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This is the most successful calculus textbook in the world. The proof of this success is the text's use in such a wide variety of colleges and universities. The new edition of this best-selling text has been carefully and thoroughly revised by enhancing the features that make it such a powerful teaching and learning tool for calculus: integrity, meticulous accuracy, precision, a clear exposition and patient explanations, character, and attention to detail. It continues to embrace the best aspects of reform (many were incorporated in the previous edition) by combining the traditional theoretical aspects of calculus with creative teaching and learning techniques. This is accomplished by a focus on conceptual understanding, the use of real world data and real-life applications, projects, and the use of technology (where appropriate).
Everyone agrees that the main goal of calculus instruction is for the student to understand the basic ideas. The goal of this book is to support this while motivating students through the use real-world applications, building the essential mathematical reasoning skills, and helping them develop an appreciation and enthusiasm for calculus.
Features:
Author Bio
Stewart, James : McMaster University
James Stewart, McMaster University; Ph.D., University of Toronto
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function.
Mathematical Models.
New Functions from Old Functions.
Graphing Calculators and Computers.
Review.
Principles of Problem Solving.
2. LIMITS AND RATES OF CHANGE.
The Tangent and Velocity Problems.
The Limit of a Function.
Calculating Limits Using the Limit Laws.
The Precise Definition of a Limit.
Continuity.
Tangents, Velocities, and Other Rates of Change.
Review.
Problems Plus.
3. DERIVATIVES.
Derivatives.
The Derivative as a Function.
Differentiation Formulas.
Rates of Change in the Natural and Social Sciences.
Derivatives of Trigonometric Functions.
The Chain Rule.
Implicit Differentiation.
Higher Derivatives.
Related Rates.
Linear Approximations and Differentials.
Review.
Problems Plus.
4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values.
The Mean Value Theorem.
How Derivatives Affect the Shape of a Graph.
Limits at Infinity; Horizontal Asymptotes.
Summary of Curve Sketching.
Graphing with Calculus and Calculators.
Optimization Problems.
Applications to Economics.
Newton's Method.
Antiderivatives.
Review.
Problems Plus.
5. INTEGRALS.
Areas and Distances.
The Definite Integral.
The Fundamental Theorem of Calculus.
Indefinite Integrals and the Total Change Theorem.
The Substitution Rule.
Review.
Problems Plus.
6. APPLICATIONS OF INTEGRATION.
Areas Between Curves.
Volume.
Volumes by Cylindrical Shells.
Work.
Average Value of a Function.
Review.
Problems Plus.
7. INVERSE FUNCTIONS.
Inverse Functions.
Exponential Functions and Their Derivatives.
Logarithmic Functions.
Derivatives of Logarithmic Functions.
The Natural Logarithmic Function.
The Natural Exponential Function.
General Logarithmic and Exponential Functions.
Inverse Trigonometric Functions.
Hyperbolic Functions.
Indeterminate Forms and l'Hospital's Rule.
Review.
Problems Plus.
8. TECHNIQUES OF INTEGRATION.
Integration by Parts.
Trigonometric Integrals.
Trigonometric Substitution.
Integration of Rational Functions by Partial Fractions.
Strategy for Integration.
Integration Using Tables and Computer Algebra Systems.
Approximate Integration.
Improper Integrals.
Review.
Problems Plus.
9. FURTHER APPLICATIONS OF INTEGRATION.
Arc Length.
Area of a Surface of Revolution.
Applications to Physics and Engineering.
Applications to Economics and Biology.
Probability.
Review.
Problems Plus.
10. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations.
Direction Fields and Euler's Method.
Separable Equations.
Exponential Growth and Decay.
The Logistic Equation.
Linear Equations.
Predator-Prey Systems.
Review.
Problems Plus.
11. PARAMETRIC EQUATIONS AND POLAR COORDINATES.
Curves Defined by Parametric Equations.
Tangents and Areas.
Arc Length and Surface Area.
Polar Coordinates.
Areas and Lengths in Polar Coordinates.
Conic Sections.
Conic Sections in Polar Coordinates.
Review.
Problems Plus.
12. INFINITE SEQUENCES AND SERIES.
Sequences. Series.
The Integral Test and Estimates of Sums.
The Comparison Tests.
Alternating Series.
Absolute Convergence and the Ratio and Root Tests.
Strategy for Testing Series.
Power Series.
