This vector calculus textbook helps students gain a solid, intuitive understanding of this important subject. The book's careful contemporary balance between theory, application and historical development, provides readers with insights into how mathematics progresses and is in turn influenced by the natural world. The new edition offers a contemporary design, an increased number of practice exercises and content changes based on reviewer feedback, giving this classic text a modern appeal.
Now in its sixth edition, this textbook has been completely redesigned and improved, and yet retains and improves on the carefuk balance between theory, applications, optional material and historical notes that were present in earlier editions. The sixth edition of Marsden and Tromba's Vector Calculus is an essential resource for students new to the subject.
Jerrold Eldon Marsden was the Carl F. Braun Professor of Engineering and Control & Dynamical Systems at the California Institute of Technology. Marsden is listed as an ISI highly cited researcher. Anthony Tromba is Professor of Mathematics at the University of California, Santa Cruz. He has authored, or co-authored over nine books, two of which, including Vector Calculus, have been translated into multiple languages.
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.- PART VIII: THE INTEGRAL THEOREMS OFVECTOR ANALYSIS.- Green's Theorem.- Stokes' Theorem.- Conservative Fields.- Gauss' Theorem.-Differential Forms.