%{search_type} search results

• Frontmatter
• Contents
• Preface
• 1. Introduction
• 2. Calculus of Vector Functions
• 3. Tangent Spaces and 1-forms
• 4. Line Integrals
• 5. Differential Calculus of Mappings
• 6. Applications of Differential Calculus
• 7. Double and Triple Integrals
• 8. Wedge Products and Exterior Derivatives
• 9. Integration of Forms
• 10. Stokes' Theorem and Applications
• Bibliography
• Index

This textbook offers a high-level introduction to multi-variable differential calculus. Differential forms are introduced incrementally in the narrative, eventually leading to a unified treatment of Green's, Stokes' and Gauss' theorems. Furthermore, the presentation offers a natural route to differential geometry. Contents: Calculus of Vector Functions Tangent Spaces and 1-forms Line Integrals Differential Calculus of Mappings Applications of Differential Calculus Double and Triple Integrals Wedge Products and Exterior Derivatives Integration of Forms Stokes' Theorem and Applications.
(source: Nielsen Book Data)

• Frontmatter
• Preface
• Contents
• 1. Prerequisites for calculus
• 2. Limits and continuity
• 3. The derivative
• 4. Applications of the derivative
• 5. The definite integral
• 6. Techniques for integration and improper integrals
• 7. Applications of the definite integral
• 8. Infinite series, sequences, and approximations
• Index

The book is a comprehensive yet compressed entry-level introduction on single variable calculus, focusing on the concepts and applications of limits, continuity, derivative, defi nite integral, series, sequences and approximations. Chapters are arranged to outline the essence of each topic and to address learning diffi culties, making it suitable for students and lecturers in mathematics, physics and engineering. Contents Prerequisites for calculus Limits and continuity The derivative Applications of the derivative The definite integral Techniques for integration and improper integrals Applications of the definite integral Infinite series, sequences, and approximations.
(source: Nielsen Book Data)

• Frontmatter
• Contents
• Preface to the Paperback Edition
• Preface
• Calculus Topics Discussed by Chapter
• CHAPTER 1. Wake Up and Smell the Functions
• CHAPTER 2. Breakfast at Newton's
• CHAPTER 3. Driven by Derivatives
• CHAPTER 4. Connected by Calculus
• CHAPTER 5. Take a Derivative and You'll Feel Better
• CHAPTER 6. Adding Things Up, the Calculus Way
• CHAPTER 7. Derivatives Integrals: The Dream Team
• Epilogue
• Appendix A. Functions and Graphs
• Appendices 1-7
• Notes
• Index

Calculus. For some of us, the word conjures up memories of ten-pound textbooks and visions of tedious abstract equations. And yet, in reality, calculus is fun and accessible, and surrounds us everywhere we go. In Everyday Calculus, Oscar Fernandez demonstrates that calculus can be used to explore practically any aspect of our lives, including the most effective number of hours to sleep and the fastest route to get to work. He also shows that calculus can be both useful-determining which seat at the theater leads to the best viewing experience, for instance-and fascinating-exploring topics such as time travel and the age of the universe. Throughout, Fernandez presents straightforward concepts, and no prior mathematical knowledge is required. For advanced math fans, the mathematical derivations are included in the appendixes. The book features a new preface that alerts readers to new interactive online content, including demonstrations linked to specific figures in the book as well as an online supplement. Whether you're new to mathematics or already a curious math enthusiast, Everyday Calculus will convince even die-hard skeptics to view this area of math in a whole new way

• Frontmatter
• Foreword
• Preface
• Contents
• 1. Introduction to fractional calculus and fractional-order control
• 2. Mathematical prerequisites
• 3. Definitions and computation algorithms of fractional-order derivatives and integrals
• 4. Solutions of linear fractional-order differential equations
• 5. Approximation of fractional-order operators
• 6. Modelling and analysis of multivariable fractional-order transfer function matrices
• 7. State space modelling and analysis of linear fractional-order systems
• 8. Numerical solutions of nonlinear fractional-order differential equations
• 9. Design of fractional-order PID controllers
• 10. Frequency domain controller design for multivariable fractional-order systems
• A. Inverse Laplace transforms involving fractional and irrational operations
• B. FOTF Toolbox functions and models
• C. Benchmark problems for the assessment of fractional-order differential equation algorithms
• Bibliography
• Index

