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Introduction to Integral Calculus Systematic Studies with Engineering Applications for Beginners

ISBN-10: 111811776X

ISBN-13: 9781118117767

Edition: 2012

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

List price: $78.95
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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.
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Book details

List price: $78.95
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