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Designed for the first two semesters of a three-semester engineering calculus course, Calculus of a Single Variable: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of this book: 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/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student.
Calculus of a Single Variable: Early Transcendental Functions, 4/e, contains Chapters 1-10 of the full Calculus: Early Transcendental Functions, 4/e, text.
Every edition from the first to the fourth of Calculus: Early Transcendental Function, 4/e, has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.
1. Preparation for Calculus
1.1 Graphs and Models
1.2 Linear Models and Rates of Change
1.3 Functions and Their Graphs
1.4 Fitting Models to Data
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
2. Limits and Their Properties
2.1 A Preview of Calculus
2.2 Finding Limits Graphically and Numerically
2.3 Evaluating Limits Analytically
2.4 Continuity and One-Sided Limits
2.5 Infinite Limits
Section Project: Graphs and Limits of Trig Functions
3. Differentiation
3.1 The Derivative and the Tangent Line Problem
3.2 Basic Differentiation Rules and Rates of Change
3.3 The Product and Quotient Rules and Higher-Order Derivatives
3.4 The Chain Rule
3.5 Implicit Differentiation
Section Project: Optical Illusions
3.6 Derivatives of Inverse Functions
3.7 Related Rates
3.8 Newton's Method
4. Applications of Differentiation
4.1 Extrema on an Interval
4.2 Rolle's Theorem and the Mean Value Theorem
4.3 Increasing and Decreasing Functions and the First Derivative Test
Section Project: Rainbows
4.4 Concavity and the Second Derivative Test
4.5 Limits at Infinity
4.6 A Summary of Curve Sketching
4.7 Optimization Problems
Section Project: Connecticut River
4.8 Differentials
5. Integration
5.1 Antiderivatives and Indefinite Integration
5.2 Area
5.3 Riemann Sums and Definite Integrals
5.4 The Fundamental Theorem of Calculus
Section Project: Demonstrating the Fundamental Theorem
5.5 Integration by Substitution
5.6 Numerical Integration
5.7 The Natural Logarithmic Function: Integration
5.8 Inverse Trigonometric Functions: Integration
5.9 Hyperbolic Functions
Section Project: St. Louis Arch
6. Differential Equations
6.1 Slope Fields and Euler's Method
6.6 Differential Equations: Growth and Decay
6.7 Differential Equations: Separation of Variables
6.4 The Logistic Equation
6.5 First-Order Linear Differential Equations
Section Project: Weight Loss
6.6 Predator-Prey Differential Equations
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
7.4 Arc Length and Surfaces of Revolution
7.5 Work
7.6 Moments, Centers of Mass, and Centroids
7.7 Fluid Pressure and Fluid Force
8. Integration Techniques, L'Hopital's Rule, and Improper Integrals
8.1 Basic Integration Rules
8.2 Integration by Parts
8.3 Trigonometric Integrals
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
8.8 Improper Integrals
9. Infinite Series
9.1 Sequences
9.2 Series and Convergence
9.3 The Integral Test and p-Series
9.4 Comparisons of Series
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
10. Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
10.2 Plane Curves and Parametric Equations
10.3 Parametric Equations and Calculus
10.4 Polar Coordinates and Polar Graphs
10.5 Area and Arc Length in Polar Coordinates
10.6 Polar Equations of Conics and Kepler's Laws
Appendices
Appendix A Proofs of Selected Theorems
Appendix B Integration Tables
Appendix C Business and Economic Applications
Additional Appendices
The following appendices are available at the textbook website, on the HM mathSpace Student CD-ROM, and the HM ClassPrep with HM Testing CD-ROM.
Appendix D Precalculus Review
Appendix E Rotation and the General Second-Degree Equation
Appendix F Complex Numbers
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Ron Larson, Robert Hostetler and Bruce H. Edwards
ISBN13: 978-0618606252Designed for the first two semesters of a three-semester engineering calculus course, Calculus of a Single Variable: Early Transcendental Functions, 4/e, continues to offer instructors and students innovative teaching and learning resources. Two primary objectives guided the authors in the revision of this book: 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/Hostetler/Edwards Calculus program offers a solution to address the needs of any calculus course and any level of calculus student.
Calculus of a Single Variable: Early Transcendental Functions, 4/e, contains Chapters 1-10 of the full Calculus: Early Transcendental Functions, 4/e, text.
Every edition from the first to the fourth of Calculus: Early Transcendental Function, 4/e, has made the mastery of traditional calculus skills a priority, while embracing the best features of new technology and, when appropriate, calculus reform ideas. Now, the Fourth Edition is part of the first calculus program to offer algorithmic homework and testing created in Maple so that answers can be evaluated with complete mathematical accuracy.
