Calculus And Differential Equations With Mathematica
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Calculus and Differential Equations with Mathematica by Pramote Dechaumphai Pdf
Symbolic mathematics software have played an important role in learning calculus and differential equations. MATHEMATICA is one of the most powerful software being used to solve various types of problems in mathematics. This book presents a clear and easy-to-understand on how to use MATHEMATICA to solve calculus and differential equation problems. The book contains essential topics that are taught in calculus and differential equation courses. These topics are the limits, differentiation, integration, series, ordinary differential equations, Laplace and Fourier transforms, as well as special functions normally encountered in solving science and engineering problems. Numerical methods, in addition, are employed when the exact solutions are not available. The finite element method developed in the latest MATHEMATICA version is used to analyse partial differential equations for problems with complex geometry. The partial differential equations could be in elliptic, parabolic and hyperbolic forms. A large number of examples are presented with detailed derivation for their solutions before using MATHEMATICA to confirm the same results. With the clear explanation of all topics in this book and with the help of MATHEMATICA software, students will enjoy learning calculus and differential equations as compared to the traditional way in the past.
Differential Equations with Mathematica by Martha L. L. Abell,James P. Braselton Pdf
Differential Equations with Mathematica, Fourth Edition is a supplementing reference which uses the fundamental concepts of the popular platform to solve (analytically, numerically, and/or graphically) differential equations of interest to students, instructors, and scientists. Mathematica’s diversity makes it particularly well suited to performing calculations encountered when solving many ordinary and partial differential equations. In some cases, Mathematica’s built-in functions can immediately solve a differential equation by providing an explicit, implicit, or numerical solution. In other cases, mathematica can be used to perform the calculations encountered when solving a differential equation. Because one goal of elementary differential equations courses is to introduce students to basic methods and algorithms so that they gain proficiency in them, nearly every topic covered this book introduces basic commands, also including typical examples of their application. A study of differential equations relies on concepts from calculus and linear algebra, so this text also includes discussions of relevant commands useful in those areas. In many cases, seeing a solution graphically is most meaningful, so the book relies heavily on Mathematica’s outstanding graphics capabilities. Demonstrates how to take advantage of the advanced features of Mathematica 10 Introduces the fundamental theory of ordinary and partial differential equations using Mathematica to solve typical problems of interest to students, instructors, scientists, and practitioners in many fields Showcases practical applications and case studies drawn from biology, physics, and engineering
Introduction to Ordinary Differential Equations with Mathematica by Alfred Gray,Michael Mezzino,Mark A. Pinsky Pdf
These materials - developed and thoroughly class tested over many years by the authors -are for use in courses at the sophomore/junior level. A prerequisite is the calculus of one variable, although calculus of several variables, and linear algebra are recommended. The text covers the standard topics in first and second order equations, power series solutions, first order systems, Laplace transforms, numerical methods and stability of non-linear systems. Liberal use is made of programs in Mathematica, both for symbolic computations and graphical displays. The programs are described in separate sections, as well as in the accompanying Mathematica notebooks. However, the book has been designed so that it can be read with or without Mathematica and no previous knowledge of Mathematica is required. The CD-ROM contains the Mathematica solution of worked examples, a selection of various Mathematica notebooks, Mathematica movies and sample labs for students. Mathematica programs and additional problem/example files will be available online through the TELOS Web site and the authors dedicated web site.
Differential Equations with Mathematica by Martha L. Abell,James P. Braselton Pdf
The second edition of this groundbreaking book integrates new applications from a variety of fields, especially biology, physics, and engineering. The new handbook is also completely compatible with Mathematica version 3.0 and is a perfect introduction for Mathematica beginners. The CD-ROM contains built-in commands that let the users solve problems directly using graphical solutions.
Integral Calculus and Differential Equations Using Mathematica by Cesar Perez Lopez Pdf
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: 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.
Mathematica by Example by Martha L Abell,James P. Braselton Pdf
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.