Representation of Functions as Power Series.
Taylor and Maclaurin Series.
The Binomial Series.
Applications of Taylor Polynomials.
Review. Problems Plus.
13. VECTORS AND THE GEOMETRY OF SPACE.
Three-Dimensional Coordinate Systems.
Vectors.
The Dot Product.
The Cross Product.
Equations of Lines and Planes.
Cylinders and Quadratic Surfaces.
Cylindrical and Spherical Coordinates.
Review.
Problems Plus.
14. VECTOR FUNCTIONS.
Vector Functions and Space Curves.
Derivatives and Integrals of Vector Functions.
Arc Length and Curvature.
Motion in Space: Velocity and Acceleration.
Review.
Problems Plus.
15. PARTIAL DERIVATIVES.
Functions of Several Variables.
Limits and Continuity.
Partial Derivatives.
Tangent Planes and Differentials.
The Chain Rule.
Directional Derivatives and the Gradient Vector.
Maximum and Minimum Values.
Lagrange Multipliers.
Review.
Problems Plus.
16. MULTIPLE INTEGRALS.
Double Integrals over Rectangles.
Iterated 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.
Problems Plus.
17. VECTOR CALCULUS.
Vector Fields. Line Integrals.
The Fundamental Theorem for Line Integrals.
Green's Theorem.
Curl and Divergence.
Parametric Surfaces and Their Areas.
Surface Integrals.
Stokes' Theorem.
The Divergence Theorem.
Summary.
Review.
Problems Plus.
18. SECOND-ORDER DIFFERENTIAL EQUATIONS.
Second-Order Linear Equations.
Nonhomogeneous Linear Equations.
Applications of Second-Order Differential Equations.
Series Solutions.
Review.
Problems Plus.
APPENDICES.
A. Integers, Inequalities, and Absolute Values.
B. Coordinate Geometry and Lines.
C. Graphs of Second-Degree Equations.
D. Trigonometry.
E. Sigma Notation.
F. Proofs of Theorems.
G. Complex Numbers.
H. Answers to Odd-Numbered Exercises.
This is the most successful calculus textbook in the world. The proof of this success is the text's use in such a wide variety of colleges and universities. The new edition of this best-selling text has been carefully and thoroughly revised by enhancing the features that make it such a powerful teaching and learning tool for calculus: integrity, meticulous accuracy, precision, a clear exposition and patient explanations, character, and attention to detail. It continues to embrace the best aspects of reform (many were incorporated in the previous edition) by combining the traditional theoretical aspects of calculus with creative teaching and learning techniques. This is accomplished by a focus on conceptual understanding, the use of real world data and real-life applications, projects, and the use of technology (where appropriate).
Everyone agrees that the main goal of calculus instruction is for the student to understand the basic ideas. The goal of this book is to support this while motivating students through the use real-world applications, building the essential mathematical reasoning skills, and helping them develop an appreciation and enthusiasm for calculus.
Features:
Author Bio
Stewart, James : McMaster University
James Stewart, McMaster University; Ph.D., University of Toronto
Table of Contents
1. FUNCTIONS AND MODELS.
Four Ways to Represent a Function.
Mathematical Models.
New Functions from Old Functions.
Graphing Calculators and Computers.
Review.
Principles of Problem Solving.
2. LIMITS AND RATES OF CHANGE.
The Tangent and Velocity Problems.
The Limit of a Function.
Calculating Limits Using the Limit Laws.
The Precise Definition of a Limit.
Continuity.
Tangents, Velocities, and Other Rates of Change.
Review.
Problems Plus.
3. DERIVATIVES.
Derivatives.
The Derivative as a Function.
Differentiation Formulas.
Rates of Change in the Natural and Social Sciences.
Derivatives of Trigonometric Functions.
The Chain Rule.
Implicit Differentiation.
Higher Derivatives.
Related Rates.
Linear Approximations and Differentials.
Review.
Problems Plus.
4. APPLICATIONS OF DIFFERENTIATION.
Maximum and Minimum Values.
The Mean Value Theorem.
How Derivatives Affect the Shape of a Graph.
Limits at Infinity; Horizontal Asymptotes.
Summary of Curve Sketching.
Graphing with Calculus and Calculators.
Optimization Problems.
Applications to Economics.
Newton's Method.
Antiderivatives.
Review.
Problems Plus.
5. INTEGRALS.
Areas and Distances.
