Multivariable Calculus : A Geometric Approach
For a one-semester sophomore-level course in multivariable calculus, for Engineering, Mathematics, or Science students.Reform ideas, traditional ideas, and original ideas are combined in this text that is designed to teach concepts and computations, especially intuitive ones about the geometry of 3 space. The core concepts of multivariable calculus are presented in a straightforward, but never simplistic language that will familiarize students with the thinking and speaking habits of mathematicians and ease their access to the mathematics of applications and higher mathematics courses.
- Paperback | 456 pages
- 198.1 x 251.5 x 17.8mm | 861.84g
- 14 Aug 2001
- Pearson Education (US)
- Upper Saddle River, NJ, United States
Table of contents
Preface. 1. Vectors and Curves. Vectors in the Plane. Lines and Curves in the Plane. Acceleration. The Dot Product. Coordinates and Vectors in Space. Lines in Space. The Dot Product of Space Vectors. The Cross Product. Planes. Curves in Space. Normals of Curves.2. Functions and Differentiation. Functions of Two Variables. Functions of Three Variables. Limits and Continuity. Partial Derivatives. Linear Approximation. The Chain Rule. Directional Derivatives: Functions of Two Variables. Directional Derivatives: Functions of Three Variables. Higher Order Approximations. Local (or Relative) Extrema. Constrained Extrema. Global (or Absolute) Extrema.3. Integration. Double Integrals I - Description and Properties. Double Integrals II - Cartesian Coordinates. Double Integrals in Polar Coordinates. Triple Integrals. Triple Integrals in Cylindrical Coordinates. Triple Integrals in Spherical Coordinates.4. Vector Fields. Vector Fields in the Plane. Flow Lines of a Vector Field in the Plane. Vector Fields in Space. The Symbol o.5. Line Integrals. Force Fields and Work. Work and Line Integrals. Conservative Vector Fields. The Curl-Test.6. Surface Integrals. Parametrized Planes. Parametrized Surfaces. Velocity Fields and Flux. Flux and Surface Integrals.7. The Theorems of Green, Gauss, and Stokes. The Boundary of Solids, Surfaces, and Curves. Gauss' Divergence Theorem. Stokes' Theorem.Answers to Odd Problems.