Calculus Using Mathematica is intended for college students taking a course in calculus. It teaches the basic skills of differentiation and integration and how to use Mathematica, a scientific software language, to perform very elaborate symbolic and numerical computations. This is a set composed of the core text, science and math projects, and computing software for symbolic manipulation and graphics generation. Topics covered in the core text include an introduction on how to get started with the program, the ideas of independent and dependent variables and parameters in the context of some down-to-earth applications, formulation of the main approximation of differential calculus, and discrete dynamical systems. The fundamental theory of integration, analytical vector geometry, and two dimensional linear dynamical systems are elaborated as well. This publication is intended for beginning college students.
This book gives a complete and elementary account of fundamental results on hyperfinite measures and their application to stochastic processes, including the *-finite Stieltjes sum approximation of martingale integrals. Many detailed examples, not found in the literature, are included. It begins with a brief chapter on tools from logic and infinitesimal (or non-standard) analysis so that the material is accessible to beginning graduate students.
Calculus Using Mathematica: Scientific Projects and Mathematical Background is a companion to the core text, Calculus Using Mathematica. The book contains projects that illustrate applications of calculus to a variety of practical situations. The text consists of 14 chapters of various projects on how to apply the concepts and methodologies of calculus. Chapters are devoted to epidemiological applications; log and exponential functions in science; applications to mechanics, optics, economics, and ecology. Applications of linear differential equations; forced linear equations; differential equations from vector geometry; and to chemical reactions are presented as well. College students of calculus will find this book very helpful.
This package is designed for the three-semester calculus course offered at undergraduate institutions. It features Mathematica NoteBooks on diskette for symbolic manipulation and graphics generation, and includes a separate Mathematical Background and Scientific Projects volume which provides interdisciplinary applications, enabling the instructor to apply and illustrate the concepts under discussion.
Projects for Calculus is designed to add depth and meaning to any calculus course. The fifty-two projects presented in this text offer the opportunity to expand the use and understanding of mathematics. The wide range of topics will appeal to both instructors and students. Shorter, less demanding projects can be managed by the independent learner, while more involved, in-depth projects may be used for group learning. Each task draws on special mathematical topics and applications from subjects including medicine, engineering, economics, ecology, physics, and biology. Subjects including: * Medicine * Engineering * Economics * Ecology * Physics * Biology.
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