Integral Calculus And Differential Equations Using Mathematica
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Integral Calculus And Differential Equations Using Mathematica
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Author : Cesar Perez Lopez
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2016-01-16
Integral Calculus And Differential Equations Using Mathematica written by Cesar Perez Lopez and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-16 with categories.
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 And Differential Equations With Mathematica
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Author : Pramote Dechaumphai
language : en
Publisher:
Release Date : 2016
Calculus And Differential Equations With Mathematica written by Pramote Dechaumphai and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Calculus categories.
Differential Calculus Using Mathematica
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Author : Cesar Perez
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2016-01-16
Differential Calculus Using Mathematica written by Cesar Perez and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-01-16 with categories.
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
Advanced Calculus Revised Edition
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Author : Lynn Harold Loomis
language : en
Publisher: World Scientific Publishing Company
Release Date : 2014-02-26
Advanced Calculus Revised Edition written by Lynn Harold Loomis and has been published by World Scientific Publishing Company this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-02-26 with Mathematics categories.
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.
Mathematica Navigator
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Author : Heikki Ruskeepaa
language : en
Publisher: Gulf Professional Publishing
Release Date : 2004-02-06
Mathematica Navigator written by Heikki Ruskeepaa and has been published by Gulf Professional Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-02-06 with Computers categories.
Mathematica Navigator gives you a general introduction to Mathematica. The book emphasizes graphics, methods of applied mathematics and statistics, and programming. Mathematica Navigator can be used both as a tutorial and as a handbook. While no previous experience with Mathematica is required, most chapters also include advanced material, so that the book will be a valuable resource for both beginners and experienced users.
Feynman Integral Calculus
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Author : Vladimir A. Smirnov
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-08-02
Feynman Integral Calculus written by Vladimir A. Smirnov and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-08-02 with Mathematics categories.
The goal of the book is to summarize those methods for evaluating Feynman integrals that have been developed over a span of more than fifty years. The book characterizes the most powerful methods and illustrates them with numerous examples starting from very simple ones and progressing to nontrivial examples. The book demonstrates how to choose adequate methods and combine evaluation methods in a non-trivial way. The most powerful methods are characterized and then illustrated through numerous examples. This is an updated textbook version of the previous book (Evaluating Feynman integrals, STMP 211) of the author.
Mathematica By Example
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Author : Martha L Abell
language : en
Publisher: Academic Press
Release Date : 2014-05-09
Mathematica By Example written by Martha L Abell and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-09 with Mathematics categories.
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.
A First Course In Calculus
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-09-17
A First Course In Calculus written by Serge Lang and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-17 with Mathematics categories.
The purpose of a first course in calculus is to teach the student the basic notions of derivative and integral, and the basic techniques and applica tions which accompany them. The very talented students, with an ob vious aptitude for mathematics, will rapidly require a course in functions of one real variable, more or less as it is understood by professional is not primarily addressed to them (although mathematicians. This book I hope they will be able to acquire from it a good introduction at an early age). I have not written this course in the style I would use for an advanced monograph, on sophisticated topics. One writes an advanced monograph for oneself, because one wants to give permanent form to one's vision of some beautiful part of mathematics, not otherwise ac cessible, somewhat in the manner of a composer setting down his sym phony in musical notation. This book is written for the students to give them an immediate, and pleasant, access to the subject. I hope that I have struck a proper com promise, between dwelling too much on special details and not giving enough technical exercises, necessary to acquire the desired familiarity with the subject. In any case, certain routine habits of sophisticated mathematicians are unsuitable for a first course. Rigor. This does not mean that so-called rigor has to be abandoned.
Mathematica For Physicists And Engineers
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Author : K. B. Vijaya Kumar
language : en
Publisher: John Wiley & Sons
Release Date : 2023-06-06
Mathematica For Physicists And Engineers written by K. B. Vijaya Kumar and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-06-06 with Science categories.
Mathematica for Physicists and Engineers Hands-on textbook for learning how to use Mathematica to solve real-life problems in physics and engineering Mathematica for Physicists and Engineers provides the basic concepts of Mathematica for scientists and engineers, highlights Mathematica’s several built-in functions, demonstrates mathematical concepts that can be employed to solve problems in physics and engineering, and addresses problems in basic arithmetic to more advanced topics such as quantum mechanics. The text views mathematics and physics through the eye of computer programming, fulfilling the needs of students at master’s levels and researchers from a physics and engineering background and bridging the gap between the elementary books written on Mathematica and the reference books written for advanced users. Mathematica for Physicists and Engineers contains information on: Basics to Mathematica, its nomenclature and programming language, and possibilities for graphic output Vector calculus, solving real, complex and matrix equations and systems of equations, and solving quantum mechanical problems in infinite-dimensional linear vector spaces Differential and integral calculus in one and more dimensions and the powerful but elusive Dirac Delta function Fourier and Laplace transform, two integral transformations that are instrumental in many fields of physics and engineering for the solution of ordinary and partial differential equations Serving as a complete first course in Mathematica to solve problems in science and engineering, Mathematica for Physicists and Engineers is an essential learning resource for students in physics and engineering, master’s students in material sciences, geology, biological sciences theoretical chemists. Also lecturers in these and related subjects will benefit from the book.
Mathematical Analysis
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Author : Mariano Giaquinta
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-08-31
Mathematical Analysis written by Mariano Giaquinta and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-08-31 with Mathematics categories.
This volume! aims at introducing some basic ideas for studying approxima tion processes and, more generally, discrete processes. The study of discrete processes, which has grown together with the study of infinitesimal calcu lus, has become more and more relevant with the use of computers. The volume is suitably divided in two parts. In the first part we illustrate the numerical systems of reals, of integers as a subset of the reals, and of complex numbers. In this context we intro duce, in Chapter 2, the notion of sequence which invites also a rethinking of the notions of limit and continuity2 in terms of discrete processes; then, in Chapter 3, we discuss some elements of combinatorial calculus and the mathematical notion of infinity. In Chapter 4 we introduce complex num bers and illustrate some of their applications to elementary geometry; in Chapter 5 we prove the fundamental theorem of algebra and present some of the elementary properties of polynomials and rational functions, and of finite sums of harmonic motions. In the second part we deal with discrete processes, first with the process of infinite summation, in the numerical case, i.e., in the case of numerical series in Chapter 6, and in the case of power series in Chapter 7. The last chapter provides an introduction to discrete dynamical systems; it should be regarded as an invitation to further study.