Table of Contents
1. Preparation for Calculus
1.1 Graphs and Models
1.2 Linear Models and Rates of Change
1.3 Functions and Their Graphs
1.4 Fitting Models to Data
1.5 Inverse Functions
1.6 Exponential and Logarithmic Functions
2. Limits and Their Properties
2.1 A Preview of Calculus
2.2 Finding Limits Graphically and Numerically
2.3 Evaluating Limits Analytically
2.4 Continuity and One-Sided Limits
2.5 Infinite Limits
Section Project: Graphs and Limits of Trig Functions
3. Differentiation
3.1 The Derivative and the Tangent Line Problem
3.2 Basic Differentiation Rules and Rates of Change
3.3 The Product and Quotient Rules and Higher-Order Derivatives
3.4 The Chain Rule
3.5 Implicit Differentiation
Section Project: Optical Illusions
3.6 Derivatives of Inverse Functions
3.7 Related Rates
3.8 Newton's Method
4. Applications of Differentiation
4.1 Extrema on an Interval
4.2 Rolle's Theorem and the Mean Value Theorem
4.3 Increasing and Decreasing Functions and the First Derivative Test
Section Project: Rainbows
4.4 Concavity and the Second Derivative Test
4.5 Limits at Infinity
4.6 A Summary of Curve Sketching
4.7 Optimization Problems
Section Project: Connecticut River
4.8 Differentials
5. Integration
5.1 Antiderivatives and Indefinite Integration
5.2 Area
5.3 Riemann Sums and Definite Integrals
5.4 The Fundamental Theorem of Calculus
Section Project: Demonstrating the Fundamental Theorem
5.5 Integration by Substitution
5.6 Numerical Integration
5.7 The Natural Logarithmic Function: Integration
5.8 Inverse Trigonometric Functions: Integration
5.9 Hyperbolic Functions
Section Project: St. Louis Arch
6. Differential Equations
6.1 Slope Fields and Euler's Method
6.6 Differential Equations: Growth and Decay
6.7 Differential Equations: Separation of Variables
6.4 The Logistic Equation
6.5 First-Order Linear Differential Equations
Section Project: Weight Loss
6.6 Predator-Prey Differential Equations
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
7.4 Arc Length and Surfaces of Revolution
7.5 Work
7.6 Moments, Centers of Mass, and Centroids
7.7 Fluid Pressure and Fluid Force
8. Integration Techniques, L'Hopital's Rule, and Improper Integrals
8.1 Basic Integration Rules
8.2 Integration by Parts
8.3 Trigonometric Integrals
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
8.8 Improper Integrals
9. Infinite Series
9.1 Sequences
9.2 Series and Convergence
9.3 The Integral Test and p-Series
9.4 Comparisons of Series
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
10. Conics, Parametric Equations, and Polar Coordinates
10.1 Conics and Calculus
10.2 Plane Curves and Parametric Equations
10.3 Parametric Equations and Calculus
10.4 Polar Coordinates and Polar Graphs
10.5 Area and Arc Length in Polar Coordinates
10.6 Polar Equations of Conics and Kepler's Laws
Appendices
Appendix A Proofs of Selected Theorems
Appendix B Integration Tables
Appendix C Business and Economic Applications
Additional Appendices
The following appendices are available at the textbook website, on the HM mathSpace Student CD-ROM, and the HM ClassPrep with HM Testing CD-ROM.
Appendix D Precalculus Review
Appendix E Rotation and the General Second-Degree Equation
Appendix F Complex Numbers
Digital Rights
eTextbooks and eChapters can be viewed by using the free reader listed below.
Be sure to check the format of the eTextbook/eChapter you purchase to know which reader you will need. After purchasing your eTextbook or eChapter, you will be emailed instructions on where and how to download your free reader.
Download Requirements:Due to the size of eTextbooks, a high-speed Internet connection (cable modem, DSL, LAN) is required for download stability and speed. Your connection can be wired or wireless.
Being online is not required for reading an eTextbook after successfully downloading it. You must only be connected to the Internet during the download process.
User Help:
Click Here to access the VitalSource Bookshelf FAQ
Digital Rights Management (DRM) Key
Printing - Books that cannot be printed will show "Not Allowed." Otherwise, this will detail the number of times it can be printed, or "Allowed with no limits."
Expires - Books that have no expiration (the date upon which you will no longer be able to access your eBook) will read "No Expiration." Otherwise it will state the number of days from activation (the first time you actually read it).
Reading Aloud - Books enabled with the "text-to-speech" feature so that they can be read aloud will show "Allowed."
Sharing - Books that cannot be shared with other computers will show "Not Allowed."
Min. Software Version - This is the minimum software version needed to read this book.
Suitable Devices - Hardware known to be compatable with this book. Note: Reader software still needs to be installed.