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| calculus using mathematica: Calculus Using Mathematica K.D. Stroyan, 2014-05-10 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. |
| calculus using mathematica: Calculus Using Mathematica K.D. Stroyan, 2014-05-10 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. |
| calculus using mathematica: Multivariable Calculus and Mathematica® Kevin R. Coombes, Ronald Lipsman, Jonathan Rosenberg, 1998-05-15 Aiming to modernise the course through the integration of Mathematica, this publication introduces students to its multivariable uses, instructs them on its use as a tool in simplifying calculations, and presents introductions to geometry, mathematical physics, and kinematics. The authors make it clear that Mathematica is not algorithms, but at the same time, they clearly see the ways in which Mathematica can make things cleaner, clearer and simpler. The sets of problems give students an opportunity to practice their newly learned skills, covering simple calculations, simple plots, a review of one-variable calculus using Mathematica for symbolic differentiation, integration and numerical integration, and also cover the practice of incorporating text and headings into a Mathematica notebook. The accompanying diskette contains both Mathematica 2.2 and 3.0 version notebooks, as well as sample examination problems for students, which can be used with any standard multivariable calculus textbook. It is assumed that students will also have access to an introductory primer for Mathematica. |
| calculus using mathematica: Calculus Projects Using Mathematica Alfred D. Andrew, 1996 This book contains the Mathematica-based projects used in calculus at the Georgia Institute of Technology. Among the authors interests when writing these projects were to capture student interest through projects closely tied to their mathematics, science, and engineering curricula. This book will e |
| calculus using mathematica: Exploring Calculus Crista Arangala, Karen A. Yokley, 2016-08-03 This text is meant to be a hands-on lab manual that can be used in class every day to guide the exploration of the theory and applications of differential and integral calculus. For the most part, labs can be used individually or in a sequence. Each lab consists of an explanation of material with integrated exercises. Some labs are split into multiple subsections and thus exercises are separated by those subsections. The exercise sections integrate problems, technology, Mathematica R visualization, and Mathematica CDFs that allow students to discover the theory and applications of differential and integral calculus in a meaningful and memorable way. |
| calculus using mathematica: The Student's Introduction to MATHEMATICA ® Bruce F. Torrence, Eve A. Torrence, 2009-01-29 The unique feature of this compact student's introduction is that it presents concepts in an order that closely follows a standard mathematics curriculum, rather than structure the book along features of the software. As a result, the book provides a brief introduction to those aspects of the Mathematica software program most useful to students. The second edition of this well loved book is completely rewritten for Mathematica 6 including coverage of the new dynamic interface elements, several hundred exercises and a new chapter on programming. This book can be used in a variety of courses, from precalculus to linear algebra. Used as a supplementary text it will aid in bridging the gap between the mathematics in the course and Mathematica. In addition to its course use, this book will serve as an excellent tutorial for those wishing to learn Mathematica and brush up on their mathematics at the same time. |
| calculus using mathematica: Hands-on Start to Wolfram Mathematica Cliff Hastings, Kelvin Mischo, Michael Morrison, 2015 For more than 25 years, Mathematica has been the principal computation environment for millions of innovators, educators, students, and others around the world. This book is an introduction to Mathematica. The goal is to provide a hands-on experience introducing the breadth of Mathematica, with a focus on ease of use. Readers get detailed instruction with examples for interactive learning and end-of-chapter exercises. Each chapter also contains authors tips from their combined 50+ years of Mathematica use. |
| calculus using mathematica: Calculus Kevin M. O'Connor, O'Connor, 2005 Correlated directly to Calculus: The Language of Change, an engaging new text by David Cohen and James Henle, this outstanding lab manual provides numerous labs, projects, and exercises to teach students how to use MATLAB. Written in a friendly and accessible style, this is the ideal resource for students to practice what they've learned in the text. |
