Calculus, 3rd edition

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

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Overview

Calculus builds from a foundation of strong exercise sets, then draws you into the narrative through writing that reflects an instructor's voice. Examples are stepped out and thoroughly annotated, and figures are designed carefully to work with the content. The 3rd Edition introduces important advances and refinements while retaining its proven hallmark features. Extensively revised exercise sets are rearranged and relabeled, with some modified and other new ones added. Chapter Review exercises are thoroughly revised to provide more exercises (more than 26% are new), more intermediate-level problems, and more opportunities to choose a strategy of solution.

Published by Pearson (March 17th 2021) - Copyright © 2021

ISBN-13: 9780136880639

Subject: Calculus

Category: Calculus

Overview

1. Functions

  • 1.1 Review of Functions
  • 1.2 Representing Functions
  • 1.3 Trigonometric Functions
  • 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 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 and Exponential Functions

  • 7.1 Inverse Functions
  • 7.2 The Natural Logarithmic and Exponential Functions
  • 7.3 Logarithmic and Exponential Functions with Other Bases
  • 7.4 Exponential Models
  • 7.5 Inverse Trigonometric Functions
  • 7.6 L' Hôpital's Rule and Growth Rates of Functions
  • 7.7 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

APPENDICES

  1. Proofs of Selected Theorems
  2. Algebra Review ONLINE
  3. Complex Numbers ONLINE

Answers

Index

Table of Integrals

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