Mathematica® by Example by Martha L Abell,James P. Braselton Pdf
Mathematica by Example, Revised Edition 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 7 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. Chapter 7 discusses some of the more frequently used commands contained in various graphics packages available with Mathematica. Engineers, computer scientists, physical scientists, mathematicians, business professionals, and students will find the book useful.
Introduction to Ordinary Differential Equations with Mathematica® by Alfred Gray,Mike Mezzino,Mark Pinsky Pdf
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.
Introduction to Ordinary Differential Equations with Mathematica® by Alfred Gray,Mike Mezzino,Mark Pinsky Pdf
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.
Introduction to Ordinary Differential Equations with Mathematica by Alfred Gray,Michael Mezzino,Mark A. Pinsky Pdf
These materials - developed and thoroughly class tested over many years by the authors -are for use in courses at the sophomore/junior level. A prerequisite is the calculus of one variable, although calculus of several variables, and linear algebra are recommended. The text covers the standard topics in first and second order equations, power series solutions, first order systems, Laplace transforms, numerical methods and stability of non-linear systems. Liberal use is made of programs in Mathematica, both for symbolic computations and graphical displays. The programs are described in separate sections, as well as in the accompanying Mathematica notebooks. However, the book has been designed so that it can be read with or without Mathematica and no previous knowledge of Mathematica is required. The CD-ROM contains the Mathematica solution of worked examples, a selection of various Mathematica notebooks, Mathematica movies and sample labs for students. Mathematica programs and additional problem/example files will be available online through the TELOS Web site and the authors dedicated web site.
The first edition (94301-3) was published in 1995 in TIMS and had 2264 regular US sales, 928 IC, and 679 bulk. This new edition updates the text to Mathematica 5.0 and offers a more extensive treatment of linear algebra. It has been thoroughly revised and corrected throughout.
Differential Calculus Using Mathematica by Cesar Perez Pdf
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
The Joy of Mathematica by Alan Shuchat,Fred Shultz Pdf
Joy of Mathematica, Second Edition, is a book and software combination for Windows and Macintosh that makes Mathematica easier to use and learn. The software includes the most common Mathematica operations needed in the first two years of college and university courses. The book is a manual for the software and an introduction to using Mathematica for mathematics and its applications to other fields. It contains material for students in calculus, differential equations, and linear algebra courses. Students and professionals will benefit from this user-friendly, practical guide to Mathematica. * The CD: * Runs on both Windows and Power Macintosh platforms * Is optimized for Mathematica 4.0 * Requires that Mathematica's kernel and front end be on the same computer * Includes a palette for easy entry of common mathematical notation The Book: * Contains ready-to-use exercises and labs for the mathematics classroom * Now includes more coverage of multivariable calculus and differential equations, in addition to single-variable calculus and linear algebra
Scientific Computing with Mathematica® by Addolorata Marasco,Antonio Romano Pdf
Many interesting behaviors of real physical, biological, economical, and chemical systems can be described by ordinary differential equations (ODEs). Scientific Computing with Mathematica for Ordinary Differential Equations provides a general framework useful for the applications, on the conceptual aspects of the theory of ODEs, as well as a sophisticated use of Mathematica software for the solutions of problems related to ODEs. In particular, a chapter is devoted to the use ODEs and Mathematica in the Dynamics of rigid bodies. Mathematical methods and scientific computation are dealt with jointly to supply a unified presentation. The main problems of ordinary differential equations such as, phase portrait, approximate solutions, periodic orbits, stability, bifurcation, and boundary problems are covered in an integrated fashion with numerous worked examples and computer program demonstrations using Mathematica. Topics and Features:*Explains how to use the Mathematica package ODE.m to support qualitative and quantitative problem solving *End-of- chapter exercise sets incorporating the use of Mathematica programs *Detailed description and explanation of the mathematical procedures underlying the programs written in Mathematica *Appendix describing the use of ten notebooks to guide the reader through all the exercises. This book is an essential text/reference for students, graduates and practitioners in applied mathematics and engineering interested in ODE's problems in both the qualitative and quantitative description of solutions with the Mathematica program. It is also suitable as a self-