| calculus using mathematica: Mathematica by Example Martha L Abell, James P. Braselton, 2014-05-09 Mathematica by Example presents the commands and applications of Mathematica, a system for doing mathematics on a computer. This text serves as a guide to beginning users of Mathematica and users who do not intend to take advantage of the more specialized applications of Mathematica. The book combines symbolic manipulation, numerical mathematics, outstanding graphics, and a sophisticated programming language. It is comprised of 10 chapters. Chapter 1 gives a brief background of the software and how to install it in the computer. Chapter 2 introduces the essential commands of Mathematica. Basic operations on numbers, expressions, and functions are introduced and discussed. Chapter 3 provides Mathematica's built-in calculus commands. The fourth chapter presents elementary operations on lists and tables. This chapter is a prerequisite for Chapter 5 which discusses nested lists and tables in detail. The purpose of Chapter 6 is to illustrate various computations Mathematica can perform when solving differential equations. Chapters 7, 8, and 9 introduce Mathematica Packages that are not found in most Mathematica reference book. The final chapter covers the Mathematica Help feature. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful. |
| calculus using mathematica: Projects for Calculus Keith D. Stroyan, 1998-11-03 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 |
| calculus using mathematica: Animating Calculus Edward W. Packel, Stan Wagon, 1997 Animating Calculus is designed to help you explore calculus and visualize concepts through the use of computation and animation. This collection of 22 labs, together with the computer algebra system Mathematica, can be used for self-study, demonstration, or as a laboratory supplement to an existing calculus sequence. Standard calculus topics as well as new and unusual extensions and applications are presented, including derivatives and rate of change, calculus and landing airplanes, population dynamics and iteration, the fundamental theorem, The Buffon needle problem, numerical and symbolic integration, rolling wheels (round and square), subtleties of the harmonic series, and more. Animating Calculus includes exercises and demonstrations that focus on important and fundamental ideas and applications rather than the everyday mechanics of a computer algebra system. Sophisticated animations are used to clarify geometric concepts in calculus. In addition, discussions of numerical and graphical pitfalls help the student to understand the importance of verifying results. Originally published by W. H. Freeman, this new TELOS edition of Animating Calculus includes the full set of labs for DOS/Windows as well as Macintosh platforms. |
| calculus using mathematica: Integral Calculus and Differential Equations Using Mathematica Cesar Perez Lopez, 2016-01-16 This book provides all the material needed to work on Integral Calculus and Differential Equations using Mathematica. It includes techniques for solving all kinds of integral and its applications for calculating lengths of curves, areas, volumes, surfaces of revolution... With Mathematica is possible solve ordinary and partial differential equations of various kinds, and systems of such equations, either symbolically or using numerical methods (Euler's method,, the Runge-Kutta method,...). It also describes how to implement mathematical tools such as the Laplace transform, orthogonal polynomials, and special functions (Airy and Bessel functions), and find solutions of differential equations in partial derivatives.The main content of the book is as follows:PRACTICAL INTRODUCTION TO MATHEMATICA 1.1 CALCULATION NUMERIC WITH MATHEMATICA 1.2 SYMBOLIC CALCULATION WITH MATHEMATICA 1.3 GRAPHICS WITH MATHEMATICA 1.4 MATHEMATICA AND THE PROGRAMMING INTEGRATION AND APPLICATIONS 2.1 INDEFINITE INTEGRALS 2.1.1 Inmediate integrals 2.2 INTEGRATION BY SUBSTITUTION (OR CHANGE OF VARIABLES) 2.2.1 Exponential, logarithmic, hyperbolic and inverse circular functions 2.2.2 Irrational functions, binomial integrals 2.3 INTEGRATION BY PARTS 2.4 INTEGRATION BY REDUCTION AND CYCLIC INTEGRATION DEFINITE INTEGRALS. CURVE ARC LENGTH, AREAS, VOLUMES AND SURFACES OF REVOLUTION. IMPROPER INTEGRALS 3.1 DEFINITE INTEGRALS 3.2 CURVE ARC LENGTH 3.3 THE AREA ENCLOSED BETWEEN CURVES 3.4 SURFACES OF REVOLUTION 3.5 VOLUMES OF REVOLUTION 3.6 CURVILINEAR