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

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

Calculus Using Mathematica

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Author : K.D. Stroyan
language : en
Publisher: Academic Press
Release Date : 2014-05-10

Calculus Using Mathematica written by K.D. Stroyan and has been published by Academic Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-10 with Mathematics categories.

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.

The Differential And Integral Calculus

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Author : Augustus De Morgan
language : en
Publisher:
Release Date : 1842

The Differential And Integral Calculus written by Augustus De Morgan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1842 with Calculus categories.

Exploring Calculus

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Author : Crista Arangala
language : en
Publisher: CRC Press
Release Date : 2016-08-19

Exploring Calculus written by Crista Arangala and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-19 with Mathematics categories.

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. Employs Mathematica to calculate and explore concepts and theories of calculus Uses engaging labs to inspire learning Includes many applications to a variety of fields that can promote research projects User-friendly approach that can be used for classroom work or independent exploratory learning

Scripta Mathematica

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Author :
language : en
Publisher:
Release Date : 1960

Scripta Mathematica written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1960 with Mathematics categories.

Includes section "Book reviews."

Nature

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Author : Sir Norman Lockyer
language : en
Publisher:
Release Date : 1899

Nature written by Sir Norman Lockyer and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1899 with Electronic journals categories.

Nature

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Author :
language : en
Publisher:
Release Date : 1899

Nature written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1899 with categories.

Abstracts Of Papers Presented To The American Mathematical Society

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Author : American Mathematical Society
language : en
Publisher:
Release Date : 2005

Abstracts Of Papers Presented To The American Mathematical Society written by American Mathematical Society and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Mathematics categories.

Mathematics For Engineers I

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Author : Gerd Baumann
language : en
Publisher: Oldenbourg Verlag
Release Date : 2010-10-01

Mathematics For Engineers I written by Gerd Baumann and has been published by Oldenbourg Verlag this book supported file pdf, txt, epub, kindle and other format this book has been release on 2010-10-01 with Mathematics categories.

"Mathematics for Engineers I" gehört zu einer vierbändigen Reihe und gibt eine Einführung in die Mathematik für Undergraduates, die ein Bachelor-Studium im Bereich Ingenieurwissenschaften aufgenommen haben. In Band I sind die Grundzüge des klassischen Calculus dargestellt. Die Reihe unterscheidet sich von traditionellen Texten dadurch, dass sie interaktiv ist und mit Hilfe des Computer-Algebra-Systems Mathematica die Berechnungen darstellt. Die vormalig beiliegende CD ist nun online bei Band IV als Zusatzmaterial zum kostenfreien Download verfügbar.