This book explains the essentials of fractional calculus and demonstrates its application in control system modeling, analysis and design. It presents original research to find high-precision solutions to fractional-order differentiations and differential equations. Numerical algorithms and their implementations are proposed to analyze multivariable fractional-order control systems. Through high-quality MATLAB programs, it provides engineers and applied mathematicians with theoretical and numerical tools to design control systems. Contents Introduction to fractional calculus and fractional-order control Mathematical prerequisites Definitions and computation algorithms of fractional-order derivatives and Integrals Solutions of linear fractional-order differential equations Approximation of fractional-order operators Modelling and analysis of multivariable fractional-order transfer function Matrices State space modelling and analysis of linear fractional-order Systems Numerical solutions of nonlinear fractional-order differential Equations Design of fractional-order PID controllers Frequency domain controller design for multivariable fractional-order Systems Inverse Laplace transforms involving fractional and irrational Operations FOTF Toolbox functions and models Benchmark problems for the assessment of fractional-order differential equation algorithms.
(source: Nielsen Book Data)

• Intro
• Contents iii
• Part 1: The Roots of Calculus 1
• 1 What Is Calculus, Anyway? 3
• What's the Purpose of Calculus? 4
• Finding the Slopes of Curves 4
• Calculating the Area of Bizarre Shapes 4
• Justifying Old Formulas 5
• Calculating Complicated x-Intercepts 5
• Visualizing Graphs 5
• Finding the Average Value of a Function 6
• Calculating Optimal Values 6
• Who's Responsible for This? 7
• Ancient Influences 7
• Newton vs Leibniz 9
• I Ever Learn This? 11
• 2 Polish Up Your Algebra Skills 13
• Walk the Line: Linear Equations 14
• Common Forms of Linear Equations 14
• Calculating Slope 16
• Interpreting Linear Graphs 18
• You've Got the Power: Exponential Rules 21
• Breaking Up Is Hard to Do: Factoring Polynomials 22
• Greatest Common Factor 23
• Special Factoring Patterns 23
• Solving Quadratic Equations 24
• Method One: Factoring 25
• Method Two: Completing the Square 25
• Method Three: The Quadratic Formula 26
• Synthesizing the Quadratic Solution Methods 27
• 3 Equations, Relations, and Functions 31
• What Makes a Function Tick? 31
• Working with Graphs of Functions 36
• Functional Symmetry 39
• Graphs to Know by Heart 43
• Constructing an Inverse Function 45
• Parametric Equations 47
• What's a Parameter? 47
• Converting to Rectangular Form 48
• 4 Trigonometry: Last Stop Before Calculus 51
• Getting Repetitive: Periodic Functions 51
• Introducing the Trigonometric Functions 53
• Sine (Written as y = sin x) 54
• Cosine (Written as y = cos x) 54
• Tangent (Written as y = tan x) 55
• Cotangent (Written as y = cot x) 56
• Secant (Written as y = sec x) 57
• Cosecant (Written as y = csc x) 57
• What's Your Sine: The Unit Circle 59
• Incredibly Important Identities 61
• Pythagorean Identities 62
• Double-Angle Formulas 63
• Solving Trigonometric Equations 64.

• Part 2: Laying the Foundation for Calculus 67
• 5 Take It to the Limit 69
• What Is a Limit? 70
• Can Something Be Nothing? 71
• One-Sided Limits 74
• When Does a Limit Exist? 78
• When Does a Limit Not Exist? 79
• 6 Evaluating Limits Numerically 85
• The Major Methods 86
• Substitution Method 86
• Factoring Method 87
• Conjugate Method 88
• What If Nothing Works? 90
• Limits and Infinity 90
• Vertical Asymptotes 90
• Horizontal Asymptotes 92
• Special Limit Theorems 96
• Evaluating Limits Graphically 97
• Technology Focus: Calculating Limits 99
• 7 Continuity 103
• What Does Continuity Look Like? 104
• The Mathematical Definition of Continuity 104
• Types of Discontinuity 109
• Jump Discontinuity 109
• Point Discontinuity 113
• Infinite/Essential Discontinuity 114
• Removable vs Nonremovable Discontinuity 117
• The Intermediate Value Theorem 118
• 8 The Difference Quotient 121
• When a Secant Becomes a Tangent 122
• Honey, I Shrunk the x 123
• Applying the Difference Quotient 127
• The Alternate Difference Quotient 129
• Part 3: The Derivative 131
• 9 Laying Down the Law for Derivatives 133
• When Does a Derivative Exist? 134
• Discontinuity 134
• Sharp Point in the Graph 134
• Vertical Tangent Line 135
• Basic Derivative Techniques 136
• The Power Rule 136
• The Product Rule 138
• The Quotient Rule 139
• The Chain Rule 140
• Rates of Change 141
• Trigonometric Derivatives 144
• Tabular and Graphical Derivatives 145
• Technology Focus: Calculating Derivatives 150
• 10 Common Differentiation Tasks 155
• Finding Equations of Tangent Lines 156
• Implicit Differentiation 159
• Differentiating an Inverse Function 161
• Parametric Derivatives 164
• Technology Focus: Solving Gross Equations 166
• Using the Built-In Equation Solver 166
• The Equation-Function Connection 170.