INTEGRALS 3.7 IMPROPER INTEGRALS 3.8 PARAMETER DEPENDENT INTEGRALS 3.9 THE RIEMANN INTEGRAL INTEGRATION IN SEVERAL VARIABLES AND APPLICATIONS. AREAS AND VOLUMES. DIVERGENCE, STOKES AND GREEN'S THEOREMS 4.1 AREAS AND DOUBLE INTEGRALS 4.2 SURFACE AREA BY DOUBLE INTEGRATION 4.3 VOLUME CALCULATION BY DOUBLE INTEGRALS 4.4 VOLUME CALCULATION AND TRIPLE INTEGRALS 4.5 GREEN'S THEOREM 4.6 THE DIVERGENCE THEOREM 4.7 STOKES' THEOREM FIRST ORDER DIFFERENTIAL EQUATIONS. SEPARATES VARIABLES, EXACT EQUATIONS, LINEAR AND HOMOGENEOUS EQUATIONS. NUMERIACAL METHODS 5.1 SEPARATION OF VARIABLES 5.2 HOMOGENEOUS DIFFERENTIAL EQUATIONS 5.3 EXACT DIFFERENTIAL EQUATIONS 5.4 LINEAR DIFFERENTIAL EQUATIONS 5.5 NUMERICAL SOLUTIONS TO DIFFERENTIAL EQUATIONS OF THE FIRST ORDER HIGH-ORDER DIFFERENTIAL EQUATIONS AND SYSTEMS OF DIFFERENTIAL EQUATIONS 6.1 ORDINARY HIGH-ORDER EQUATIONS 6.2 HIGHER-ORDER LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.3 NON-HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS. VARIATION OF PARAMETERS 6.4 NON-HOMOGENEOUS LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS. CAUCHY-EULER EQUATIONS 66.5 THE LAPLACE TRANSFORM 6.6 SYSTEMS OF LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.7 SYSTEMS OF LINEAR NON-HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS HIGHER ORDEN DIFFERENTIAL EQUATIONS AND SYSTEMS USING APPROXIMATION METHODS. DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES 7.1 HIGHER ORDER EQUATIONS AND APPROXIMATION METHODS 7.2 THE EULER METHOD 7.3 THE RUNGE-KUTTA METHOD 7.4 DIFFERENTIAL EQUATIONS SYSTEMS BY APPROXIMATE METHODS 7.5 DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES 7.6 ORTHOGONAL POLYNOMIALS 7.7 AIRY AND BESSEL FUNCTIONS |
| calculus using mathematica: Calculus and Differential Equations with Mathematica Pramote Dechaumphai, 2016 |
| calculus using mathematica: Essentials of Mathematica Nino Boccara, 2007-10-17 Essential Mathematica: With Applications to Mathematics and Physics, based on the lecture notes of a course taught at the University of Illinois at Chicago to advanced undergrad and graduate students, teaches how to use Mathematica to solve a wide variety problems in mathematics and physics. It is illustrated with many detailed examples that require the student to construct meticulous, step-by-step, easy to read Mathematica programs. The first section, in which the reader learns how to use a variety of Mathematica commands, avoids long discussions and overly sophisticated techniques. Its aim is to provide the reader with Mathematica proficiency quickly and efficiently. The second section covers a broad range of applications in physics, engineering and applied mathematics, including Egyptian Fractions, Happy Numbers, Mersenne Numbers, Multibases, Quantum Harmonic Oscillator, Quantum Square Potential, Van der Pol Oscillator, Electrostatics, Motion of a Charged Particle inan Electromagnetic Field, Duffing Oscillator, Negative and Complex Bases, Tautochrone Curves, Kepler’s Laws, Foucault’s Pendulum, Iterated Function Systems, Public-Key Encryption, and Julia and Mandelbrot Sets. The first part - examples, not long explanations. The second part-attractive applications. |
| calculus using mathematica: Calculus II Tunc Geveci, 2010-10 Calculus II is the second volume of the three-volume calculus sequence by Tunc Geveci. The series is designed for the usual three-semester calculus sequence that the majority of science and engineering majors in the United States are required to take. The distinguishing features of the book are the focus on the concepts, essential functions and formulas of calculus and the effective use of graphics as an integral part of the exposition. Formulas that are not significant and exercises that involve artificial algebraic difficulties are avoided. The three-volume calculus sequence is organized as follows: Calculus I covers the usual topics of the first semester: limits, continuity, the derivative, the integral and special functions such as exponential functions, logarithms and inverse trigonometric functions. Calculus II covers techniques and applications of integration, improper integrals, infinite series, linear and separable first-order differential equations, parametrized curves and polar coordinates. Calculus III covers vectors, the differential calculus of functions of several variables, multiple integrals, line integrals, surface integrals, Green's Theorem, Stokes' Theorem and Gauss' Theorem. |
