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Introduction to differential calculus : systematic studies with engineering applications for beginners /
"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,...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Hoboken, N.J. :
Wiley,
2012.
|
| Edición: | 1st ed. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 245 | 0 | 0 | |a Introduction to differential calculus : |b systematic studies with engineering applications for beginners / |c Ulrich L. Rohde [and others]. |
| 250 | |a 1st ed. | ||
| 260 | |a Hoboken, N.J. : |b Wiley, |c 2012. | ||
| 300 | |a 1 online resource | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 505 | 0 | |a Frontmatter -- From Arithmetic to Algebra -- The Concept of a Function -- Discovery of Real Numbers: Through Traditional Algebra -- From Geometry to Coordinate Geometry -- Trigonometry and Trigonometric Functions -- More About Functions -- The Concept of Limit of a Function -- Methods for Computing Limits of Algebraic Functions -- The Concept of Continuity of a Function, and Points of Discontinuity -- The Idea of a Derivative of a Function -- Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions -- Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions -- Methods of Computing Limits of Trigonometric Functions -- Exponential Form(s) of a Positive Real Number and its Logarithm(s): Pre-Requisite for Understanding Exponential and Logarithmic Functions -- Exponential and Logarithmic Functions and Their Derivatives -- Methods for Computing Limits of Exponential and Logarithmic Functions -- Inverse Trigonometric Functions and Their Derivatives -- Implicit Functions and Their Differentiation -- Parametric Functions and Their Differentiation -- Differentials ₃d₄ and ₃d₄: Meanings and Applications -- Derivatives and Differentials of Higher Order -- Applications of Derivatives in Studying Motion in a Straight Line -- Increasing and Decreasing Functions and the Sign of the First Derivative -- Maximum and Minimum Values of a Function -- Rolle's Theorem and the Mean Value Theorem (MVT) -- The Generalized Mean Value Theorem (Cauchy's MVT), L' Hospital's Rule, and their Applications -- Extending the Mean Value Theorem to Taylor's Formula: Taylor Polynomials for Certain Functions -- Hyperbolic Functions and Their Properties -- Appendix A (Related To Chapter-2): Elementary Set Theory -- Appendix B (Related To Chapter-4) -- Appendix C (Related To Chapter-20) -- Index. | |
| 520 | |a "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"-- |c Provided by publisher. | ||
| 520 | |a "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"-- |c Provided by publisher. | ||
| 504 | |a Includes bibliographical references and index. | ||
| 500 | |a Machine generated contents note: Chapter One. From Arithmetic to Algebra. Chapter Two. The Concept of Function. Chapter Three. Discovery of Real Numbers (Through Traditional Algebra). Chapter Four. From Geometry to Co-ordinate Geometry. Chapter Five. Trigonometry and Trigonometric Functions. Chapter Six. More about Functions. Chapter Seven. (a): The Concept of Limit of a Function. Chapter Seven. (b): Methods for Computing Limits of Algebraic Functions. Chapter Eight. The Concept of Continuity of a Function and the Points of Discontinuity. Chapter Nine. The Idea of Derivative of a Function. Chapter Ten. Algebra of Derivatives: Rules for Computing Derivatives of Various Combinations of Differentiable Functions. Chapter Eleven. (a): Basic Trigonometric Limits and Their Applications in Computing Derivatives of Trigonometric Functions. Chapter Eleven. (b): Methods of Computing Limits of Trigonometric Functions. Chapter Twelve: Exponential Form(s) of a Positive Real Numbers and its Logarithms. Chapter Thirteen. (a): Exponential and Logarithmic Functions as Their Derivatives. Chapter Thirteen. (b): Methods for Computing Limits and Exponential and Logarithmic Functions. Chapter Fourteen. Inverse Trigonometric Functions and Their Derivatives. Chapter Fifteen. (a): Implicit Functions and Their Differentiation. Chapter Fifteen. (b): Parametric Functions and Their Differentiation. Chapter Sixteen. Differentials 'dy' and 'dx': Meanings and Applications. Chapter Seventeen. Derivatives and Differentials of Higher Order. Chapter Eighteen. Applications of Derivatives in Studying Motion in a Straight Line. Chapter Nineteen. (a): Increasing and Decreasing Functions and the Sign of the First Derivative. Chapter Nineteen. (b): Maximum and Minimum Values of a Function. Chapter Twenty. Rolle's Theorem and the Mean Value Theorem (MVT). Chapter Twenty One. The Generalized Mean Value Theorem (Cauchy's MVT), L'Hospital's Rule, and Its Applications. Chapter Twenty Two. Extending the Mean Value Theorem to Taylor's Formula: Taylor Polynomials for Certain Functions. Chapter Twenty Three. Hyperbolic Functions and Their Properties. | ||