• 11 Using Derivatives to Graph 173
• Relative Extrema 174
• Finding Critical Numbers 175
• Classifying Extrema 176
• The Wiggle Graph 178
• The Extreme Value Theorem 180
• Determining Concavity 182
• Another Wiggle Graph 183
• The Second Derivative Test 184
• 12 Derivatives and Motion 187
• The Position Equation 188
• Velocity 190
• Acceleration 191
• Vertical Projectile Motion 193
• 13 Common Derivative Applications 195
• Newton's Method 196
• Evaluating Limits: L'Hôpital's Rule 199
• More Existence Theorems 200
• The Mean Value Theorem 201
• Rolle's Theorem 203
• Related Rates 204
• Optimization 208
• Part 4: The Integral 215
• 14 Approximating Area 217
• Riemann Sums 218
• Right and Left Sums 219
• Midpoint Sums 221
• The Trapezoidal Rule 222
• Simpson's Rule 225
• 15 Antiderivatives 227
• The Power Rule for Integration 228
• Integrating Trigonometric Functions 230
• Separation 232
• The Fundamental Theorem of Calculus 233
• Part One: Areas and Integrals Are Related 233
• Part Two: Derivatives and Integrals Are Opposites 235
• u-Substitution 236
• Tricky u-Substitution and Long Division 237
• Technology Focus: Definite and Indefinite Integrals 239
• 16 Applications of the Fundamental Theorem 245
• Calculating Area Between Two Curves 246
• The Mean Value Theorem for Integration 249
• A Geometric Interpretation 249
• The Average Value Theorem 251
• Finding Distance Traveled 253
• Accumulation Functions 255
• Arc Length 256
• Rectangular Equations 256
• Parametric Equations 257
• Part 5: Differential Equations and More 259
• 17 Differential Equations 261
• Separation of Variables 262
• Types of Solutions 263
• Family of Solutions 264
• Specific Solutions 266
• Exponential Growth and Decay 267
• 18 Visualizing Differential Equations 275
• Linear Approximation 276
• Slope Fields 277.

• Euler's Method 281
• Technology Focus: Slope Fields 285
• 19 Final Exam 289
• A Solutions to "You've Got Problems" 301
• B Glossary 317
• Index 323.

"Let's face it: the thought of Calculus I can be daunting. But it needn't be. in this helpful guide, the fundamentals of Calculus I are taught in easy-to-understand terms, with lots of explanatory graphs and illustrations and over 150 practice problems that feature simple, step-by-step solutions to really explain what you need to know, "-- Provided by publisher.

• Frontmatter
• Introduction
• Contents
• Supplementary Notational References
• PART I. Elementary Theory of Automorphic Forms on a Bounded Domain
• Chapter 1. General Notions and Examples
• Chapter 2. Analytic Functions and Analytic Spaces
• Chapter 3. Holomorphic Functions and Mappings on a Bounded Domain
• Chapter 4. Analysis on Domains in Cn
• Chapter 5. Automorphic forms on bounded domains
• Part II. Automorphic forms on a bounded symmetric domain and analysis on a semi-simple Lie group
• Chapter 6. Examples for algebraic groups
• Chapter 7. Algebraic groups
• Chapter 8. Representations of compact groups
• Chapter 9. Some work of Harish-Chandra
• Chapter 10. Functional analysis for automorphic forms
• Chapter 11. Construction of automorphic forms
• Part III. Some special topics
• Chapter 12. Fourier Coefficients of Eisenstein Series
• Chapter 13. Theta Functions and Automorphic Forms
• Bibliography
• Index

