978-1-118-13012-4 : 140 (NL)
1-11-813015-4, 978-1-118-13015-5*electronic bk.
1-11-813012-X, 978-1-118-13012-4*electronic bk.
1-11-813014-6, 978-1-118-13014-8*electronic bk.
Weitere Ausgaben: 978-1-118-11775-0*hardback, 1-283-40323-4 (Printausgabe)
Cover; Title Page; Copyright; Foreword; Preface; Biographies; Introduction; Acknowledgments; Chapter 1: From Arithmetic to Algebra; 1.1 Introduction; 1.2 The Set of Whole Numbers; 1.3 The Set of Integers; 1.4 The Set of Rational Numbers; 1.5 The Set of Irrational Numbers; 1.6 The Set of Real Numbers; 1.7 Even and Odd Numbers; 1.8 Factors; 1.9 Prime and Composite Numbers; 1.10 Coprime Numbers; 1.11 Highest Common Factor (H.C.F.); 1.12 Least Common Multiple (L.C.M.); 1.13 The Language of Algebra; 1.14 Algebra as a Language for Thinking; 1.15 Induction
1.16 An Important Result: The Number of Primes is Infinite1.17 Algebra as the Shorthand of Mathematics; 1.18 Notations in Algebra; 1.19 Expressions and Identities in Algebra; 1.20 Operations Involving Negative Numbers; 1.21 Division by Zero; Chapter 2: The Concept of a Function; 2.1 Introduction; 2.2 Equality of Ordered Pairs; 2.3 Relations and Functions; 2.4 Definition; 2.5 Domain, Codomain, Image, and Range of a Function; 2.6 Distinction Between "f " and "f(x)"; 2.7 Dependent and Independent Variables; 2.8 Functions at a Glance; 2.9 Modes of Expressing a Function; 2.10 Types of Functions
2.11 Inverse Function f-12.12 Comparing Sets without Counting their Elements; 2.13 The Cardinal Number of a Set; 2.14 Equivalent Sets (Definition); 2.15 Finite Set (Definition); 2.16 Infinite Set (Definition); 2.17 Countable and Uncountable Sets; 2.18 Cardinality of Countable and Uncountable Sets; 2.19 Second Definition of an Infinite Set; 2.20 The Notion of Infinity; 2.21 An Important Note About the Size of Infinity; 2.22 Algebra of Infinity (8); Chapter 3: Discovery of Real Numbers: Through Traditional Algebra; 3.1 Introduction; 3.2 Prime and Composite Numbers
3.3 The Set of Rational Numbers3.4 The Set of Irrational Numbers; 3.5 The Set of Real Numbers; 3.6 Definition of a Real Number; 3.7 Geometrical Picture of Real Numbers; 3.8 Algebraic Properties of Real Numbers; 3.9 Inequalities (Order Properties in Real Numbers); 3.10 Intervals; 3.11 Properties of Absolute Values; 3.12 Neighborhood of a Point; 3.13 Property of Denseness; 3.14 Completeness Property of Real Numbers; 3.15 (Modified) Definition II (l.u.b.); 3.16 (Modified) Definition II (g.l.b.); Chapter 4: From Geometry to Coordinate Geometry; 4.1 Introduction
4.2 Coordinate Geometry (or Analytic Geometry)4.3 The Distance Formula; 4.4 Section Formula; 4.5 The Angle of Inclination of a Line; 4.6 Solution(s) of an Equation and its Graph; 4.7 Equations of a Line; 4.8 Parallel Lines; 4.9 Relation Between the Slopes of (Nonvertical) Lines that are Perpendicular to One Another; 4.10 Angle Between Two Lines; 4.11 Polar Coordinate System; Chapter 5: Trigonometry and Trigonometric Functions; 5.1 Introduction; 5.2 (Directed) Angles; 5.3 Ranges of sin ? and cos ?; 5.4 Useful Concepts and Definitions; 5.5 Two Important Properties of Trigonometric Functions
5.6 Graphs of Trigonometric Functions
"Through the use of examples and graphs, this book maintains a high level of precision in clarifying prerequisite materials such as algebra, geometry, coordinate geometry, trigonometry, and the concept of limits. The book explores concepts of limits of a function, limits of algebraic functions, applications and limitations for limits, and the algebra of limits. It also discusses methods for computing limits of algebraic functions, and explains the concept of continuity and related concepts in depth. This introductory submersion into differential calculus is an essential guide for engineering and the physical sciences students"--
"This book explores the differential calculus and its plentiful applications in engineering and the physical sciences. The first six chapters offer a refresher of algebra, geometry, coordinate geometry, trigonometry, the concept of function, etc. since these topics are vital to the complete understanding of calculus. The book then moves on to the concept of limit of a function. Suitable examples of algebraic functions are selected, and their limits are discussed to visualize all possible situations that may occur in evaluating limit of a function, other than algebraic functions"--
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