| 588 | 0 | |a Print version record. | |
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Differential calculus |v Textbooks. | |
| 650 | 7 | |a MATHEMATICS |x Calculus. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Differential Equations |x General. |2 bisacsh | |
| 650 | 7 | |a Differential calculus |2 fast | |
| 650 | 7 | |a Càlcul diferencial. |2 thub | |
| 655 | 7 | |a Textbooks |2 fast | |
| 655 | 7 | |a Llibres electrònics. |2 thub | |
| 700 | 1 | |a Rohde, Ulrich L. | |
| 776 | 0 | 8 | |i Print version: |t Introduction to differential calculus. |b 1st ed. |d Hoboken, N.J. : Wiley, 2012 |z 9781118117750 |w (DLC) 2011018421 |w (OCoLC)731913148 |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=818446 |z Texto completo |
| 880 | 8 | |6 505-00/(S |a 6.7 Raising a Function to a Power -- 6.8 Composition of Functions -- 6.9 Equality of Functions -- 6.10 Important Observations -- 6.11 Even and Odd Functions -- 6.12 Increasing and Decreasing Functions -- 6.13 Elementary and Nonelementary Functions -- 7a The Concept of Limit of a Function (What must you know to learn Calculus) -- 7a.1 Introduction -- 7a.2 Useful Notations -- 7a.3 The Concept of Limit of a Function: Informal Discussion -- 7a.4 Intuitive Meaning of Limit of a Function -- 7a.5 Testing the Definition [Applications of the ε, δ Definition of Limit] -- 7a.6 Theorem (B): Substitution Theorem -- 7a.7 Theorem (C): Squeeze Theorem or Sandwich Theorem -- 7a.8 One-Sided Limits (Extension to the Concept of Limit) -- 7b Methods for Computing Limits of Algebraic Functions (What must you know to learn Calculus) -- 7b.1 Introduction -- 7b.2 Methods for Evaluating Limits of Various Algebraic Functions -- 7b.3 Limit at Infinity -- 7b.4 Infinite Limits -- 7b.5 Asymptotes -- 8 The Concept of Continuity of a Function, and Points of Discontinuity (What must you know to learn Calculus) -- 8.1 Introduction -- 8.2 Developing the Definition of Continuity "At a Point" -- 8.3 Classification of the Points of Discontinuity: Types of Discontinuities -- 8.4 Checking Continuity of Functions Involving Trigonometric, Exponential, and Logarithmic Functions -- 8.5 From One-Sided Limit to One-Sided Continuity and its Applications -- 8.6 Continuity on an Interval -- 8.7 Properties of Continuous Functions -- 9 The Idea of a Derivative of a Function -- 9.1 Introduction -- 9.2 Definition of the Derivative as a Rate Function -- 9.3 Instantaneous Rate of Change of y [=f(x)] at x=x1 and the Slope of its Graph at x=x1 -- 9.4 A Notation for Increment(s) -- 9.5 The Problem of Instantaneous Velocity -- 9.6 Derivative of Simple Algebraic Functions. | |
| 880 | 8 | |6 505-00/(S |a 3 Discovery of Real Numbers: Through Traditional Algebra (What must you know to learn Calculus) -- 3.1 Introduction -- 3.2 Prime and Composite Numbers -- 3.3 The Set of Rational Numbers -- 3.3 The Set of Rational Numbers -- 3.4 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.) -- 4 From Geometry to Coordinate Geometry (What must you know to learn Calculus) -- 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 -- 5 Trigonometry and Trigonometric Functions (What must you know to learn Calculus) -- 5.1 Introduction -- 5.2 (Directed) Angles -- 5.3 Ranges of sin θ and cos θ -- 5.4 Useful Concepts and Definitions -- 5.5 Two Important Properties of Trigonometric Functions -- 5.6 Graphs of Trigonometric Functions -- 5.7 Trigonometric Identities and Trigonometric Equations -- 5.8 Revision of Certain Ideas in Trigonometry -- 6 More About Functions (What must you know to learn Calculus) -- 6.1 Introduction -- 6.2 Function as a Machine -- 6.3 Domain and Range -- 6.4 Dependent and Independent Variables -- 6.5 Two Special Functions -- 6.6 Combining Functions. | |
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