Intended as an introductory guide, this work takes for its subject complex, analytic, automorphic forms and functions on (a domain equivalent to) a bounded domain in a finite-dimensional, complex, vector space, usually denoted Cn).Part I, essentially elementary, deals with complex analytic automorphic forms on a bounded domain; it presents H. Cartan's proof of the existence of the projective imbedding of the compact "ient of such a domain by a discrete group. Part II treats the construction and properties of automorphic forms with respect to an arithmetic group acting on a bounded symmetric domain; this part is highly technical, and based largely on relevant results in functional analysis due to Godement and Harish-Chandra. In Part III, Professor Baily extends the discussion to include some special topics, specifically, the arithmetic propertics of Eisenstein series and their connection with the arithmetic theory of quadratic forms.Unlike classical works on the subject, this book deals with more than one variable, and it differs notably in its treatment of analysis on the group of automorphisms of the domain. It is concerned with the case of complex analytic automorphic forms because of their connection with algebraic geometry, and so is distinct from other modern treatises that deal with automorphic forms on a semi-simple Lie group.Having had its inception as graduate- level lectures, the book assumes some knowledge of complex function theory and algebra, for the serious reader is expected to supply certain details for himself, especially in such related areas as functional analysis and algebraic groups.Originally published in 1973.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905

• Preface xi
• Chapter 1. Fourier Series 1
• 1.1. Theoretical background 1
• 1.1.1. Orthogonal functions 1
• 1.1.2. Fourier Series 3
• 1.1.3. Periodic functions 5
• 1.1.4. Properties of Fourier series 6
• 1.1.5. Discrete spectra. Power distribution 8
• 1.2. Exercises 9
• 1.2.1. Exercise 1.1. Examples of decomposition calculations 10
• 1.2.2. Exercise 1.2 11
• 1.2.3. Exercise 1.3 12
• 1.2.4. Exercise 1.4 12
• 1.2.5. Exercise 1.5 12
• 1.2.6. Exercise 1.6. Decomposing rectangular functions 13
• 1.2.7. Exercise 1.7. Translation and composition of functions 14
• 1.2.8. Exercise 1.8. Time derivation of a function 15
• 1.2.9. Exercise 1.9. Time integration of functions 15
• 1.2.10. Exercise 1.10 15
• 1.2.11. Exercise 1.11. Applications in electronic circuits 16
• 1.3. Solutions to the exercises 17
• 1.3.1. Exercise 1.1. Examples of decomposition calculations 17
• 1.3.2. Exercise 1.2 25
• 1.3.3. Exercise 1.3 26
• 1.3.4. Exercice 1.4 26
• 1.3.5. Exercise 1.5 27
• 1.3.6. Exercise 1.6 27
• 1.3.7. Exercise 1.7. Translation and composition of functions 29
• 1.3.8. Exercise 1.8. Time derivation of functions 31
• 1.3.9. Exercise 1.9. Time integration of functions 32
• 1.3.10. Exercise 1.10 32
• 1.3.11. Exercise 1.11 35
• Chapter 2. Fourier Transform 39
• 2.1. Theoretical background 39
• 2.1.1. Fourier transform 39
• 2.1.2. Properties of the Fourier transform 42
• 2.1.3. Singular functions 46
• 2.1.4. Fourier transform of common functions 51
• 2.1.5. Calculating Fourier transforms using the Dirac impulse method 53
• 2.1.6. Fourier transform of periodic functions 54
• 2.1.7. Energy density 54
• 2.1.8. Upper limits to the Fourier transform 55
• 2.2. Exercises 56
• 2.2.1. Exercise 2.1 56
• 2.2.2. Exercise 2.2 57
• 2.2.3. Exercise 2.3 58
• 2.2.4. Exercise 2.4 59
• 2.2.5. Exercise 2.5 59
• 2.2.6. Exercise 2.6 59
• 2.2.7. Exercise 2.7 60
• 2.2.8. Exercise 2.8 60
• 2.2.9. Exercise 2.9 61
• 2.2.10. Exercise 2.10 62
• 2.2.11. Exercise 2.11 62
• 2.2.12. Exercise 2.12 63
• 2.2.13. Exercise 2.13 63
• 2.2.14. Exercise 2.14 64
• 2.2.15. Exercise 2.15 64
• 2.2.16. Exercise 2.16 65
• 2.2.17. Exercise 2.17 66
• 2.3. Solutions to the exercises 67
• 2.3.1. Exercise 2.1 67
• 2.3.2. Exercise 2.2 68
• 2.3.3. Exercise 2.3 74