| calculus using mathematica: Multivariable Calculus with Mathematica Robert P. Gilbert, Michael Shoushani, Yvonne Ou, 2020-11-24 Multivariable Calculus with Mathematica is a textbook addressing the calculus of several variables. Instead of just using Mathematica to directly solve problems, the students are encouraged to learn the syntax and to write their own code to solve problems. This not only encourages scientific computing skills but at the same time stresses the complete understanding of the mathematics. Questions are provided at the end of the chapters to test the student’s theoretical understanding of the mathematics, and there are also computer algebra questions which test the student’s ability to apply their knowledge in non-trivial ways. Features Ensures that students are not just using the package to directly solve problems, but learning the syntax to write their own code to solve problems Suitable as a main textbook for a Calculus III course, and as a supplementary text for topics scientific computing, engineering, and mathematical physics Written in a style that engages the students’ interest and encourages the understanding of the mathematical ideas |
| calculus using mathematica: Mathematica for Calculus-based Physics Marvin L. De Jong, 1999 This workbook/laboratory manual, designed for the first- or second-year physics student, integrates a computer algebra system, Mathematica, with calculus-based physics. Students learn physics, mathematics, and Mathematica by applying the system to numerous physics problems drawn from a broad range of topics in introductory calculus-based physics. Mathematica's extensive use of graphs helps students visualize solutions as well as find analytical solutions to the problems, which often are skills needed in physics research. |
| calculus using mathematica: Symmetry Analysis of Differential Equations with Mathematica® Gerd Baumann, 2000-04-20 The first book to explicitly use Mathematica so as to allow researchers and students to more easily compute and solve almost any kind of differential equation using Lie's theory. Previously time-consuming and cumbersome calculations are now much more easily and quickly performed using the Mathematica computer algebra software. The material in this book, and on the accompanying CD-ROM, will be of interest to a broad group of scientists, mathematicians and engineers involved in dealing with symmetry analysis of differential equations. Each section of the book starts with a theoretical discussion of the material, then shows the application in connection with Mathematica. The cross-platform CD-ROM contains Mathematica (version 3.0) notebooks which allow users to directly interact with the code presented within the book. In addition, the author's proprietary MathLie software is included, so users can readily learn to use this powerful tool in regard to performing algebraic computations. |
| calculus using mathematica: The Mathematica GuideBook for Programming Michael Trott, 2004-10-28 This comprehensive, detailed reference provides readers with both a working knowledge of Mathematica in general and a detailed knowledge of the key aspects needed to create the fastest, shortest, and most elegant implementations possible. It gives users a deeper understanding of Mathematica by instructive implementations, explanations, and examples from a range of disciplines at varying levels of complexity. The three volumes -- Programming, Graphics, and Mathematics, total 3,000 pages and contain more than 15,000 Mathematica inputs, over 1,500 graphics, 4,000+ references, and more than 500 exercises. This first volume begins with the structure of Mathematica expressions, the syntax of Mathematica, its programming, graphic, numeric and symbolic capabilities. It then covers the hierarchical construction of objects out of symbolic expressions, the definition of functions, the recognition of patterns and their efficient application, program flows and program structuring, and the manipulation of lists. An indispensible resource for students, researchers and professionals in mathematics, the sciences, and engineering. |
| calculus using mathematica: The Mathematica Handbook Martha L Abell, James P. Braselton, 2014-05-09 The Mathematica Handbook provides all the Mathematica commands and objects along with typical examples of them. This handbook is intended as a reference of all built-in Mathematica Version 2.0 objects to both beginning and advanced users of Mathematica. The book contains commands and examples of those commands found in the packages of Mathematica, a system for doing mathematics on a computer. The Preface describes how to use the entries of The Handbook and then briefly discusses elementary rules of Mathematica syntax, defining functions, and using commands that are contained in the standard Mathematica packages. Subsequent chapters provide commands for calculations in Calculus, Statistics, and Numerical Math. The commands in these sections are listed within each package, and the packages are listed alphabetically within each folder (or directory) as well. The book will be of use to engineers, computer scientists, physical scientists, mathematicians, business professionals, and students. |
