Introduction to Integral Calculus Systematic Studies with Engineering Applications for Beginners

Name: Introduction to Integral Calculus Systematic Studies with Engineering Applications for Beginners
Price: 114.32 USD
Availability: InStock
ISBN: 9781118117767

ISBN-10: 111811776X

ISBN-13: 9781118117767

Edition: 2012

Authors: Ulrich L. Rohde, Ajay K. Poddar, A. K. Ghosh, G. C. Jain

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Description:

Introduction to Integral Calculus develops an intellectually stimulating level of understanding of the subject while giving numerous applications and incorporating various scientific problems. The authors outline how to find volumes and lengths of curves, anti-differentiation, integration of trigonometric functions, integration by substitution, methods of substitution, the definite integral, methods for evaluating definite integrals, differential equations and their solutions, and ordinary differential equations of first order and first degree. This book is an immensely accessible go-to resource that maintains the highest standards for those in this field.

Book details

Copyright year: 2012
Publisher: John Wiley & Sons, Limited
Publication date: 2/9/2012
Binding: Hardcover
Pages: 432
Size: 6.25" wide x 9.00" long x 1.25" tall
Weight: 1.628
Language: English



Foreword


Preface


Biographies


Introduction


Acknowledgment



Antiderivative(s) [or Indefinite Integral(s)]



Introduction



Useful Symbols, Terms, and Phrases Frequently Needed



Table(s) of Derivatives and their corresponding Integrals



Integration of Certain Combinations of Functions



Comparison Between the Operations of Differentiation and Integration



Integration Using Trigonometric Identities



Introduction



Some Important Integrals Involving sin x and cos x



Integrals of the Form (dx/(a sin x + b cos x)), where a, b r



Integration by Substitution: Change of Variable of Integration



Introduction



Generalized Power Rule



Theorem



To Evaluate Integrals of the Form , where a, b, c, and d are constant



Further Integration by Substitution: Additional Standard Integrals



Introduction



Special Cases of Integrals and Proof for Standard Integrals



Some New Integrals



Four More Standard Integrals



Integration by Parts



Introduction



Obtaining the Rule for Integration by Parts



Helpful Pictures Connecting Inverse Trigonometric Functions with Ordinary Trigonometric Functions



Rule for Proper Choice of First Function



Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side



Introduction



An Important Result: A Corollary to Integration by Parts



Application of the Corollary to Integration by Parts to Integrals that cannot be Solved Otherwise



Simpler Method(s) for Evaluating Standard Integrals



To Evaluate



Preparation for the Definite Integral: The Concept of Area



Introduction



Preparation for the Definite Integral



The Definite Integral as an Area



Definition of Area in Terms of the Definite Integral



Riemann Sums and the Analytical Definition of the Definite Integral



The Fundamental Theorems of Calculus



Introduction



Definite Integrals



The Area of Function A(x)



Statement and Proof of the Second Fundamental Theorem of Calculus



Differentiating a Definite Integral with Respect to a Variable Upper Limit



The Integral Function Identified as lnx or log<sub>e</sub>x



Introduction



Definition of Natural Logarithmic Function



The Calculus of lnx



The Graph of the Natural Logarithmic Function lnx



The Natural Exponential Function [exp(x) or e<sup>x</sup>]



Methods for Evaluating Definite Integrals



Introduction



The Rule for Evaluating Definite Integrals



Some Rules (Theorems) for Evaluation of Definite Integrals



Method of Integration by Parts in Definite Integrals



Some Important Properties of Definite Integrals



Introduction



Some Important Properties of Definite Integrals



Proof of Property (P<sub>0</sub>)



Proof of Property (P<sub>5</sub>)



Definite Integrals: Types of Functions



Applying the Definite Integral to Compute the Area of a Plane Figure



Introduction



Computing the Area of a Plane Region



Constructing the Rough Sketch [Cartesian Curves]



Computing the Area of a Circle (Developing Simpler Techniques)



To Find Length(s) of Arc(s) of Curve(s), the Volume(s) of Solid(s) of Revolution, and the Area(s) of Surface(s) of Solid(s) of Revolution



Introduction



Methods of Integration



Equation for the Length of a Curve in Polar Coordinates



Solids of Revolution



Formula for the Volume of a "Solid of Revolution"



Area(s) of Surface(s) of Revolution



Differential Equations: Related Concepts and Terminology



Introduction



Important Formal Applications of Differentials (dy and dx)



Independent Arbitrary Constants (or Essential Arbitrary Constants)



Definition: Integral Curve



Formation of a Differential Equation from a Given Relation, Involving Variables and the Essential Arbitrary Constants (or Parameters)



General Procedure for Eliminating "Two" Independent Arbitrary Constants (Using the Concept of Determinant)



The Simplest Type of Differential Equations



Methods of Solving Ordinary Differential Equations of the First Order and of the First Degree



Introduction



Methods of Solving Differential Equations



Linear Differential Equations



Type III: Exact Differential Equations



Applications of Differential Equations


INDEX