Research Catalog

Title

Vector calculus / Jerrold E. Marsden, Anthony J. Tromba.

Author

Marsden, Jerrold E.

Publication

New York : W.H. Freeman, ©2003.

Items in the Library & Off-site

Details

Additional Authors

Tromba, Anthony.

Description

xxvii, 676 pages : illustrations; 24 cm

Summary

'Vector Calculus' helps students foster computational skills and intuitive understanding with a careful balance of theory, applications, and optional materials. This new edition offers revised coverage in several areas as well as a large number of new exercises and expansion of historical notes.

Subject

• Calculus
• Vector analysis
• calculus
• Vektoranalysis
• Vectoren (wiskunde)
• Vektoranalysis.

Genre/Form

• Examinations.
• Lehrbuch.

Note

• Includes index.

Bibliography (note)

• Includes bibliographical references and index.

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.

ISBN

• 0716749920
• 9780716749929

LCCN

2003049184

OCLC

• ocm52377580
• 52377580
• SCSB-1301097

Owning Institutions

Princeton University Library