| calculus using mathematica: Mathematical Statistics with Mathematica Colin Rose, Murray D. Smith, 2002 This text and software package presents a unified approach for doing mathematical statistics with Mathematica. The mathStatica software empowers the student with the ability to solve difficult problems. The professional statistician should be able to tackle tricky multivariate distributions, generating functions, inversion theorems, symbolic maximum likelihood estimation, unbiased estimation, and the checking and correcting of textbook formulae. This is the ideal companion for researchers and students in statistics, econometrics, engineering, physics, psychometrics, economics, finance, biometrics, and the social sciences. The mathStatica CD-ROM includes: mathStatica - the applications pack for mathematical statistics, custom Mathematica palettes, live interactive book that is identical to the printed text, online help, and a trial version of Mathematica 4.0. |
| calculus using mathematica: Advanced Calculus Lynn H. Loomis, Shlomo Sternberg, 2014 An authorised reissue of the long out of print classic textbook, Advanced Calculus by the late Dr Lynn Loomis and Dr Shlomo Sternberg both of Harvard University has been a revered but hard to find textbook for the advanced calculus course for decades. This book is based on an honors course in advanced calculus that the authors gave in the 1960's. The foundational material, presented in the unstarred sections of Chapters 1 through 11, was normally covered, but different applications of this basic material were stressed from year to year, and the book therefore contains more material than was covered in any one year. It can accordingly be used (with omissions) as a text for a year's course in advanced calculus, or as a text for a three-semester introduction to analysis. The prerequisites are a good grounding in the calculus of one variable from a mathematically rigorous point of view, together with some acquaintance with linear algebra. The reader should be familiar with limit and continuity type arguments and have a certain amount of mathematical sophistication. As possible introductory texts, we mention Differential and Integral Calculus by R Courant, Calculus by T Apostol, Calculus by M Spivak, and Pure Mathematics by G Hardy. The reader should also have some experience with partial derivatives. In overall plan the book divides roughly into a first half which develops the calculus (principally the differential calculus) in the setting of normed vector spaces, and a second half which deals with the calculus of differentiable manifolds. |
| calculus using mathematica: The Student's Introduction to Mathematica and the Wolfram Language Bruce F. Torrence, Eve A. Torrence, 2019-05-16 An introduction to Mathematica® and the Wolfram Language(TM) in the familiar context of the standard university mathematics curriculum. |
| calculus using mathematica: Mathematics for Machine Learning Marc Peter Deisenroth, A. Aldo Faisal, Cheng Soon Ong, 2020-04-23 Distills key concepts from linear algebra, geometry, matrices, calculus, optimization, probability and statistics that are used in machine learning. |
| calculus using mathematica: Calculus: Concepts and Methods Ken Binmore, Joan Davies, 2002-02-07 The pebbles used in ancient abacuses gave their name to the calculus, which today is a fundamental tool in business, economics, engineering and the sciences. This introductory book takes readers gently from single to multivariate calculus and simple differential and difference equations. Unusually the book offers a wide range of applications in business and economics, as well as more conventional scientific examples. Ideas from univariate calculus and linear algebra are covered as needed, often from a new perspective. They are reinforced in the two-dimensional case, which is studied in detail before generalisation to higher dimensions. Although there are no theorems or formal proofs, this is a serious book in which conceptual issues are explained carefully using numerous geometric devices and a wealth of worked examples, diagrams and exercises. Mathematica has been used to generate many beautiful and accurate, full-colour illustrations to help students visualise complex mathematical objects. This adds to the accessibility of the text, which will appeal to a wide audience among students of mathematics, economics and science. |
