Calculus: Early Transcendentals, 3rd edition

  • William L. Briggs, 
  • Lyle Cochran, 
  • Bernard Gillett, 
  • Eric Schulz

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Overview

Calculus features clear, instructional narrative and a wealth of meticulously crafted exercise sets. Examples are stepped out and thoughtfully annotated, and figures are designed to help you learn important concepts.

Published by Pearson (September 1st 2020) - Copyright © 2021

ISBN-13: 9780136880677

Subject: Calculus

Category: Calculus

Table of contents

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

Your questions answered

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