Vector calculus

This textbook by respected authors helps students foster computational skillsand intuitive understanding with a careful balance of theory, applications, historical development and optional materials. JERROLD E. MARSDEN, California Institute of Technology, Pasadena, USA. ANTHONY J. TROMBA, University of California, Santa Cruz, USA. INDICE: PART I: THE GEOMETRY OF EUCLIDEAN SPACE - Vectors in Two- and Three-Dimensional Space - The Inner Product, Length, and Distance - Matrices, Determinants, and the Cross Product - Cylindrical and Spherical Coordinates - n-Dimensional Euclidean Space - PART II: DIFFERENTIATION - The Geometry of Real-Valued Functions - Limits and Continuity - Differentiation - Introduction to Paths and Curves - Properties of the Derivative - Gradients and Directional Derivatives - PART III: HIGHER-ORDER DERIVATIVES: MAXIMA AND MINIMA - Iterated Partial Derivatives - Taylor's Theorem - Extrema of Real-Valued Functions - Constrained Extrema and Lagrange Multipliers - The Implicit Function Theorem - PART IV: VECTOR-VALUED FUNCTIONS - Acceleration and Newton's Second Law - Arc Length - Vector Fields - Divergence and Curl - PART V: DOUBLE AND TRIPLE INTEGRALS - Introduction - The Double Integral Over a Rectangle - The Double Integral Over More General Regions - Changing the Order of Integration - The Triple Integral - PART VI: THE CHANGE OF VARIABLES FORMULA AND APPLICATION OF INTEGRATION - The Geometry of Maps from R2 to R2 - The Change of Variables Theorem - Applications - Improper Integrals - PART VII: INTEGRALS OVER PATHS AND SURFACES - The Path Integral - Line Integrals - Parametrized Surfaces - Area of a Surface - Integrals of Scalar Functions Over Surfaces - Surface Integrals of Vector Fields - Applications to Differential Geometry, Physics and Forms of Life - PARTVIII: THE INTEGRAL THEOREMS OFVECTOR ANALYSIS - Green's Theorem - Stokes' Theorem - Conservative Fields - Gauss' Theorem - Differential Forms

• ISBN: 978-1-4292-2404-8
• Editorial: WH Freeman
• Encuadernacion: Cartoné
• Páginas: 676
• Fecha Publicación: 01/03/2012
• Nº Volúmenes: 1
• Idioma: Inglés