| calculus using mathematica: Computational Financial Mathematics using MATHEMATICA® Srdjan Stojanovic, 2012-12-06 Given the explosion of interest in mathematical methods for solving problems in finance and trading, a great deal of research and development is taking place in universities, large brokerage firms, and in the supporting trading software industry. Mathematical advances have been made both analytically and numerically in finding practical solutions. This book provides a comprehensive overview of existing and original material, about what mathematics when allied with Mathematica can do for finance. Sophisticated theories are presented systematically in a user-friendly style, and a powerful combination of mathematical rigor and Mathematica programming. Three kinds of solution methods are emphasized: symbolic, numerical, and Monte-- Carlo. Nowadays, only good personal computers are required to handle the symbolic and numerical methods that are developed in this book. Key features: * No previous knowledge of Mathematica programming is required * The symbolic, numeric, data management and graphic capabilities of Mathematica are fully utilized * Monte--Carlo solutions of scalar and multivariable SDEs are developed and utilized heavily in discussing trading issues such as Black--Scholes hedging * Black--Scholes and Dupire PDEs are solved symbolically and numerically * Fast numerical solutions to free boundary problems with details of their Mathematica realizations are provided * Comprehensive study of optimal portfolio diversification, including an original theory of optimal portfolio hedging under non-Log-Normal asset price dynamics is presented The book is designed for the academic community of instructors and students, and most importantly, will meet the everyday trading needs of quantitatively inclined professional and individual investors. |
| calculus using mathematica: Advanced Calculus Explored , 2019-11-29 |
| calculus using mathematica: Vector Calculus Using Mathematica Second Edition Steven Tan, 2020-07-11 An introduction to vector calculus with the aid of Mathematica® computer algebra system to represent them and to calculate with them. The unique features of the book, which set it apart from the existing textbooks, are the large number of illustrative examples. It is the author’s opinion a novice in science or engineering needs to see a lot of examples in which mathematics is used to be able to “speak the language.” All these examples and all illustrations can be replicated and used to learn and discover vector calculus in a new and exciting way. Reader can practice with the solutions, and then modify them to solve the particular problems assigned. This should move up problem solving skills and to use Mathematica® to visualize the results and to develop a deeper intuitive understanding. Usually, visualization provides much more insight than the formulas themselves. The second edition is an addition of the first. Two new chapters on line integrals, Green's Theorem, Stokes's Theorem and Gauss's Theorem have been added. |
| calculus using mathematica: Differential Equations Clay C. Ross, 2013-03-09 Goals and Emphasis of the Book Mathematicians have begun to find productive ways to incorporate computing power into the mathematics curriculum. There is no attempt here to use computing to avoid doing differential equations and linear algebra. The goal is to make some first ex plorations in the subject accessible to students who have had one year of calculus. Some of the sciences are now using the symbol-manipulative power of Mathemat ica to make more of their subject accessible. This book is one way of doing so for differential equations and linear algebra. I believe that if a student's first exposure to a subject is pleasant and exciting, then that student will seek out ways to continue the study of the subject. The theory of differential equations and of linear algebra permeates the discussion. Every topic is supported by a statement of the theory. But the primary thrust here is obtaining solutions and information about solutions, rather than proving theorems. There are other courses where proving theorems is central. The goals of this text are to establish a solid understanding of the notion of solution, and an appreciation for the confidence that the theory gives during a search for solutions. Later the student can have the same confidence while personally developing the theory. |
