced text at a lower price for students. This text continues the Larson tradition by offering instructors proven pedagogical techniques and accessible content and innovative learning resources for student success.

Features and Benefits

  • Clear, multi-step examples with worked-out solutions help students learn complex mathematical concepts. Examples correspond to the exercises, serving as a supportive reference for students. This is the only text on the market where every example, proof, and explanation begins and ends on the same page.
  • A variety of exercise types are included in each exercise set involving skills, writing, critical thinking, problem solving, applications, and real-data applications.
  • Explorations help students develop an intuitive understanding of calculus concepts. These optional activities are short enough to integrate into class, but they can also be omitted without loss of continuity.
  • Putnam Exam Questions--taken from the William Lowell Putnam Mathematical Competition--offer challenging problems, requiring students to look for creative solutions; Graphical Analysis exercises offer the opportunity to analyze graphs; Think About It exercises ask students to use critical reasoning skills to explore calculus.
  • Writing About Concepts exercises help students develop a better understanding of the key concepts of each section. Writing questions help teachers assess students' ability to explain concepts accurately.
  • Notes integrated in the margins throughout the text enhance student understanding and help students to avoid common errors and misunderstandings.Theorem boxes clearly present important mathematical concepts.

Table of Contents

Note: Each chapter concludes with Review Exercises.
1. Limits and Their Properties
1.1 Linear Models and Rates of Change
1.2 Functions and Their Graphs
1.3 Inverse Functions
1.4 Exponential and Logarithmic Functions
1.5 Finding Limits Graphically and Numerically
1.6 Evaluating Limits Analytically
1.7 Continuity and One-Sided Limits
1.8 Infinite Limits
2. Differentiation
2.1 The Derivative and the Tangent Line Problem
2.2 Basic Differentiation Rules and Rates of Change
2.3 Product and Quotient Rules and Higher-Order Derivatives
2.4 The Chain Rule
2.5 Implicit Differentiation
2.6 Derivatives of Inverse Functions
2.7 Related Rates
2.8 Newton''s Method
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
3.4 Concavity and the Second Derivative Test
3.5 Limits at Infinity
3.6 Optimization Problems
3.7 Differentials
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
4.5 Integration by Substitution
4.6 Numerical Integration
4.7 The Natural Logarithmic Function: Integration
4.8 Inverse Trigonometric Functions: Integration
4.9 Hyperbolic Functions
5. Applications of Integration
5.1 Area of a Region Between Two Curves
5.2 Volume: The Disk Method
5.3 Volume: The Shell Method
5.4 Arc Length and Surfaces of Revolution
5.5 Applications in Physics and Engineering
5.6 Differential Equations: Growth and Decay
6. Integration Techniques, L''Hôpital''s Rule, and Improper Integrals
6.1 Integration by Parts
6.2 Trigonometric Integrals
6.3 Trigonometric Substitution
6.4 Partial Fractions
6.5 Integration by Tables and Other Integration Techniques
6.6 Indeterminate Forms and L''Hôpital''s Rule
6.7 Improper Integrals
7. Infinite Series
7.1 Sequences
7.2 Series and Convergence
7.3 The Integral and Comparison Tests
7.4 Other Convergence Tests
7.5 Taylor Polynomials and Approximations
7.6 Power Series
7.7 Representation of Functions by Power Series
7.8 Taylor and Maclaurin Series
8. Conics, Parametric Equations, and Polar Coordinates
8.1 Plane Curves and Parametric Equations
8.2 Parametric Equations and Calculus
8.3 Polar Coordinates and Polar Graphs
8.4 Area and Arc Length in Polar Coordinates
8.5 Polar Equations and Conics and Kepler''s Laws
9. Vectors and the Geometry of Space
9.1 Vectors in the Plane
9.2 Space Coordinates and Vectors in Space
9.3 The Dot Product of Two Vectors
9.4 The Cross Product of Two Vectors in Space
9.5 Lines and Planes in Space
9.6 Surfaces in Space
9.7 Cylindrical and Spherical Coordinates
10. Vector-Valued Functions
10.1 Vector-Valued Functions
10.2 Differentiation and Integration of Vector-Valued Functions
10.3 Velocity and Acceleration
10.4 Tangent Vectors and Normal Vectors
10.5 Arc Length and Curvature
11. Functions of Several Variables
11.1 Introduction to Functions of Several Variables
11.2 Limits and Continuity
11.3 Partial Derivatives
11.4 Differentials and the Chain Rule
11.5 Directional Derivatives and Gradients
11.6 Tangent Planes and Normal Lines
11.7 Extrema of Functions of Two Variables
11.8 Lagrange Multipliers
12. Multiple Integration
12.1 Iterated Integrals and Area in the Plane
12.2 Double Integrals and Volume
12.3 Change of Variables: Polar Coordinates
12.4 Center of Mass and Moments of Inertia
12.5 Surface Area
12.6 Triple Integrals and Applications
12.7 Triple Integrals in Cylindrical and Spherical Coordinates
12.8 Change of Variables: Jacobians
13. Vector Analysis
13.1 Vector Fields
13.2 Line Integrals
13.3 Conservative Vector Fields and Independence of Path
13.4 Green''s Theorem
13.5 Parametric Surfaces
13.6 Surface Integrals
13.7 Divergence Theorem
13.8 Stokes''s Theorem
Appendix A Proofs of Selected Theorems
Appendix B Integration Tables
Appendix C Business and Economic Applications
Answers to Odd-Numbered Exercises
Index
Additional Appendices
Appendix D Precalculus Review
D.1 Real Numbers and the Real Number Line
D.2 The Cartesian Plane
D.3 Review of Trigonometric Functions
Appendix E Rotation and General Second-Degree Equation
Appendix F Complex Numbers

Supplements

All supplements have been updated in coordination with the main title. Select the main title's "About" tab, then select "What's New" for updates specific to title's edition.

