# Adams:Calc Several Variables

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## Description

Adams Calculus is intended for the three semester calculus course. Classroom proven in North America and abroad, this classic text has been praised for its high level of mathematical integrity including complete and precise statements of theorems, use of geometric reasoning in applied problems, and the diverse range of applications across the sciences. The Sixth Edition features a full, separate chapter on differential equations and numerous updated Maple examples throughout the text.

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## Product details

- Paperback
- 210 x 272 x 22mm | 1,120.37g
- 04 May 2006
- Pearson Education Limited
- Prentice Hall Canada
- Harlow, United Kingdom
- 032130716X
- 9780321307163

## Author information

Robert Adams joined the Mathematics Department of the University of British Columbia in 1966 after completing a Ph.D. in Mathematics at the University of Toronto. His research interests in analysis led to the 1975 publication of a monograph, Sobolev Spaces, by Academic Press. It remained in print for 23 years. A second edition, joint with his colleague Professor John Fournier, was published in 2003. Professor Adams's teaching interests led to the 1982 publication of the first of his many calculus texts by Addison Wesley. These texts are now used worldwide. With a keen interest in computers, mathematical typesetting, and illustration, in 1984 Professor Adams became the first Canadian author to typeset his own textbooks using TeX on a personal computer. Since then he has also done all the illustrations for his books using the MG software program he developed with his colleague, Professor Robert Israel. Now retired from UBC, Professor Adams is currently engaged in preparing the sixth editions of his textbooks and pursuing his interest in the Linux operating system.

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## Review quote

I believe that this is one of the more mathematically precise calculus textbooks available in today's market. Dr. G.R. Nicklason University College of Cape Breton

