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.

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 INTEGRALSIntroduction.- 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.

This vector calculus text 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. The sixth edition was completely redesigned, but retains and improves on the balance between theory, applications, optional material and historical notes that was present in earlier editions. Content changes include:- Trimming some of the historical material, making it more relevant to the mathematics under discussion. - Moving some of the more difficult discussions in the Fifth Edition to the Book Companion Web Site (including Conservation Laws, the derivation of Euler's Equation of a Perfect Fluid, and a discussion of the Heat Equation). Revision highlights: New Design The modern redesign emphasizes the pedagogical features, making the text more concise, student-friendly, and accessible. More Exercises The new edition adds 15-20% new easy-to-moderate exercises graded from less difficult to more difficult, providing extra practice for students to master key concepts. New Examples The new examples were shaped by feedback from reviewers and teaching assistants teaching the course. Enhanced Three Dimensional Figures The quality of the artwork has been significantly improved, with crucial three-dimensional figures better reflecting key concepts to students. Definitions/Theorems/Proofs/Corollaries/Key Concepts These pedagogical features are now more clearly boxed to better highlight them for students and differentiate from the main text.    

The new, modern redesign emphasizes the pedagogical features, making the text more concise, student-friendly, and accessible.The 6th edition increases the amount of exercises by 20%, including new easy-to-moderate exercises graded from less difficult to more difficult, providing extra practice for students to master key concepts.The new examples contained in the book have been shaped by feedback from reviewers and teaching assistants currently teaching the course.The quality of the artwork has been significantly improved, with the crucial three-dimensional figures better reflecting key concepts to students, helping to better illustrate important concepts in the book.These pedagogical features are now more clearly highlighted within the text to better spotlight them for students and differentiate them from the main text.New_to_this_editionThis 6th edition has been completely redesigned, but retains and improves on the balance between theory, applications, optional material, and historical notes.A new, modern redesign emphasizes the pedagogical features, making the text more concise, readable and student-friendly.The new edition adds 15-20% new easy/moderate exercises graded from less difficult to more difficult, providing extra practice for students to master key concepts.The quality of the artwork has been significantly improved, with crucial three-dimensional figures better reflecting key concepts to students.