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Basic Multivariable Calculus

Basic Multivariable Calculus - 93 edition

ISBN13: 978-0716724438

Cover of Basic Multivariable Calculus 93 (ISBN 978-0716724438)
ISBN13: 978-0716724438
ISBN10: 071672443X
Cover type:
Edition/Copyright: 93
Publisher: Springer-Verlag New York
Published: 1993
International: No

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Basic Multivariable Calculus - 93 edition

ISBN13: 978-0716724438

Jerrold E. Marsden

ISBN13: 978-0716724438
ISBN10: 071672443X
Cover type:
Edition/Copyright: 93
Publisher: Springer-Verlag New York

Published: 1993
International: No
Summary

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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