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Calculus : Concepts and Contexts,9780534437367
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Calculus : Concepts and Contexts

by
Edition:
2nd
ISBN13:

9780534437367

ISBN10:
0534437362
Format:
Hardcover
Pub. Date:
12/13/2000
Publisher(s):
Brooks Cole
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Summary

James Stewart's well-received CALCULUS: CONCEPTS AND CONTEXTS, Second Edition follows in the path of the other best-selling books by this remarkable author. The First Edition of this book was highly successful because it reconciled two schools of thought: it skillfully merged the best of traditional calculus with the best of the reform movement. This new edition continues to offer the balanced approach along with Stewart's hallmark features: meticulous accuracy, patient explanations, and carefully graded problems. The content has been refined and the examples and exercises have been updated. In addition, CALCULUS: CONCEPTS AND CONTEXTS, Second Edition now includes a free CD-ROM for students that contains animations, activities, and homework hints. The book integrates the use of the CD throughout by using icons that show students when to use the CD to deepen their understanding of a difficult concept. In CALCULUS: CONCEPTS AND CONTEXTS, this well respected author emphasizes conceptual understanding - motivating students with real world applications and stressing the Rule of Four in numerical, visual, algebraic, and verbal interpretations. All concepts are presented in the classic Stewart style: with simplicity, character, and attention to detail. In addition to his clear exposition, Stewart also creates well thought-out problems and exercises. The definitions are precise and the problems create an ideal balance between conceptual understanding and algebraic skills.

Table of Contents

1. FUNCTIONS AND MODELS
Four Ways to Represent a Function
Mathematical Models
New Functions from Old Functions
Graphing Calculators and Computers
Exponential Functions
Inverse Functions and Logarithms
Parametric Curves
Review
Principles of Problem Solving
2. LIMITS AND DERIVATIVES
The Tangent and Velocity Problems
The Limit of a Function
Calculating Limits Using the Limit Laws
Continuity
Limits Involving Infinity
Tangents, Velocities, and Other Rates of Change
Derivatives
The Derivative as a Function
Linear Approximations
What does f' say about f?
Review
Focus on Problem Solving
3. DIFFERENTIATION RULES
Derivatives of Polynomials and Exponential Functions
The Product and Quotient Rules
Rates of Change in the Natural and Social Sciences
Derivatives of Trigonometric Functions
The Chain Rule
Implicit Differentiation
Derivatives of Logarithmic Functions
Linear Approximations and Differentials
Review
Focus on Problem Solving
4. APPLICATIONS OF DIFFERENTIATION
Related Rates
Maximum and Minimum Values
Derivatives and the Shapes of Curves
Graphing with Calculus and Calculators
Indeterminate Forms and l'Hospital's Rule
Optimization Problems
Applications to Economics
Newton's Method
Antiderivatives
Review
Focus on Problem Solving
5. INTEGRALS
Areas and Distances
The Definite Integral
Evaluating Definite Integrals
The Fundamental Theorem of Calculus
The Substitution Rule
Integration by Parts
Additional Techniques of Integration
Integration Using Tables and Computer Algebra Systems
Approximate Integration
Improper Integrals
Review
Focus on Problem Solving
6. APPLICATIONS OF INTEGRATION
More about Areas
Volumes
Arc Length
Average Value of a Function
Applications to Physics and Engineering
Applications to Economics and Biology
Probability
Review
Focus on Problem Solving
7. DIFFERENTIAL EQUATIONS
Modeling with Differential Equations
Direction Fields and Euler's Method
Separable Equations
Exponential Growth and Decay
The Logistic Equation
Predator-Prey Systems
Review
Focus on Problem Solving
8. INFINITE SEQUENCES AND SERIES
Sequences
Series
The Integral and Comparison Tests; Estimating Sums
Other Convergence Tests
Power Series
Representation of Functions as Power Series
Taylor and Maclaurin Series
The Binomial Series
Applications of Taylor Polynomials
Using Series to Solve Differential Equations
Review
Focus on Problem Solving
9. VECTORS AND THE GEOMETRY OF SPACE
Three Dimensional Coordinate Systems
Vectors
The Dot Product
The Cross Product
Equations of Lines and Planes
Functions and Surfaces
Cylindrical and Spherical Coordinates
Review
Focus on Problem Solving
10. VECTOR FUNCTIONS
Vector Functions and Space Curves
Derivatives and Integrals of Vector Functions
Arc Length and Curvature
Motion in Space
Parametric Surfaces
Review
Focus on Problem Solving
11. PARTIAL DERIVATIVES
Functions of Several Variables
Limits and Continuity
Partial Derivatives
Tangent Planes and Linear Approximations
The Chain Rule
Directional Derivatives and the Gradient Vector
Maximum and Minimum Values
Lagrange Multipliers
Review
Focus on Problem Solving
12. MULTIPLE INTEGRALS
Double Integrals over Rectangles
Integrated Integrals
Double Integrals over General Regions
Double Integrals in Polar Coordinates
Applications of Double Integrals
Surface Area
Triple Integrals
Triple Integrals in Cylindrical and Spherical Coordinates
Change of Variables in Multiple Integrals
Review
Focus on Problem Solving
13. VECTOR CALCULUS
Vector Fields
Line Integrals
The Fundamental Theorem for Line Integrals
Green's Theorem
Curl and Divergence
Surface Integrals
Stokes' Theorem
The Divergence Theorem
Summary
Review
Focus on Problem Solving
Appendix A: Intervals, Inequalities, And Absolute Values
Appendix B: Coordinate Geometry
Appendix C: Trigonometry
Appendix D: Precise Definitions Of Limits
Appendix E: A Few Proofs
Appendix F: Sigma Notation
Appendix G: Integration Of Rational Functions By Partial Fractions
Appendix H: Polar Coordinates
Appendix I: Complex Numbers
Appendix J: Answers To Odd-Numbered Exercises
Index


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