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## Table of contents

Preface To the Student To the Instructor Acknowledgments R. A Brief Review of Single-Variable Calculus Limits and Continuity Tangents and Derivatives Implicit Differentiation The Trigonometric Functions The Mean-Value Theorem Higher-Order Derivatives Antiderivatives and Indefinite Integrals Differential Equations and Initial-Value Problems Inverse Functions The Natural Logarithm and Exponential The Inverse Trigonometric Functions Hyperbolic Functions Maximum and Minimum Values Linear Approximations and Newton's Method The Shape of a Graph Higher-Order Approximations Indeterminate Forms and l'Hopital's Rule Riemann Sums and the Definite Integral Areas Between Curves Integration Formulas and Techniques Improper Integrals Numerical Integration Volumes Arc Length and Surface Area Centres of Mass and Centroids Conics Parametric Curves Polar Coordinates 9. Sequences, Series, and Power Series 9.1 Sequences and Convergence 9.2 Infinite Series 9.3 Convergence Tests for Positive Series 9.4 Absolute and Conditional Convergence 9.5 Power Series 9.6 Taylor and Maclaurin Series 9.7 Applications of Taylor and Maclaurin Series 9.8 The Binomial Theorem and Binomial Series 9.9 Fourier Series Chapter Review 10. Vectors and Coordinate Geometry in 3-Space 10.1 Analytic Geometry in Three Dimensions 10.2 Vectors 10.3 The Cross Product in 3-Space 10.4 Planes and Lines 10.5 Quadric Surfaces 10.6 A Little Linear Algebra 10.7 Using Maple for Vector and Matrix Calculations Chapter Review 11. Vector Functions and Curves 11.1 Vector Functions of One Variable 11.2 Some Applications of Vector Differentiation 11.3 Curves and Parametrizations 11.4 Curvature, Torsion, and the Frenet Frame 11.5 Curvature and Torsion for General Parametrizations 11.6 Kepler's Laws of Planetary Motion Chapter Review 12. Partial Differentiation 12.1 Functions of Several Variables 12.2 Limits and Continuity 12.3 Partial Derivatives 12.4 Higher-Order Derivatives 12.5 The Chain Rule 12.6 Linear Approximations, Differentiability, and Differentials 12.7 Gradients and Directional Derivatives 12.8 Implicit Functions 12.9 Taylor Series and Approximations Chapter Review 13. Applications of Partial Derivatives 13.1 Extreme Values 13.2 Extreme Values of Functions Defined on Restricted Domains 13.3 Lagrange Multipliers 13.4 The Method of Least Squares 13.5 Parametric Problems 13.6 Newton's Method 13.7 Calculations with Maple Chapter Review 14. Multiple Integration 14.1 Double Integrals 14.2 Iteration of Double Integrals in Cartesian Coordinates 14.3 Improper Integrals and a Mean-Value Theorem 14.4 Double Integrals in Polar Coordinates 14.5 Triple Integrals 14.6 Change of Variables in Triple Integrals 14.7 Applications of Multiple Integrals Chapter Review 15. Vector Fields 15.1 Vector and Scalar Fields 15.2 Conservative Fields 15.3 Line Integrals 15.4 Line Integrals of Vector Fields 15.5 Surfaces and Surface Integrals 15.6 Oriented Surfaces and Flux Integrals Chapter Review 16. Vector Calculus 16.1 Gradient, Divergence, and Curl 16.2 Some Identities Involving Grad, Div, and Curl 16.3 Green's Theorem in the Plane 16.4 The Divergence Theorem in 3-Space 16.5 Stokes's Theorem 16.6 Some Physical Applications of Vector Calculus 16.7 Orthogonal Curvilinear Coordinates Chapter Review 17. Ordinary Differential Equations 17.1 Classifying Differential Equations 17.2 Solving First-Order Equations 17.3 Existence, Uniqueness, and Numerical Methods 17.4 Differential Equations of Second Order 17.5 Linear Differential Equations with Constant Coefficients 17.6 Nonhomogeneous Linear Equations 17.7 Series Solutions of Differential Equations Chapter Review Appendix I Complex Numbers Appendix II Complex Functions Appendix III Continuous Functions Appendix IV The Riemann Appendix V Doing Calculus with Maple Answers to Odd-Numbered Exercises Index Preface To the Student To the Instructor Acknowledgments R. A Brief Review of Single-Variable Calculus Limits and Continuity Tangents and Derivatives Implicit Differentiation The Trigonometric Functions The Mean-Value Theorem Higher-Order Derivatives Antiderivatives and Indefinite Integrals Differential Equations and Initial-Value Problems Inverse Functions The Natural Logarithm and Exponential The Inverse Trigonometric Functions Hyperbolic Functions Maximum and Minimum Values Linear Approximations and Newton's Method The Shape of a Graph Higher-Order Approximations Indeterminate Forms and l'Hopital's Rule Riemann Sums and the Definite Integral Areas Between Curves Integration Formulas and Techniques Improper Integrals Numerical Integration Volumes Arc Length and Surface Area Centres of Mass and Centroids Conics Parametric Curves Polar Coordinates 9. Sequences, Series, and Power Series 9.1 Sequences and Convergence 9.2 Infinite Series 9.3 Convergence Tests for Positive Series 9.4 Absolute and Conditional Convergence 9.5 Power Series 9.6 Taylor and Maclaurin Series 9.7 Applications of Taylor and Maclaurin Series 9.8 The Binomial Theorem and Binomial Series 9.9 Fourier Series Chapter Review 10. Vectors and Coordinate Geometry in 3-Space 10.1 Analytic Geometry in Three Dimensions 10.2 Vectors 10.3 The Cross Product in 3-Space 10.4 Planes and Lines 10.5 Quadric Surfaces 10.6 A Little Linear Algebra 10.7 Using Maple for Vector and Matrix Calculations Chapter Review 11. Vector Functions and Curves 11.1 Vector Functions of One Variable 11.2 Some Applications of Vector Differentiation 11.3 Curves and Parametrizations 11.4 Curvature, Torsion, and the Frenet Frame 11.5 Curvature and Torsion for General Parametrizations 11.6 Kepler's Laws of Planetary Motion Chapter Review 12. Partial Differentiation 12.1 Functions of Several Variables 12.2 Limits and Continuity 12.3 Partial Derivatives 12.4 Higher-Order Derivatives 12.5 The Chain Rule 12.6 Linear Approximations, Differentiability, and Differentials 12.7 Gradients and Directional Derivatives 12.8 Implicit Functions 12.9 Taylor Series and Approximations Chapter Review 13. Applications of Partial Derivatives 13.1 Extreme Values 13.2 Extreme Values of Functions Defined on Restricted Domains 13.3 Lagrange Multipliers 13.4 The Method of Least Squares 13.5 Parametric Problems 13.6 Newton's Method 13.7 Calculations with Maple Chapter Review 14. Multiple Integion of Double Integrals in Cartesian Coordinates 14.3 Improper Integrals and a Mean-Value Theorem 14.4 Double Integrals in Polar Coordinates 14.5 Triple Integrals 14.6 Change of Variables in Triple Integrals 14.7 Applications of Multiple Integrals Chapter Review 15. Vector Fields 15.1 Vector and Scalar Fields 15.2 Conservative Fields 15.3 Line Integrals 15.4 Line Integrals of Vector Fields 15.5 Surfaces and Surface Integrals 15.6 Oriented Surfaces and Flux Integrals Chapter Review 16. Vector Calculus 16.1 Gradient, Divergence, and Curl 16.2 Some Identities Involving Grad, Div, and Curl 16.3 Green's Theorem in the Plane 16.4 The Divergence Theorem in 3-Space 16.5 Stokes's Theorem 16.6 Some Physical Applications of Vector Calculus 16.7 Orthogonal Curvilinear Coordinates Chapter Review 17. Ordinary Differential Equations 17.1 Classifying Differential Equations 17.2 Solving First-Order Equations 17.3 Existence, Uniqueness, and Numerical Methods 17.4 Differential Equations of Second Order 17.5 Linear Differential Equations with Constant Coefficients 17.6 Nonhomogeneous Linear Equations 17.7 Series Solutions of Differential Equations Chapter Review Appendix I Complex Numbers Appendix II Complex Functions Appendix III Continuous Functions Appendix IV The Riemann Appendix V Doing Calculus with Maple Answers to Odd-Numbered Exercises Index

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