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Calculus: Early Transcendentals, 3rd edition

  • W L. Briggs
  • Lyle Cochran
  • Bernard Gillett
  • Eric Schulz

Published by Pearson (February 2nd 2018) - Copyright © 2019

3rd edition

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Overview

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For 3- to 4-semester courses covering single-variable and multivariable calculus, taken by students of mathematics, engineering, natural sciences, or economics.

This package includes MyLab Math.


Available for fall 2020 classes

The DIGITAL UPDATE gives you revised content and resources that keep your course current 


The most successful new calculus text in the last two decades

The much-anticipated 3rd Edition of Briggs’ Calculus: Early Transcendentals retains its hallmark features while introducing important advances and refinements. Briggs, Cochran, Gillett, and Schulz build from a foundation of meticulously crafted exercise sets, then draw students into the narrative through writing that reflects the voice of the instructor. Examples are stepped out and thoughtfully annotated, and figures are designed to teach rather than simply supplement the narrative. The groundbreaking eText contains approximately 700 Interactive Figures that can be manipulated to shed light on key concepts. For the 3rd Edition, the authors synthesized feedback on the text and MyLab™ Math content from over 140 instructors. This thorough and extensive review process, paired with the authors’ own teaching experiences, helped create a text that is designed for today’s calculus instructors and students.


This MyLab Update of the 3rd Edition introduces a much requested change: The Wolfram CDF Player has been replaced by Wolfram Cloud. So the interactive eText with its 700 Interactive Figures now runs on all browsers, with no plug-in required! Upgrade now to take advantage of this great new feature!


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0134995996 / 9780134995991 Calculus: Early Transcendentals and MyLab Math with Pearson eText - Title-Specific Access Card Package, 3/e
Package consists of:
  • 0134763645 / 9780134763644 Calculus: Early Transcendentals
  • 0134856929 / 9780134856926 MyLab Math with Pearson eText - Standalone Access Card - for Calculus: Early Transcendentals

Table of contents

1. Functions

1.1 Review of Functions

1.2 Representing Functions

1.3 Inverse, Exponential, and Logarithmic Functions

1.4 Trigonometric Functions and Their Inverses

Review Exercises


2. Limits

2.1 The Idea of Limits

2.2 Definitions of Limits

2.3 Techniques for Computing Limits

2.4 Infinite Limits

2.5 Limits at Infinity

2.6 Continuity

2.7 Precise Definitions of Limits

Review Exercises


3. Derivatives

3.1 Introducing the Derivative

3.2 The Derivative as a Function

3.3 Rules of Differentiation

3.4 The Product and Quotient Rules

3.5 Derivatives of Trigonometric Functions

3.6 Derivatives as Rates of Change

3.7 The Chain Rule

3.8 Implicit Differentiation

3.9 Derivatives of Logarithmic and Exponential Functions

3.10 Derivatives of Inverse Trigonometric Functions

3.11 Related Rates

Review Exercises


4. Applications of the Derivative

4.1 Maxima and Minima

4.2 Mean Value Theorem

4.3 What Derivatives Tell Us

4.4 Graphing Functions

4.5 Optimization Problems

4.6 Linear Approximation and Differentials

4.7 L’Hôpital’s Rule

4.8 Newton’s Method

4.9 Antiderivatives

Review Exercises


5. Integration

5.1 Approximating Areas under Curves

5.2 Definite Integrals

5.3 Fundamental Theorem of Calculus

5.4 Working with Integrals

5.5 Substitution Rule

Review Exercises


6. Applications of Integration

6.1 Velocity and Net Change

6.2 Regions Between Curves

6.3 Volume by Slicing

6.4 Volume by Shells

6.5 Length of Curves

6.6 Surface Area

6.7 Physical Applications

Review Exercises


7. Logarithmic, Exponential, and Hyperbolic Functions

7.1  Logarithmic and Exponential Functions Revisited

7.2 Exponential Models

7.3 Hyperbolic Functions

Review Exercises


8. Integration Techniques

8.1 Basic Approaches

8.2 Integration by Parts

8.3 Trigonometric Integrals

8.4 Trigonometric Substitutions

8.5 Partial Fractions

8.6 Integration Strategies

8.7 Other Methods of Integration

8.8 Numerical Integration

8.9 Improper Integrals

Review Exercises


9. Differential Equations

9.1 Basic Ideas

9.2 Direction Fields and Euler’s Method

9.3 Separable Differential Equations

9.4 Special First-Order Linear Differential Equations

9.5 Modeling with Differential Equations

Review Exercises


10. Sequences and Infinite Series

10.1 An Overview

10.2 Sequences

10.3 Infinite Series

10.4 The Divergence and Integral Tests

10.5 Comparison Tests

10.6 Alternating Series

10.7 The Ratio and Root Tests

10.8 Choosing a Convergence Test

Review Exercises


11. Power Series

11.1 Approximating Functions with Polynomials

11.2 Properties of Power Series

11.3 Taylor Series

11.4 Working with Taylor Series

Review Exercises


12. Parametric and Polar Curves

12.1 Parametric Equations

12.2 Polar Coordinates

12.3 Calculus in Polar Coordinates

12.4 Conic Sections

Review Exercises


13. Vectors and the Geometry of Space

13.1 Vectors in the Plane

13.2 Vectors in Three Dimensions

13.3 Dot Products

13.4 Cross Products

13.5 Lines and Planes in Space

13.6 Cylinders and Quadric Surfaces

Review Exercises


14. Vector-Valued Functions

14.1 Vector-Valued Functions

14.2 Calculus of Vector-Valued Functions

14.3 Motion in Space

14.4 Length of Curves

14.5 Curvature and Normal Vectors

Review Exercises


15. Functions of Several Variables

15.1 Graphs and Level Curves

15.2 Limits and Continuity

15.3 Partial Derivatives

15.4 The Chain Rule

15.5 Directional Derivatives and the Gradient

15.6 Tangent Planes and Linear Approximation

15.7 Maximum/Minimum Problems

15.8 Lagrange Multipliers

Review Exercises


16. Multiple Integration

16.1 Double Integrals over Rectangular Regions

16.2 Double Integrals over General Regions

16.3 Double Integrals in Polar Coordinates

16.4 Triple Integrals

16.5 Triple Integrals in Cylindrical and Spherical Coordinates

16.6 Integrals for Mass Calculations

16.7 Change of Variables in Multiple Integrals

Review Exercises


17. Vector Calculus

17.1 Vector Fields

17.2 Line Integrals

17.3 Conservative Vector Fields

17.4 Green’s Theorem

17.5 Divergence and Curl

17.6 Surface Integrals

17.7 Stokes’ Theorem

17.8 Divergence Theorem

Review Exercises


D2 Second-Order Differential Equations ONLINE

D2.1 Basic Ideas

D2.2 Linear Homogeneous Equations

D2.3 Linear Nonhomogeneous Equations

D2.4 Applications

D2.5 Complex Forcing Functions

Review Exercises


Appendix A. Proofs of Selected Theorems

Appendix B. Algebra Review ONLINE

Appendix C. Complex Numbers ONLINE

Answers

Index

Table of Integrals


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