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Vector calculus

Author: Jerrold E Marsden; Anthony Tromba
Publisher: New York : W.H. Freeman, ©2003.
Edition/Format:   Print book : English : 5th edView all editions and formats
Summary:

This text helps students foster computational skills and intuitive understanding with a balance of theory, applications and optional materials. This edition offers revised coverage in several areas  Read more...

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Genre/Form: Lehrbuch
Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Jerrold E Marsden; Anthony Tromba
ISBN: 0716749920 9780716749929
OCLC Number: 52377580
Description: xxvii, 676 pages : illustrations ; 24 cm
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 --
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.
Responsibility: Jerrold E. Marsden, Anthony J. Tromba.
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