• 2.3.4. Exercise 2.4 74
• 2.3.5. Exercise 2.5 76
• 2.3.6. Exercise 2.6 76
• 2.3.7. Exercise 2.7 77
• 2.3.8. Exercise 2.8 79
• 2.3.9. Exercise 2.9 82
• 2.3.10. Exercise 2.10 85
• 2.3.11 Exercise 2.11 86
• 2.3.12 Exercise 2.12 88
• 2.3.13 Exercise 2.13 91
• 2.3.14 Exercise 2.14 91
• 2.3.15 Exercice 2.15 92
• 2.3.16 Exercise 2.16 94
• 2.3.17 Exercise 2.17 95
• Chapter 3. Laplace Transform 97
• 3.1. Theoretical background 97
• 3.1.1. Definition 97
• 3.1.2. Existence of the Laplace transform 98
• 3.1.3. Properties of the Laplace transform 98
• 3.1.4. Final value and initial value theorems 102
• 3.1.5. Determining reverse transforms 102
• 3.1.6. Approximation methods 105
• 3.1.7. Laplace transform and differential equations 107
• 3.1.8. Table of common Laplace transforms 108
• 3.1.9. Transient state and steady state 110
• 3.2. Exercise instruction 111
• 3.2.1. Exercise 3.1 111
• 3.2.2. Exercise 3.2 111
• 3.2.3. Exercise 3.3 112
• 3.2.4. Exercise 3.4 112
• 3.2.5. Exercise 3.5 112
• 3.2.6. Exercise 3.6 113
• 3.2.7. Exercise 3.7 113
• 3.2.8. Exercise 3.8 115
• 3.2.9. Exercise 3.9 115
• 3.2.10. Exercise 3.10 115
• 3.3. Solutions to the exercises 116
• 3.3.1. Exercise 3.1 116
• 3.3.2. Exercise 3.2 117
• 3.3.3. Exercise 3.3 121
• 3.3.4. Exercise 3.4 122
• 3.3.5. Exercise 3.5 130
• 3.3.6. Exercise 3.6 131
• 3.3.7. Exercise 3.7 132
• 3.3.8. Exercise 3.8 136
• 3.3.9. Exercise 3.9 138
• 3.3.10. Exercise 3.10 139
• Chapter 4. Integrals and Convolution Product 143
• 4.1. Theoretical background 143
• 4.1.1. Analyzing linear systems using convolution integrals 143
• 4.1.2. Convolution properties 144
• 4.1.3. Graphical interpretation of the convolution product 145
• 4.1.4. Convolution of a function using a unit impulse 145
• 4.1.5. Step response from a system 147
• 4.1.6. Eigenfunction of a convolution operator 148
• 4.2. Exercises 149
• 4.2.1. Exercise 4.1 149
• 4.2.2. Exercise 4.2 150
• 4.2.3. Exercise 4.3 150
• 4.2.4. Exercise 4.4 151
• 4.2.5. Exercise 4.5 151
• 4.2.6. Exercise 4.6 152
• 4.3. Solutions to the exercises 153
• 4.3.1. Exercise 4.1 153
• 4.3.2. Exercise 4.2 156
• 4.3.3. Exercise 4.3 160
• 4.3.4. Exercise 4.4 163
• 4.3.5. Exercise 4.5 164
• 4.3.6. Exercise 4.6 165
• Chapter 5. Correlation 169
• 5.1. Theoretical background 169
• 5.1.1. Comparing signals 169
• 5.1.2. Correlation function 170
• 5.1.3. Properties of correlation functions 172
• 5.1.4. Energy of a signal 176
• 5.2. Exercises 177
• 5.2.1. Exercise 5.1 177
• 5.2.2. Exercise 5.2 178
• 5.2.3. Exercise 5.3 178
• 5.2.4. Exercise 5.4 178
• 5.2.5. Exercice 5.5 179
• 5.2.6. Exercice 5.6 179
• 5.2.7. Exercise 5.7 179
• 5.2.8. Exercice 5.8 180
• 5.2.9. Exercise 5.9 180
• 5.2.10. Exercise 5.10 181
• 5.2.11. Exercise 5.11 181
• 5.2.12. Exercise 5.12 182
• 5.2.13. Exercise 5.13 182
• 5.2.14. Exercise 5.14 183
• 5.3. Solutions to the exercises 183
• 5.3.1. Exercise 5.1 183
• 5.3.2. Exercice 5.2 188
• 5.3.3. Exercise 5.3 191
• 5.3.4. Exercice 5.4 192
• 5.3.5. Exercise 5.5 193
• 5.3.6. Exercise 5.6 196
• 5.3.7. Exercise 5.7 197
• 5.3.8. Exercise 5.8 201
• 5.3.9. Exercise 5.9 204
• 5.3.10. Exercise 5.10 205
• 5.3.11 Exercise 5.11 206
• 5.3.12 Exercise 5.12 207
• 5.3.13 Exercise 5.13 208
• 5.3.14 Exercise 5.14 209
• Chapter 6. Signal Sampling 213
• 6.1. Theoretical background 213
• 6.1.1. Sampling principle 213
• 6.1.2. Ideal sampling 214
• 6.1.3. Finite width sampling 218
• 6.1.4. Sample and hold (S/H) sampling 221
• 6.2. Exercises 225
• 6.2.1. Exercise 6.1 225
• 6.2.2. Exercise 6.2 225
• 6.2.3. Exercise 6.3 226
• 6.2.4. Exercise 6.4 226
• 6.2.5. Exercise 6.5 226
• 6.2.6. Exercise 5.6 227
• 6.2.7. Exercise 6.7 227
• 6.2.8. Exercice 6.8 228
• 6.3. Solutions to the exercises 229
• 6.3.1. Exercise 6.1 229
• 6.3.2. Exercise 6.2 229
• 6.3.3. Exercise 6.3 233
• 6.3.4. Exercice 6.4 235
• 6.3.5. Exercise 6.5 236
• 6.3.6. Exercise 6.6 238
• 6.3.7. Exercise 6.7 240
• 6.3.8. Exercise 6.8 242
• Bibliography 245
• Index 247.
• (source: Nielsen Book Data)

