Systematic Studies with Engineering Applications for Beginners
E-Book, Englisch, 428 Seiten, E-Book
ISBN: 978-1-118-13031-5
Verlag: John Wiley & Sons
Format: PDF
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)
I ntegration is an important function of calculus, andIntroduction to Integral Calculus combines fundamental conceptswith scientific problems to develop intuition and skills forsolving mathematical problems related to engineering and thephysical sciences. The authors provide a solid introduction tointegral calculus and feature applications of integration,solutions of differential equations, and evaluation methods. Withlogical organization coupled with clear, simple explanations, theauthors reinforce new concepts to progressively build skills andknowledge, and numerous real-world examples as well as intriguingapplications help readers to better understand the connectionsbetween the theory of calculus and practical problem solving.
The first six chapters address the prerequisites needed tounderstand the principles of integral calculus and explore suchtopics as anti-derivatives, methods of converting integrals intostandard form, and the concept of area. Next, the authors reviewnumerous methods and applications of integral calculus,including:
* Mastering and applying the first and second fundamental theoremsof calculus to compute definite integrals
* Defining the natural logarithmic function using calculus
* Evaluating definite integrals
* Calculating plane areas bounded by curves
* Applying basic concepts of differential equations to solveordinary differential equations
With this book as their guide, readers quickly learn to solve abroad range of current problems throughout the physical sciencesand engineering that can only be solved with calculus. Examplesthroughout provide practical guidance, and practice problems andexercises allow for further development and fine-tuning of variouscalculus skills. Introduction to Integral Calculus is an excellentbook for upper-undergraduate calculus courses and is also an idealreference for students and professionals who would like to gain afurther understanding of the use of calculus to solve problems in asimplified manner.
Autoren/Hrsg.
Weitere Infos & Material
FOREWORD ix
PREFACE xiii
BIOGRAPHIES xxi
INTRODUCTION xxiii
ACKNOWLEDGMENT xxv
1 Antiderivative(s) [or Indefinite Integral(s)] 1
1.1 Introduction 1
1.2 Useful Symbols, Terms, and Phrases Frequently Needed 6
1.3 Table(s) of Derivatives and their corresponding Integrals7
1.4 Integration of Certain Combinations of Functions 10
1.5 Comparison Between the Operations of Differentiation andIntegration 15
2 Integration Using Trigonometric Identities 17
2.1 Introduction 17
2.2 Some Important Integrals Involving sin x and cos x 34
2.3 Integrals of the Form ? (d/( a sin + b cos x)), where a, b
epsilon r 37
3a Integration by Substitution: Change of Variable ofIntegration 43
3b Further Integration by Substitution: Additional StandardIntegrals 67
4a Integration by Parts 97
4b Further Integration by Parts: Where the Given IntegralReappears on Right-Hand Side 117
5 Preparation for the Definite Integral: The Concept of Area139
5.1 Introduction 139
5.2 Preparation for the Definite Integral 140
5.3 The Definite Integral as an Area 143
5.4 Definition of Area in Terms of the Definite Integral 151
5.5 Riemann Sums and the Analytical Definition of the DefiniteIntegral 151
6a The Fundamental Theorems of Calculus 165
6b The Integral Function D x 1 1 t dt, (x > 0)Identified as ln x or loge x 183
7a Methods for Evaluating Definite Integrals 197
7b Some Important Properties of Definite Integrals 213
8a Applying the Definite Integral to Compute the Area of aPlane Figure 249
8b To Find Length(s) of Arc(s) of Curve(s), the Volume(s) ofSolid(s) of Revolution, and the Area(s) of Surface(s) of Solid(s)of Revolution 295
9a Differential Equations: Related Concepts and Terminology321
9a.4 Definition: Integral Curve 332
9b Methods of Solving Ordinary Differential Equations of theFirst Order and of the First Degree 361
INDEX 399