For more information about these supplements, or to obtain them, contact your Learning Consultant.

Instructor Supplements

Online Complete Solutions Guide, Volume 3  (ISBN-10: 0618879250 | ISBN-13: 9780618879250)

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Online Complete Solutions Guide, Volume 2  (ISBN-10: 0618879242 | ISBN-13: 9780618879243)

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Online Complete Solutions Guide, Volume 1  (ISBN-10: 0618879234 | ISBN-13: 9780618879236)

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Eduspace Plus: Essential Calculus  (ISBN-10: 0618925929 | ISBN-13: 9780618925926)

Your Eduspace Plus Student Passkey will be sent to you digitally via your online purchase receipt and also sent via email.Your passkey is needed in order to access an Eduspace Plus course. Individual passkeys must be purchased for each course enrollment.Eduspace is Houghton Mifflin's online learning tool. It may be required by your instructor to complete online homework and assignments. Eduspace also offers powerful tools and text-specific content that will help you get a better grade.Eduspace Plus courses contain:

List Price = $100.00  | College Bookstore Wholesale Price = $100.00

Blackboard/WebCT - Essential Calculus: Early Transcendental Functions  (ISBN-10: 0618879285 | ISBN-13: 9780618879281)

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Online Instructor's Resource Guide  (ISBN-10: 0618879218 | ISBN-13: 9780618879212)

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Enhanced WebAssign Homework Only Printed Access Card for Math and Science  (ISBN-10: 1305408047 | ISBN-13: 9781305408043)

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $70.50

Enhanced Webassign Homework Only Printed Access Card for Multiple-Term Math and Science  (ISBN-10: 1305408039 | ISBN-13: 9781305408036)

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $93.75

Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses  (ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses, Life of Edition  (ISBN-10: 1285858263 | ISBN-13: 9781285858265)

IMPORTANT: When purchasing this printed access card for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If your students need to retake the course and you are using the same book AND edition then they will not need to buy a new code. If you are not certain this is the correct access code for your course, please contact your Cengage Learning Consultant.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Student Supplements

Eduspace Plus: Essential Calculus  (ISBN-10: 0618925929 | ISBN-13: 9780618925926)

Your Eduspace Plus Student Passkey will be sent to you digitally via your online purchase receipt and also sent via email.Your passkey is needed in order to access an Eduspace Plus course. Individual passkeys must be purchased for each course enrollment.Eduspace is Houghton Mifflin's online learning tool. It may be required by your instructor to complete online homework and assignments. Eduspace also offers powerful tools and text-specific content that will help you get a better grade.Eduspace Plus courses contain:

List Price = $100.00  | College Bookstore Wholesale Price = $100.00

Blackboard/WebCT - Essential Calculus: Early Transcendental Functions  (ISBN-10: 0618879285 | ISBN-13: 9780618879281)

List Price = $.00  | College Bookstore Wholesale Price = $.00

Enhanced WebAssign Homework Only Printed Access Card for Math and Science  (ISBN-10: 1305408047 | ISBN-13: 9781305408043)

List Price = $94.00  | CengageBrain Price = $94.00  | College Bookstore Wholesale Price = $70.50

Enhanced Webassign Homework Only Printed Access Card for Multiple-Term Math and Science  (ISBN-10: 1305408039 | ISBN-13: 9781305408036)

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $93.75

Enhanced WebAssign Instant Access for Calculus, Multi-Term Courses  (ISBN-10: 1285858255 | ISBN-13: 9781285858258)

IMPORTANT: When purchasing this instant access code for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. This instant access code will be delivered via email when purchased. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | CengageBrain Price = $125.00  | College Bookstore Wholesale Price = $125.00

Enhanced WebAssign Printed Access Card for Calculus, Multi-Term Courses, Life of Edition  (ISBN-10: 1285858263 | ISBN-13: 9781285858265)

IMPORTANT: When purchasing this printed access card for Calculus, ensure that you are using it in a Calculus course. Use with a different course may cause complications with access. Exclusively from Cengage Learning, Enhanced WebAssign combines exceptional mathematics content with the most powerful online homework solution, WebAssign. Enhanced WebAssign engages students with immediate feedback, rich tutorial content, and an interactive, fully customizable eBook, Cengage YouBook helping students to develop a deeper conceptual understanding of their subject matter. This access code includes access to Enhanced WebAssign and life-of-edition access to the eBook for the registered edition of that text. If you need to retake the course and your instructor is using the same book AND edition then you will not need to buy a new code. If you are not certain this is the correct access code for your course, please contact your instructor.

List Price = $125.00  | College Bookstore Wholesale Price = $93.75

Meet the Author

Author Bio

Ron Larson

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 2014 Text and Academic Authors Association TEXTY Award for PRECALCULUS, 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 best-selling Calculus series published by Cengage Learning.

Robert P. Hostetler

The Pennsylvania State University, The Behrend College Bio: Robert P. Hostetler received his Ph.D. in mathematics from The Pennsylvania State University in 1970. He has taught at Penn State for many years and has authored several calculus, precalculus, and intermediate algebra textbooks. His teaching specialties include remedial algebra, calculus, and math education, and his research interests include mathematics education and textbooks.

Bruce H. Edwards

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. He has also coauthored a wide range of award winning mathematics textbooks with Professor Ron Larson.