Introduction to Integral Calculus

Ulrich L. Rohde 지음

Wiley 2012년 01월 20일 출간

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An accessible introduction to the fundamentals of calculus needed to solve current problems in engineering and the physical sciencesI ntegration is an important function of calculus, and Introduction to Integral Calculus combines fundamental concepts with scientific problems to develop intuition and skills for solving mathematical problems related to engineering and the physical sciences. The authors provide a solid introduction to integral calculus and feature applications of integration, solutions of differential equations, and evaluation methods. With logical organization coupled with clear, simple explanations, the authors reinforce new concepts to progressively build skills and knowledge, and numerous real-world examples as well as intriguing applications help readers to better understand the connections between the theory of calculus and practical problem solving.The first six chapters address the prerequisites needed to understand the principles of integral calculus and explore such topics as anti-derivatives, methods of converting integrals into standard form, and the concept of area. Next, the authors review numerous methods and applications of integral calculus, including:Mastering and applying the first and second fundamental theorems of calculus to compute definite integralsDefining the natural logarithmic function using calculusEvaluating definite integralsCalculating plane areas bounded by curvesApplying basic concepts of differential equations to solve ordinary differential equationsWith this book as their guide, readers quickly learn to solve a broad range of current problems throughout the physical sciences and engineering that can only be solved with calculus. Examples throughout provide practical guidance, and practice problems and exercises allow for further development and fine-tuning of various calculus skills. Introduction to In

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FOREWORD ixPREFACE xiiiBIOGRAPHIES xxiINTRODUCTION xxiiiACKNOWLEDGMENT xxv1 Antiderivative(s) [or Indefinite Integral(s)] 11.1 Introduction 11.2 Useful Symbols, Terms, and Phrases Frequently Needed 61.3 Table(s) of Derivatives and their corresponding Integrals 71.4 Integration of Certain Combinations of Functions 101.5 Comparison Between the Operations of Differentiation and Integration 152 Integration Using Trigonometric Identities 172.1 Introduction 172.2 Some Important Integrals Involving sin x and cos x 342.3 Integrals of the Form&? (d/( a sin& + b cos x)), where a, b&ϵ r 373a Integration by Substitution: Change of Variable of Integration 433b Further Integration by Substitution: Additional Standard Integrals 674a Integration by Parts 974b Further Integration by Parts: Where the Given Integral Reappears on Right-Hand Side 1175 Preparation for the Definite Integral: The Concept of Area 1395.1 Introduction 1395.2 Preparation for the Definite Integral 1405.3 The Definite Integral as an Area 1435.4 Definition of Area in Terms of the Definite Integral 1515.5 Riemann Sums and the Analytical Definition of the Definite Integral 1516a The Fundamental Theorems of Calculus 1656b The Integral Function Ð x 1 1 t dt, (x > 0) Identified as ln x or loge x 1837a Methods for Evaluating Definite Integrals 1977b Some Important Properties of Definite Integrals 2138a Applying the Definite Integral to Compute the Area of a Plane Figure 2498b 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 2959a Differential Equations: Related Concepts and Terminology 3219a.4 Definition: Integral Curve 3329b Methods of Solving Ordinary Differential Equations of the First Order and o

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“Introduction to Integral Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals who would like to gain a further understanding of the use of calculus to solve problems in a simplified manner.”& (Zentralblatt MATH, 2012)“Long on examples but often short of exercises, this work might best be used as a reference source.& Summing Up: Recommended.& Lower-and upper-division undergraduates.”& (Choice, 1 September 2012)

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저자(글) Ulrich L. Rohde

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ULRICH L. ROHDE, PhD, ScD, Dr-Ing, is Chairman of Synergy Microwave Corporation, President of Communications Consulting Corporation, and a Partner of Rohde Schwarz. A Fellow of the IEEE, Professor Rohde holds several patents and has published more than 200 scientific papers.G. C. JAIN, B.Sc., is a retired scientist from the Defense Research and Development Organization in India.AJAY K. PODDAR, PhD, is Chief Scientist at Synergy Microwave Corporation. A Senior Member of the IEEE, Dr. Poddar holds several dozen patents and has published more than 180 scientific papers.A. K. GHOSH, PhD, is Professor in the Department of Aerospace Engineering at the IIT Kanpur, India. He has published more than 120 scientific papers.