Vector Calculus

This book gives a comprehensive and thorough introduction to ideas and major results of the theory of functions of several variables and of modern vector calculus in two and three dimensions. Clear and easy-to-follow writing style, carefully crafted examples, wide spectrum of applications and numerous illustrations, diagrams, and graphs invite students to use the textbook actively, helping them to both enforce their understanding of the material and to brush up on necessary technical and computational skills. Particular attention has been given to the material that some students find challenging, such as the chain rule, Implicit Function Theorem, parametrizations, or the Change of Variables Theorem. Chapter 1: Vectors, Matrices, and Applications. Chapter 2: Calculus of Functions of Several Variables. Chapter 3: Vector-Valued Functions of One Variable. Chapter 4: Scalar and Vector Fields. Chapter 5: Integration Along Paths. Chapter 6: Double and Triple Integrals. Chapter 7: Integrations Over Surfaces, Properties, and Applications of Integrals. Chapter 8: Classical Integration Theorems of Vector Calculus. Appendix A: Various Results Used in This Book and Proofs of Differentiation Theorems. Appendix B: Answers to Odd-Numbered Exercises. Index.