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.
Auflage
Softcover reprint of the original 1st ed. 1998
Sprache
Verlagsort
Zielgruppe
Für höhere Schule und Studium
Für Beruf und Forschung
Lower undergraduate
Illustrationen
50
50 s/w Abbildungen
XIII, 283 p. 50 illus.
Maße
Höhe: 244 mm
Breite: 170 mm
Dicke: 17 mm
Gewicht
ISBN-13
978-0-387-98360-8 (9780387983608)
DOI
10.1007/978-1-4612-1698-8
Schweitzer Klassifikation
Benefits 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.