The Definite Integral.
The Fundamental Theorem of Calculus.
Indefinite Integrals and the Total Change Theorem.
The Substitution Rule.
Review.
Problems Plus.
6. APPLICATIONS OF INTEGRATION.
Areas Between Curves.
Volume.
Volumes by Cylindrical Shells.
Work.
Average Value of a Function.
Review.
Problems Plus.
7. INVERSE FUNCTIONS.
Inverse Functions.
Exponential Functions and Their Derivatives.
Logarithmic Functions.
Derivatives of Logarithmic Functions.
The Natural Logarithmic Function.
The Natural Exponential Function.
General Logarithmic and Exponential Functions.
Inverse Trigonometric Functions.
Hyperbolic Functions.
Indeterminate Forms and l'Hospital's Rule.
Review.
Problems Plus.
8. TECHNIQUES OF INTEGRATION.
Integration by Parts.
Trigonometric Integrals.
Trigonometric Substitution.
Integration of Rational Functions by Partial Fractions.
Strategy for Integration.
Integration Using Tables and Computer Algebra Systems.
Approximate Integration.
Improper Integrals.
Review.
Problems Plus.
9. FURTHER APPLICATIONS OF INTEGRATION.
Arc Length.
Area of a Surface of Revolution.
Applications to Physics and Engineering.
Applications to Economics and Biology.
Probability.
Review.
Problems Plus.
10. DIFFERENTIAL EQUATIONS.
Modeling with Differential Equations.
Direction Fields and Euler's Method.
Separable Equations.
Exponential Growth and Decay.
The Logistic Equation.
Linear Equations.
Predator-Prey Systems.
Review.
Problems Plus.
11. PARAMETRIC EQUATIONS AND POLAR COORDINATES.
Curves Defined by Parametric Equations.
Tangents and Areas.
Arc Length and Surface Area.
Polar Coordinates.
Areas and Lengths in Polar Coordinates.
Conic Sections.
Conic Sections in Polar Coordinates.
Review.
Problems Plus.
12. INFINITE SEQUENCES AND SERIES.
Sequences. Series.
The Integral Test and Estimates of Sums.
The Comparison Tests.
Alternating Series.
Absolute Convergence and the Ratio and Root Tests.
Strategy for Testing Series.
Power Series.
Representation of Functions as Power Series.
Taylor and Maclaurin Series.
The Binomial Series.
Applications of Taylor Polynomials.
Review. Problems Plus.
13. VECTORS AND THE GEOMETRY OF SPACE.
Three-Dimensional Coordinate Systems.
Vectors.
The Dot Product.
The Cross Product.
Equations of Lines and Planes.
Cylinders and Quadratic Surfaces.
Cylindrical and Spherical Coordinates.
Review.
Problems Plus.
14. VECTOR FUNCTIONS.
Vector Functions and Space Curves.
Derivatives and Integrals of Vector Functions.
Arc Length and Curvature.
Motion in Space: Velocity and Acceleration.
Review.
Problems Plus.
15. PARTIAL DERIVATIVES.
Functions of Several Variables.
Limits and Continuity.
Partial Derivatives.
Tangent Planes and Differentials.
The Chain Rule.
Directional Derivatives and the Gradient Vector.
Maximum and Minimum Values.
Lagrange Multipliers.
Review.
Problems Plus.
16. MULTIPLE INTEGRALS.
Double Integrals over Rectangles.
Iterated 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.
Problems Plus.
17. VECTOR CALCULUS.
Vector Fields. Line Integrals.
The Fundamental Theorem for Line Integrals.
Green's Theorem.
Curl and Divergence.
Parametric Surfaces and Their Areas.
Surface Integrals.
Stokes' Theorem.
The Divergence Theorem.
Summary.
Review.
Problems Plus.
18. SECOND-ORDER DIFFERENTIAL EQUATIONS.
Second-Order Linear Equations.
Nonhomogeneous Linear Equations.
Applications of Second-Order Differential Equations.
Series Solutions.
Review.
Problems Plus.
APPENDICES.
A. Integers, Inequalities, and Absolute Values.
B. Coordinate Geometry and Lines.
C. Graphs of Second-Degree Equations.
D. Trigonometry.
E. Sigma Notation.
F. Proofs of Theorems.
G. Complex Numbers.
H. Answers to Odd-Numbered Exercises.