About this product

Product Identifiers

PublisherSpringer New York

ISBN-100387983600

ISBN-139780387983608

eBay Product ID (ePID)1027736

Product Key Features

Number of PagesXiii, 283 Pages

Publication NameMultivariable Calculus and Mathematica : with Applications to Geometry and Physics

LanguageEnglish

SubjectProgramming / Algorithms, Geometry / Differential, Mathematical & Statistical Software, Probability & Statistics / Multivariate Analysis, Calculus, Mathematical Analysis

Publication Year1998

TypeTextbook

Subject AreaMathematics, Computers

AuthorKevin R. Coombes, Ronald L. Lipsman, Jonathan M. Rosenberg

FormatTrade Paperback

Dimensions

Item Height0.3 in

Item Weight20.8 Oz

Item Length9.6 in

Item Width6.7 in

Additional Product Features

Intended AudienceScholarly & Professional

LCCN97-044764

Dewey Edition21

Number of Volumes1 vol.

IllustratedYes

Dewey Decimal515/.84/078553042

Table Of ContentBenefits of Mathematical Software.- What's in This Book.- What's Not in This Book.- How to Use This Book.- A Word About Versions of Mathematica.- Problem Set A: Review of One-Variable Calculus.- Vectors and Graphics.- Vectors.- Parametric Curves.- Graphing Surfaces.- Parametric Surfaces.- Problem Set B: Vectors and Graphics.- Geometry of Curves.- Parametric Curves.- Geometric Invariants.- Differential Geometry of Curves.- Two More Examples.- Problem Set C: Curves.- Kinematics.- Newton's Laws of Motion.- Kepler's Laws of Planetary Motion.- Studying Equations of Motion with Mathematica.- Problem Set D: Kinematics.- Directional Derivatives.- Visualizing Functions of Two Variables.- The Gradient of a Function of Two Variables.- Functions of Three or More Variables.- Problem Set E: Directional Derivatives and the Gradient.- Geometry of Surfaces.- The Concept of a Surface.- The Implicit Function Theorem.- Geometric Invariants.- Curvature Calculations with Mathematica.- Problem Set F: Surfaces.- Optimization in Several Variables.- The One-Variable Case.- Functions of Two Variables.- Three or More Variables.- Problem Set G: Optimization.- Multiple Integrals.- Automation and Integration.- Regions in the Plane.- Viewing Simple Regions.- Polar Regions.- Viewing Solid Regions.- A More Complicated Example.- Cylindrical Coordinates.- More General Changes of Coordinates.- Problem Set H: Multiple Integrals.- Physical Applications of Vector Calculus.- Motion in a Central Force Field.- Newtonian Gravitation.- Electricity and Magnetism.- Fluid Flow.- Problem Set I: Physical Applications.- Appendix: Energy Minimization and Laplace's Equation.- Mathematica Tips.- Sample Notebook Solutions.

SynopsisOne of the authors' stated goals for this publication is to "modernize" the course through the integration of Mathematica. Besides introducing students to the multivariable uses of Mathematica, and instructing them on how to use it as a tool in simplifying calculations, they also present intoductions to geometry, mathematical physics, and kinematics, topics of particular interest to engineering and physical science students. In using Mathematica as a tool, the authors take pains not to use it simply to define things as a whole bunch of new "gadgets" streamlined to the taste of the authors, but rather they exploit the tremendous resources built into the program. They also make it clear that Mathematica is not algorithms. At the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The problem sets give students an opportunity to practice their newly learned skills, covering simple calculations with Mathematica, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numberical integration. They also cover the practice of incorporating text and headings into a Mathematica notebook. A DOS-formatted diskette accompanies the printed work, containing both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students. This supplementary work can be used with any standard multivariable calculus textbook. It is assumed that in most cases students will also have access to an introductory primer for Mathematica., The goal of this book is to integrate Mathematica into the framework of multivariable calculus. Following a self-tutorial approach, and including problem sets for additional practice, the book introduces readers to the uses of Mathematica as a tool in simplifying calculation and for solving problems in multivariable calculus., Designed to accompany any standard textbook on multivariable calculus, this innovative supplementary book and diskette provide students with important computational tools by showing them how to draw upon the tremendous power of the Mathematica software system in doing mathematics.

LC Classification NumberQA299.6-433