This book aims to learn to use the basic concepts in signal processing. Each chapter is a reminder of the basic principles is presented followed by a series of corrected exercises. After resolution of these exercises, the reader can pretend to know those principles that are the basis of this theme. "We do not learn anything by word, but by example.".
(source: Nielsen Book Data)

Elementary Analysis, Volume 1 introduces the reader to elementary analysis in an informal manner and provides the practical experience in algebraic and analytic operations to lay a sound foundation of basic skills. The preliminary ideas are illustrated by applications to the simpler algebraic functions. Emphasis is on fundamental principles, rather than manipulative techniques.

• Front Cover; Applied Calculus; Copyright Page; Table of Contents; Editor's Preface; Author's Preface; To the Reader; CHAPTER ONE. Rates of Change. Velocity. Acceleration. Area under a Curve; CHAPTER TWO. Motion with Uniform Acceleration. Angular Velocity. Mean Values. Areas and Volumes; CHAPTER THREE. Tangents and Normals. Length of Arcs. Curvature. Evolutes and Involutes. Envelopes; CHAPTER FOUR. Maxima and Minima. Points of Inflexion; Index.

• Frontmatter
• Preface
• Contents
• 1. Attractor and its dimension estimation
• 2. Inertial manifold
• 3. The approximate inertial manifold
• Bibliography
• Index

