Ulrich L. Rohde, G. C. Jain, Ajay K. Poddar, A. K. Ghosh

Introduction to Differential Calculus (eBook, PDF)

Systematic Studies with Engineering Applications for Beginners

• Format: PDF

Produktbeschreibung

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 derivative * Properties of exponential and logarithmic function * Inverse trigonometric functions and their properties * Derivatives of higher order * Methods to find maximum and minimum values of a function * Hyperbolic functions and their properties Readers 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 problems in a simplified manner.

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Produktdetails

• Verlag: John Wiley & Sons
• Seitenzahl: 784
• Erscheinungstermin: 29. November 2011
• Englisch
• ISBN-13: 9781118130124
• Artikelnr.: 38236642

Autorenporträt

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.

Inhaltsangabe

Foreword xiii Preface xvii Biographies xxv Introduction xxvii
Acknowledgments xxix 1 From Arithmetic to Algebra (What must you know to
learn Calculus?) 1 2 The Concept of a Function (What must you know to learn
Calculus?) 19 3 Discovery of Real Numbers: Through Traditional Algebra
(What must you know to learn Calculus?) 41 4 From Geometry to Coordinate
Geometry (What must you know to learn Calculus?) 63 5 Trigonometry and
Trigonometric Functions (What must you know to learn Calculus?) 97 6 More
About Functions (What must you know to learn Calculus?) 129 7a The Concept
of Limit of a Function (What must you know to learn Calculus?) 149 7a.1
Introduction 149 7a.2 Useful Notations 149 7a.3 The Concept of Limit of a
Function: Informal Discussion 151 7a.4 Intuitive Meaning of Limit of a
Function 153 7a.5 Testing the Definition [Applications of the ", d
Definition of Limit] 163 7a.6 Theorem (B): Substitution Theorem 174 7a.7
Theorem (C): Squeeze Theorem or Sandwich Theorem 175 7a.8 One-Sided Limits
(Extension to the Concept of Limit) 175 7b Methods for Computing Limits of
Algebraic Functions (What must you know to learn Calculus?) 177 7b.1
Introduction 177 7b.2 Methods for Evaluating Limits of Various Algebraic
Functions 178 7b.3 Limit at Infinity 187 7b.4 Infinite Limits 190 7b.5
Asymptotes 192 8 The Concept of Continuity of a Function, and Points of
Discontinuity (What must you know to learn Calculus?) 197 9 The Idea of a
Derivative of a Function 235 10 Algebra of Derivatives: Rules for Computing
Derivatives of Various Combinations of Differentiable Functions 275 11a
Basic Trigonometric Limits and Their Applications in Computing Derivatives
of Trigonometric Functions 307 11a.1 Introduction 307 11a.2 Basic
Trigonometric Limits 308 11a.3 Derivatives of Trigonometric Functions 314
11b Methods of Computing Limits of Trigonometric Functions 325 11b.1
Introduction 325 11b.2 Limits of the Type (I) 328 11b.3 Limits of the Type
(II) [ lim f(x), where a&rae;0] 332 11b.4 Limits of Exponential and
Logarithmic Functions 335 12 Exponential Form(s) of a Positive Real Number
and its Logarithm(s): Pre-Requisite for Understanding Exponential and
Logarithmic Functions (What must you know to learn Calculus?) 339 13a
Exponential and Logarithmic Functions and Their Derivatives (What must you
know to learn Calculus?) 359 13a.1 Introduction 359 13a.2 Origin of e 360
13a.3 Distinction Between Exponential and Power Functions 362 13a.4 The
Value of e 362 13a.5 The Exponential Series 364 13a.6 Properties of e and
Those of Related Functions 365 13a.7 Comparison of Properties of
Logarithm(s) to the Bases 10 and e 369 13a.8 A Little More About e 371
13a.9 Graphs of Exponential Function(s) 373 13a.10 General Logarithmic
Function 375 13a.11 Derivatives of Exponential and Logarithmic Functions
378 13a.12 Exponential Rate of Growth 383 13a.13 Higher Exponential Rates
of Growth 383 13a.14 An Important Standard Limit 385 13a.15 Applications of
the Function ex: Exponential Growth and Decay 390 13b Methods for Computing
Limits of Exponential and Logarithmic Functions 401 13b.1 Introduction 401
13b.2 Review of Logarithms 401 13b.3 Some Basic Limits 403 13b.4 Evaluation
of Limits Based on the Standard Limit 410 14 Inverse Trigonometric
Functions and Their Derivatives 417 15a Implicit Functions and Their
Differentiation 453 15a.1 Introduction 453 15a.2 Closer Look at the
Difficulties Involved 455 15a.3 The Method of Logarithmic Differentiation
463 15a.4 Procedure of Logarithmic Differentiation 464 15b Parametric
Functions and Their Differentiation 473 15b.1 Introduction 473 15b.2 The
Derivative of a Function Represented Parametrically 477 15b.3 Line of
Approach for Computing the Speed of a Moving Particle 480 15b.4 Meaning of
dy/dx with Reference to the Cartesian Form y = f(x) and Parametric Forms x
= f(t), y = g(t) of the Function 481 15b.5 Derivative of One Function with
Respect to the Other 483 16 Differentials "dy" and "dx": Meanings and
Applications 487 17 Derivatives and Differentials of Higher Order 511 18
Applications of Derivatives in Studying Motion in a Straight Line 535 19a
Increasing and Decreasing Functions and the Sign of the First Derivative
551 19a.1 Introduction 551 19a.2 The First Derivative Test for Rise and
Fall 556 19a.3 Intervals of Increase and Decrease (Intervals of
Monotonicity) 557 19a.4 Horizontal Tangents with a Local Maximum/Minimum
565 19a.5 Concavity, Points of Inflection, and the Sign of the Second
Derivative 567 19b Maximum and Minimum Values of a Function 575 19b.1
Introduction 575 19b.2 Relative Extreme Values of a Function 576 19b.3
Theorem A 580 19b.4 Theorem B: Sufficient Conditions for the Existence of a
Relative Extrema--In Terms of the First Derivative 584 19b.5 Sufficient
Condition for Relative Extremum (In Terms of the Second Derivative) 588
19b.6 Maximum and Minimum of a Function on the Whole Interval (Absolute
Maximum and Absolute Minimum Values) 593 19b.7 Applications of Maxima and
Minima Techniques in Solving Certain Problems Involving the Determination
of the Greatest and the Least Values 597 20 Rolle's Theorem and the Mean
Value Theorem (MVT) 605 21 The Generalized Mean Value Theorem (Cauchy's
MVT), L' Hospital's Rule, and their Applications 625 infinity / infinity
638 22 Extending the Mean Value Theorem to Taylor's Formula: Taylor
Polynomials for Certain Functions 653 23 Hyperbolic Functions and Their
Properties 677 Appendix A (Related To Chapter-2) Elementary Set Theory 703
Appendix B (Related To Chapter-4) 711 Appendix C (Related To Chapter-20)
735 Index 739