| calculus using mathematica: Calculus K. D. Stroyan, 1998 Calculus: the language of change is the second edition of the calculus reform materials formerly called Calculus using mathematica. Designed to meet the needs of what has become a large market, it tones down more radical reforms, adds new drill exercises, and includes Maple V as well as Mathematica (version 2.3). |
| calculus using mathematica: Calculus Using Mathematica K. D. Stroyan, 1993-08-01 |
| calculus using mathematica: The MATHEMATICA ® Book, Version 3 Stephen Wolfram, 1996-07-13 With over a million users around the world, the Mathematica ® software system created by Stephen Wolfram has defined the direction of technical computing for nearly a decade. With its major new document and computer language technology, the new version, Mathematica 3.0 takes the top-power capabilities of Mathematica and make them accessible to a vastly broader audience. This book presents this revolutionary new version of Mathematica. The Mathematica Book is a must-have purchase for anyone who wants to understand the revolutionary opportunities in science, technology, business and education made possible by Mathematica 3.0. This encompasses a broad audience of scientists and mathematicians; engineers; computer professionals; quantitative financial analysts; medical researchers; and students at high-school, college and graduate levels. Written by the creator of the system, The Mathematica Book includes both a tutorial introduction and complete reference information, and contains a comprehensive description of how to take advantage of Mathematica's ability to solve myriad technical computing problems and its powerful graphical and typesetting capabilities. Like previous editions, the book is sure to be found well-thumbed on the desks of many technical professionals and students around the world. |
| calculus using mathematica: Calculus for the Life Sciences James L. Cornette, Ralph A. Ackerman, 2015-12-30 Freshman and sophomore life sciences students respond well to the modeling approach to calculus, difference equations, and differential equations presented in this book. Examples of population dynamics, pharmacokinetics, and biologically relevant physical processes are introduced in Chapter 1, and these and other life sciences topics are developed throughout the text. The students should have studied algebra, geometry, and trigonometry, but may be life sciences students because they have not enjoyed their previous mathematics courses. |
| calculus using mathematica: Introduction to Ordinary Differential Equations with Mathematica® Alfred Gray, Mike Mezzino, Mark Pinsky, 1998-06-01 The purpose of this companion volume to our text is to provide instructors (and eventu ally students) with some additional information to ease the learning process while further documenting the implementations of Mathematica and ODE. In an ideal world this volume would not be necessary, since we have systematically worked to make the text unambiguous and directly useful, by providing in the text worked examples of every technique which is discussed at the theoretical level. However, in our teaching we have found that it is helpful to have further documentation of the various solution techniques introduced in the text. The subject of differential equations is particularly well-suited to self-study, since one can always verify by hand calculation whether or not a given proposed solution is a bona fide solution of the differential equation and initial conditions. Accordingly, we have not reproduced the steps of the verification process in every case, rather content with the illustration of some basic cases of verification in the text. As we state there, students are strongly encouraged to verify that the proposed solution indeed satisfies the requisite equation and supplementary conditions. |
| calculus using mathematica: Differential Calculus Using Mathematica Cesar Perez, 2016-01-16 Mathematica is a platform for scientific computing that helps you to work in virtually all areas of the experimental sciences and engineering. In particular, this software presents quite extensive capabilities and implements a large number of commands enabling you to efficiently handle problems involving Differential Calculus. Using Mathematica you will be able to work with Limits, Numerical and power series, Taylor and MacLaurin series, continuity, derivability, differentiability in several variables, optimization and differential equations. Mathematica also implements numerical methods for the approximate solution of differential