January 2007, ©2007
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.
- Comprehensive review of relevant topics in linear algebra and calculus of real-valued functions of one and several variables.
- Geometric, numeric, analytic and applied approaches to presentation of mathematics promote better understanding of the material and help build intuition and experience.
- Detailed, step-by-step solutions to all examples; end of each section contains a large number of exercises, ranging from basic and routine to challenging and thought-provoking.
- Review section at the end of each chapter includes a number of review questions, a true/false quiz and additional problems.
- Several sections entirely devoted to applications; World of Curves and World of Surfaces sections study features of interesting curves and surfaces and introduce several new applications.
- Classical integration theorems of Green, Gauss and Stokes covered in depth, illustrated with numerous examples and applications.