• Preface xi List of Acronyms xiii
• 1. Introduction 1 1.1 Finite-Time Stability (FTS) 1 1.2 Input-Output Finite-Time Stability 6 1.3 FTS and Finite-Time Convergence 10 1.4 Background 10 1.4.1 Vectors and signals 10 1.4.2 Impulsive dynamical linear systems 12 1.5 Book Organization 13
• 2. Linear Time-Varying Systems: IO-FTS Analysis 15 2.1 Problem Statement 15 2.2 IO-FTS for W2 Exogenous Inputs 16 2.2.1 Preliminaries 16 2.2.2 Necessary and sufficient conditions for IO-FTS for W2 exogenous inputs 22 2.2.3 Computational issues 25 2.3 A Sufficient Condition for IO-FTS for W Inputs 26 2.4 Summary 29
• 3. Linear Time-Varying Systems: Design of IO Finite-Time Stabilizing Controllers 33 3.1 IO Finite-Time Stabilization via State Feedback 34 3.2 IO-Finite-Time Stabilization via Output Feedback 36 3.3 Summary 42
• 4. IO-FTS with Nonzero Initial Conditions 45 4.1 Preliminaries 45 4.2 Interpretation of the Norm of the Operator LSNZ 48 4.3 Sufficient Conditions for IO-FTS-NZIC 52 4.4 Design of IO Finite-Time Stabilizing Controllers NZIC 55 4.4.1 State feedback 56 4.4.2 Output feedback 57 4.5 Summary 58
• 5. IO-FTS with Constrained Control Inputs 61 5.1 Structured IO-FTS and Problem Statement 61 5.2 Structured IO-FTS Analysis 63 5.3 State Feedback Design 65 5.4 Design of an Active Suspension Control System Using Structured IO-FTS 67 5.5 Summary 70
• 6. Robustness Issues and the Mixed H /FTS Control Problem 71 6.1 Preliminaries 72 6.1.1 System setting 72 6.1.2 IO-FTS with an H bound 73 6.2 Robust and Quadratic IO-FTS with an H Bound 77 6.2.1 Main result 78 6.2.2 A numerical example 80 6.3 State Feedback Design 82 6.3.1 Numerical example: Cont'd 85 6.4 Case study: Quadratic IO-FTS with an H Bound of the Inverted Pendulum 86 6.5 Summary 88
• 7. Impulsive Dynamical Linear Systems: IO-FTS Analysis 89 7.1 Background 90 7.1.1 Preliminary results for the W2 case 90 7.2 Main Results: Necessary and Sufficient Conditions for IO-FTS in Presence of W2 Signals 91 7.3 Example and Computational Issues 96 7.4 Main Result: A Sufficient Condition for IO-FTS in Presence of W Signals 98 7.4.1 An illustrative example 99 7.5 Summary 100
• 8. Impulsive Dynamical Linear Systems: IO Finite-Time Stabilization via Dynamical Controllers 103 8.1 Problem Statement 103 8.2 IO Finite-Time Stabilization of IDLSs: W2 Signals 104 8.2.1 A numerical example 107 8.3 IO Finite-Time Stabilization of IDLSs: W Signals 108 8.3.1 Illustrative example: Cont'd 110 8.4 Summary 111
• 9. Impulsive Dynamical Linear Systems with Uncertain Resetting Times 113 9.1 Arbitrary Switching 113 9.2 Uncertain Switching 114 9.3 Numerical Example 116 9.3.1 Known resetting times 117 9.3.2 Arbitrary switching 118 9.3.3 Uncertain switching 118 9.4 Summary 119
• 10. Hybrid Architecture for Deployment of Finite-Time Control Systems 121 10.1 Controller Architecture 121 10.2 Examples 123 10.2.1 Hybrid active suspension control 123 10.2.2 Lateral collision avoidance system 124 10.3 Summary 129 A. Fundamentals on Linear Time-Varying Systems 131 B. Schur Complements 137 C. Computation of Feasible Solutions to Optimizations Problems Involving DLMIs 139D. Solving Optimization Problems Involving DLMIs using MATLAB (R) 145 E. Examples of Applications of IO-FTS Control Design to Real-World Systems 151 References 159 Index 167.
• (source: Nielsen Book Data)

Systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, covering issues of analysis, design and robustness The interest in finite-time control has continuously grown in the last fifteen years. This book systematically presents the input-output finite-time stability (IO-FTS) analysis of dynamical systems, with specific reference to linear time-varying systems and hybrid systems. It discusses analysis, design and robustness issues, and includes applications to real world engineering problems. While classical FTS has an important theoretical significance, IO-FTS is a more practical concept, which is more suitable for real engineering applications, the goal of the research on this topic in the coming years. Key features: Includes applications to real world engineering problems. Input-output finite-time stability (IO-FTS) is a practical concept, useful to study the behavior of a dynamical system within a finite interval of time. Computationally tractable conditions are provided that render the technique applicable to time-invariant as well as time varying and impulsive (i.e. switching) systems. The LMIs formulation allows mixing the IO-FTS approach with existing control techniques (e. g. H control, optimal control, pole placement, etc.). This book is essential reading for university researchers as well as post-graduate engineers practicing in the field of robust process control in research centers and industries. Topics dealt with in the book could also be taught at the level of advanced control courses for graduate students in the department of electrical and computer engineering, mechanical engineering, aeronautics and astronautics, and applied mathematics.
(source: Nielsen Book Data)

