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ISBN13: 978-0716724438

ISBN10: 071672443X Edition: 93

Copyright: 1993

Publisher: Springer-Verlag New York

Published: 1993

International: No

ISBN10: 071672443X Edition: 93

Copyright: 1993

Publisher: Springer-Verlag New York

Published: 1993

International: No

*Basic Multivariable Calculus* helps students make the difficult transition to advanced calculus by focusing exclusively on topics traditionally covered in the third-semester course in the calculus of functions of several variables. The concepts of vector calculus are clearly and accurately explained, with an emphasis on developing students' intuitive understanding and computational technique.

Only first year calculus required--all necessary linear algebra is explained

Incorporates wide range of physical applications, dozens of graphics, and a large number of exercises

Boxes highlight important definitions and formulas

Notes to the student on exceptionally difficult topics

**1. Algebra and Geometry of Euclidean Space**

Vectors in the Plane and Space

The Inner Product and Distance

2 x 2 and 3 x 3 Matrices and Determinants

The Cross Product and Planes

n-dimensional Euclidean Space

Curves in the Plane and in Space

**2. Differentiation**

Graphs and Level Surfaces

Partial Derivatives and Continuity

Differentiability, the Derivative

Matrix and Tangent Planes

The Chain Rule

Gradients and Directional Derivatives

Implicit Differentiation

**3. Higher Derivatives and Extrema**

Higher Order Partial Derivatives

Taylor's Theorem

Maxima and Minima

Second Derivative Test

Constrained Extrema and Lagrange Multipliers

**4. Vector Valued Functions**

Acceleration

Arc Length

Vector Fields

Divergence and Curl

**5. Multiple Integrals**

Volume and Cavalieri's Principle

The Double Integral over a Rectangle

The Double Integral over Regions

The Triple Integral

Change of a Variable, Cylindrical and Spherical Coordinates

Applications of Multiple Integrals

**6. Integrals over Curves and Surfaces**

Line Integrals

Parametrized Surfaces

Area of a Surface

Surface Integrals

**7. The Integral Theorems of Vector Analysis**

Green's Theorem

Stokes' Theorem

Gauss' Theorem

Path Independence and the Fundamental Theorems of Calculus

Epilogue

Practice Exams

Answers to Odd-Numbered Exercises

Index

ISBN10: 071672443X Edition: 93

Copyright: 1993

Publisher: Springer-Verlag New York

Published: 1993

International: No

*Basic Multivariable Calculus* helps students make the difficult transition to advanced calculus by focusing exclusively on topics traditionally covered in the third-semester course in the calculus of functions of several variables. The concepts of vector calculus are clearly and accurately explained, with an emphasis on developing students' intuitive understanding and computational technique.

Only first year calculus required--all necessary linear algebra is explained

Incorporates wide range of physical applications, dozens of graphics, and a large number of exercises

Boxes highlight important definitions and formulas

Notes to the student on exceptionally difficult topics

Table of Contents

**1. Algebra and Geometry of Euclidean Space**

Vectors in the Plane and Space

The Inner Product and Distance

2 x 2 and 3 x 3 Matrices and Determinants

The Cross Product and Planes

n-dimensional Euclidean Space

Curves in the Plane and in Space

**2. Differentiation**

Graphs and Level Surfaces

Partial Derivatives and Continuity

Differentiability, the Derivative

Matrix and Tangent Planes

The Chain Rule

Gradients and Directional Derivatives

Implicit Differentiation

**3. Higher Derivatives and Extrema**

Higher Order Partial Derivatives

Taylor's Theorem

Maxima and Minima

Second Derivative Test

Constrained Extrema and Lagrange Multipliers

**4. Vector Valued Functions**

Acceleration

Arc Length

Vector Fields

Divergence and Curl

**5. Multiple Integrals**

Volume and Cavalieri's Principle

The Double Integral over a Rectangle

The Double Integral over Regions

The Triple Integral

Change of a Variable, Cylindrical and Spherical Coordinates

Applications of Multiple Integrals

**6. Integrals over Curves and Surfaces**

Line Integrals

Parametrized Surfaces

Area of a Surface

Surface Integrals

**7. The Integral Theorems of Vector Analysis**

Green's Theorem

Stokes' Theorem

Gauss' Theorem

Path Independence and the Fundamental Theorems of Calculus

Epilogue

Practice Exams

Answers to Odd-Numbered Exercises

Index

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