Introduction to Differential Calculus

Ulrich L. Rohde 지음

Wiley 2012년 01월 12일 출간

작품소개

책소개

Enables readers to apply the fundamentals of differential calculus to solve real-life problems in engineering and the physical sciences Introduction to Differential Calculus fully engages readers by presenting the fundamental theories and methods of differential calculus and then showcasing how the discussed concepts can be applied to real-world problems in engineering and the physical sciences. With its easy-to-follow style and accessible explanations, the book sets a solid foundation before advancing to specific calculus methods, demonstrating the connections between differential calculus theory and its applications.The first five chapters introduce underlying concepts such as algebra, geometry, coordinate geometry, and trigonometry. Subsequent chapters present a broad range of theories, methods, and applications in differential calculus, including:Concepts of function, continuity, and derivativeProperties of exponential and logarithmic functionInverse trigonometric functions and their propertiesDerivatives of higher orderMethods to find maximum and minimum values of a functionHyperbolic functions and their propertiesReaders are equipped with the necessary tools to quickly learn how to understand 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 Differential Calculus is an excellent book for upper-undergraduate calculus courses and is also an ideal reference for students and professionals alike who would like to gain a further understanding of the use of calculus to solve problem

목차

Foreword xiiiPreface xviiBiographies xxvIntroduction xxviiAcknowledgments xxix1 From Arithmetic to Algebra (What must you know to learn Calculus?) 11.1 Introduction 11.2 The Set of Whole Numbers 11.3 The Set of Integers 11.4 The Set of Rational Numbers 11.5 The Set of Irrational Numbers 21.6 The Set of Real Numbers 21.7 Even and Odd Numbers 31.8 Factors 31.9 Prime and Composite Numbers 31.10 Coprime Numbers 41.11 Highest Common Factor (H.C.F.) 41.12 Least Common Multiple (L.C.M.) 41.13 The Language of Algebra 51.14 Algebra as a Language for Thinking 71.15 Induction 91.16 An Important Result: The Number of Primes is Infinite 101.17 Algebra as the Shorthand of Mathematics 101.18 Notations in Algebra 111.19 Expressions and Identities in Algebra 121.20 Operations Involving Negative Numbers 151.21 Division by Zero 162 The Concept of a Function (What must you know to learn Calculus?) 192.1 Introduction 192.2 Equality of Ordered Pairs 202.3 Relations and Functions 202.4 Definition 212.5 Domain, Codomain, Image, and Range of a Function 232.6 Distinction Between &"f &" and &"f(x)&" 232.7 Dependent and Independent Variables 242.8 Functions at a Glance 242.9 Modes of Expressing a Function 242.10 Types of Functions 252.11 Inverse Function f 1 292.12 Comparing Sets without Counting their Elements 322.13 The Cardinal Number of a Set 322.14 Equivalent Sets (Definition) 332.15 Finite Set (Definition) 332.16 Infinite Set (Definition) 342.17 Countable and Uncountable Sets 362.18 Cardinality of Countable and Uncountable Sets 362.19 Second Definition of an Infinity Set 372.20 The Notion of Infinity 372.21 An Important Note About the Size of Infinity 382.22 Algebra of Infinity (1) 383 Discovery of Real Numbers: Through Traditional Algebra (What must you know to learn Calculus?) 413.1 Introduction 413.2 Prime and C

출판사 서평

“The book is addressed mainly to students studying non-mathematical subjects. It will be also helpful for those who want to understand why it is important to study Calculus and how to apply it.”& (Zentralblatt MATH, 1 December 2012)

작가정보

저자(글) Ulrich L. Rohde

저자 :

저자 :

저자 :

저자 :

저자 :
저자 :
저자 :
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, BSc, 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 IIT Kanpur, India. He has published more than 120 scientific papers.