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Vector Calculus

Vector Calculus - 5th edition

ISBN13: 978-0716749929

Cover of Vector Calculus 5TH 03 (ISBN 978-0716749929)
ISBN13: 978-0716749929
ISBN10: 0716749920
Cover type: Hardback
Edition/Copyright: 5TH 03
Publisher: W.H. Freeman
Published: 2003
International: No

List price: $205.50

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Vector Calculus - 5TH 03 edition

ISBN13: 978-0716749929

Jerrold E. Marsden and Anthony Tromba

ISBN13: 978-0716749929
ISBN10: 0716749920
Cover type: Hardback
Edition/Copyright: 5TH 03
Publisher: W.H. Freeman

Published: 2003
International: No
Summary

Now in its fifth edition, Vector Calculus helps students gain an intuitive and solid understanding of this important subject. The book's careful account is a contemporary balance between theory, application, and historical development, providing it's readers with an insight into how mathematics progresses and is in turn influenced by the natural world.

  • Expanded historical discussion introduction precedes first chapter
  • Expanded historical remarks throughout the text
  • Revised presentation of Implicit Function Theorem--now more readable and accessible to students
  • New section 7.7, "Application to Differential Geometry, Physics and Forms of Life"--with more on geometry and surface integrals
  • Revised section 6.4, "Improper Integrals"
  • 15% revised exercise material, including new and new graduated exercises
  • Enhanced material on Maxwell's Equations in Chapter 8
  • Optional Material moved to the Web site
  • Improved readability and accessibility for students
  • Completely revised, color art program


Author Bio

Marsden, Jerrold E. : California Institute of Technology

Tromba, Anthony : University of California, Santa Cruz

Table of Contents

1. THE GEOMETRY OF EUCLIDEAN SPACE

1.1 Vectors in Two- and Three-Dimensional Space
1.2 The Inner Product, Length, and Distance
1.3 Matrices, Determinants, and the Cross Product
1.4 Cylindrical and Spherical Coordinates
1.5 n-Dimensional Euclidean Space

2. DIFFERENTIATION SPACE

2.1 The Geometry of Real-Valued Functions
2.2 Limits and Continuity
2.3 Differentiation
2.4 Introduction to Paths
2.5 Properties of the Derivative
2.6 Gradients and Directional Derivatives

3. HIGHER-ORDER DERIVATIVES: MAXIMA AND MINIMA

3.1 Iterated Partial Derivatives
3.2 Taylor's Theorem
3.3 Extrema of Real-Valued Functions
3.4 Constrained Extrema and Lagrange Multipliers
3.5 The Implicit Function Theorem

4. VECTOR-VALUED FUNCTIONS

4.1 Acceleration and Newton's Second Law
4.2 Arc Length
4.3 Vector Fields
4.4 Divergence and Curl

5. DOUBLE AND TRIPLE INTEGRALS

5.1 Introduction
5.2 The Double Integral Over a Rectangle
5.3 The Double Integral Over More General Regions
5.4 Changing the Order of Integration
5.5 The Triple Integral

6. THE CHANGE OF VARIABLES FORMULA AND APPLICATIONS OF INTEGRATION

6.1 The Geometry of Maps from R2 to R2
6.2 The Change of Variables Theorem
6.3 Applications of Double and Triple
6.4 Improper Integrals

7. INTEGRALS OVER PATHS AND SURFACES

7.1 The Path Integral
7.2 Line Integrals
7.3 Parametrized Surfaces
7.4 Area of a Surface
7.5 Integrals of Scalar Functions Over Surfaces
7.6 Surface Integrals of Vector Functions
7.7 Applications to Differential Geometry, Physics and Forms of Life

8. THE INTEGRAL THEOREMS OF VECTOR ANALYSIS

8.1 Green's Theorem
8.2 Stokes' Theorem
8.3 Conservative Fields
8.4 Gauss' Theorem
8.5 Applications to Physics, Engineering, and Differential Equations
8.6 Differential Forms