equations. The main content of the book is as follows: LIMITS AND CONTINUITY. ONE AND SEVERAL VARIABLES 1.1 LIMITS OF SEQUENCES 1.2 LIMITS OF FUNCTIONS. LATERAL LIMITS 1.3 CONTINUITY 1.4 SEVERAL VARIABLES: LIMITS AND CONTINUITY. CHARACTERIZATION THEOREMS 1.5 ITERATED AND DIRECTIONAL LIMITS 1.6 CONTINUITY IN SEVERAL VARIABLES NUMERICAL SERIES AND POWER SERIES 2.1 SERIES. CONVERGENCE CRITERIA 2.2 NUMERICAL SERIES WITH NON-NEGATIVE TERMS 2.3 ALTERNATING NUMERICAL SERIES 2.4 POWER SERIES 2.5 POWER SERIES EXPANSIONS AND FUNCTIONS 2.6 TAYLOR AND LAURENT EXPANSIONS DERIVATIVES AND APPLICATIONS. ONE AND SEVERAL VARIABLES 3.1 THE CONCEPT OF THE DERIVATIVE 3.2 CALCULATING DERIVATIVES 3.3 TANGENTS, ASYMPTOTES, CONCAVITY, CONVEXITY, MAXIMA AND MINIMA, INFLECTION POINTS AND GROWTH 3.4 APPLICATIONS TO PRACTICAL PROBLEMS 3.5 PARTIAL DERIVATIVES 3.6 IMPLICIT DIFFERENTIATION DERIVABILITY IN SEVERAL VARIABLES 4.1 DIFFERENTIATION OF FUNCTIONS OF SEVERAL VARIABLES 4.2 MAXIMA AND MINIMA OF FUNCTIONS OF SEVERAL VARIABLES 4.3 CONDITIONAL MINIMA AND MAXIMA. THE METHOD OF LAGRANGE MULTIPLIERS 4.4 SOME APPLICATIONS OF MAXIMA AND MINIMA IN SEVERAL VARIABLES VECTOR DIFFERENTIAL CALCULUS AND THEOREMS IN SEVERAL VARIABLES 5.1 CONCEPTS OF VECTOR DIFFERENTIAL CALCULUS 5.2 THE CHAIN RULE 5.3 THE IMPLICIT FUNCTION THEOREM 5.4 THE INVERSE FUNCTION THEOREM 5.5 THE CHANGE OF VARIABLES THEOREM 5.6 TAYLOR'S THEOREM WITH N VARIABLES 5.7 VECTOR FIELDS. CURL, DIVERGENCE AND THE LAPLACIAN 5.8 COORDINATE TRANSFORMATION DIFFERENTIAL EQUATIONS 6.1 SEPARATION OF VARIABLES 6.2 HOMOGENEOUS DIFFERENTIAL EQUATIONS 6.3 EXACT DIFFERENTIAL EQUATIONS 6.4 LINEAR DIFFERENTIAL EQUATIONS 6.5 NUMERICAL SOLUTIONS TO DIFFERENTIAL EQUATIONS OF THE FIRST ORDER 6.6 ORDINARY HIGH-ORDER EQUATIONS 6.7 HIGHER-ORDER LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.8 NON-HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS. VARIATION OF PARAMETERS 6.9 NON-HOMOGENEOUS LINEAR EQUATIONS WITH VARIABLE COEFFICIENTS. CAUCHY-EULER EQUATIONS 6.10 THE LAPLACE TRANSFORM 6.11 SYSTEMS OF LINEAR HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.12 SYSTEMS OF LINEAR NON-HOMOGENEOUS EQUATIONS WITH CONSTANT COEFFICIENTS 6.13 HIGHER ORDER EQUATIONS AND APPROXIMATION METHODS 6.14 THE EULER METHOD 6.15 THE RUNGE-KUTTA METHOD 6.16 DIFFERENTIAL EQUATIONS SYSTEMS BY APPROXIMATE METHODS 6.17 DIFFERENTIAL EQUATIONS IN PARTIAL DERIVATIVES 6.18 ORTHOGONAL POLYNOMIALS |
| calculus using mathematica: Mathematica Stephen Wolfram, 1991 Just out, the long-waited Release 2.0 of Mathematica. This new edition of the complete reference was released simultaneously and covers all the new features of Release 2.0. Includes a comprehensive review of the increased functionality of the program. Annotation copyrighted by Book News, Inc., Portland, OR |
| calculus using mathematica: Insights Into Calculus Using Mathematica Robert T. Smith, Roland B. Minton, 2005-12-01 |
| calculus using mathematica: Insights Into Calculus Using Mathematica® Robert Thomas Smith, 2002 |
Calculus Volume 3 - OpenStax
Study calculus online free by downloading Volume 3 of OpenStax's college Calculus textbook and using …
Calculus Volume 1 - OpenStax
Study calculus online free by downloading volume 1 of OpenStax's college Calculus textbook and using …
Ch. 1 Introduction - Calculus Volume 1 | OpenStax
In this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, trigonometric, exponential, and …
1.1 Review of Functions - Calculus Volume 1 | OpenStax
This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed …
Ch. 5 Introduction - Calculus Volume 1 | OpenStax
In this chapter, we first introduce the theory behind integration and use integrals to calculate areas. From there, we develop the Fundamental …
Calculus Volume 3 - OpenStax
Study calculus online free by downloading Volume 3 of OpenStax's college Calculus textbook and using our accompanying …
Calculus Volume 1 - OpenStax
Study calculus online free by downloading volume 1 of OpenStax's college Calculus textbook and using our accompanying …
Ch. 1 Introduction - Calculus Volume 1 | OpenStax
In this chapter, we review all the functions necessary to study calculus. We define polynomial, rational, trigonometric, exponential, and logarithmic functions.
1.1 Review of Functions - Calculus Volume 1 | OpenStax
This free textbook is an OpenStax resource written to increase student access to high-quality, peer-reviewed learning materials.
Ch. 5 Introduction - Calculus Volume 1 | OpenStax
In this chapter, we first introduce the theory behind integration and use integrals to calculate areas. From there, we develop the Fundamental Theorem of Calculus, …