• PREFACE xi ACKNOWLEDGMENTS xv
• 1 Introduction, Classification, Short History, Auxiliary Results, and Methods 1 1.1 Classical and New Types of FEs 2 1.2 Main Directions in the Study of FDE 4 1.3 Metric Spaces and Related Concepts 11 1.4 Functions Spaces 15 1.5 Some Nonlinear Auxiliary Tools 21 1.6 Further Types of FEs 25
• 2 Existence Theory for Functional Equations 37 2.1 Local Existence for Continuous or Measurable Solutions 38 2.2 Global Existence for Some Classes of Functional Differential Equations 43 2.3 Existence for a Second-Order Functional Differential Equation 50 2.4 The Comparison Method in Obtaining Global Existence Results 55 2.5 A Functional Differential Equation with Bounded Solutions on the Positive Semiaxis 59 2.6 An Existence Result for Functional Differential Equations with Retarded Argument 64 2.7 A Second Order Functional Differential Equation with Bounded Solutions on the Positive Semiaxis 68 2.8 A Global Existence Result for a Class of First-Order Functional Differential Equations 72 2.9 A Global Existence Result in a Special Function Space and a Positivity Result 76 2.10 Solution Sets for Causal Functional Differential Equations 81 2.11 An Application to Optimal Control Theory 87 2.12 Flow Invariance 92 2.13 Further Examples/Applications/Comments 95 2.14 Bibliographical Notes 98
• 3 Stability Theory of Functional Differential Equations 105 3.1 Some Preliminary Considerations and Definitions 106 3.2 Comparison Method in Stability Theory of Ordinary Differential Equations 111 3.3 Stability under Permanent Perturbations 115 3.4 Stability for Some Functional Differential Equations 126 3.5 Partial Stability 133 3.6 Stability and Partial Stability of Finite Delay Systems 139 3.7 Stability of Invariant Sets 147 3.8 Another Type of Stability 155 3.9 Vector and Matrix Liapunov Functions 160 3.10 A Functional Differential Equation 163 3.11 Brief Comments on the Start and Evolution of the Comparison Method in Stability 168 3.12 Bibliographical Notes 169
• 4 Oscillatory Motion, with Special Regard to the Almost Periodic Case 175 4.1 Trigonometric Polynomials and APr-Spaces 176 4.2 Some Properties of the Spaces APr(R, C) 183 4.3 APr-Solutions to Ordinary Differential Equations 190 4.4 APr-Solutions to Convolution Equations 196 4.5 Oscillatory Solutions Involving the Space B 202 4.6 Oscillatory Motions Described by Classical Almost Periodic Functions 207 4.7 Dynamical Systems and Almost Periodicity 217 4.8 Brief Comments on the Definition of APr(R, C) Spaces and Related Topics 221 4.9 Bibliographical Notes 224
• 5 Neutral Functional Differential Equations 231 5.1 Some Generalities and Examples Related to Neutral Functional Equations 232 5.2 Further Existence Results Concerning Neutral First-Order Equations 240 5.3 Some Auxiliary Results 243 5.4 A Case Study, I 248 5.5 Another Case Study, II 256 5.6 Second-Order Causal Neutral Functional Differential Equations, I 261 5.7 Second-Order Causal Neutral Functional Differential Equations, II 268 5.8 A Neutral Functional Equation with Convolution 276 5.9 Bibliographical Notes 278 Appendix A On the Third Stage of Fourier Analysis 281 A.1 Introduction 281 A.2 Reconstruction of Some Classical Spaces 282 A.3 Construction of Another Classical Space 288 A.4 Constructing Spaces of Oscillatory Functions: Examples and Methods 290 A.5 Construction of Another Space of Oscillatory Functions 295 A.6 Searching Functional Exponents for Generalized Fourier Series 297 A.7 Some Compactness Problems 304 BIBLIOGRAPHY 307 INDEX 341.
• (source: Nielsen Book Data)

Features new results and up-to-date advances in modeling and solving differential equations Introducing the various classes of functional differential equations, Functional Differential Equations: Advances and Applications presents the needed tools and topics to study the various classes of functional differential equations and is primarily concerned with the existence, uniqueness, and estimates of solutions to specific problems. The book focuses on the general theory of functional differential equations, provides the requisite mathematical background, and details the qualitative behavior of solutions to functional differential equations. The book addresses problems of stability, particularly for ordinary differential equations in which the theory can provide models for other classes of functional differential equations, and the stability of solutions is useful for the application of results within various fields of science, engineering, and economics. Functional Differential Equations: Advances and Applications also features: Discussions on the classes of equations that cannot be solved to the highest order derivative, and in turn, addresses existence results and behavior types Oscillatory motion and solutions that occur in many real-world phenomena as well as in man-made machines Numerous examples and applications with a specific focus on ordinary differential equations and functional differential equations with finite delay An appendix that introduces generalized Fourier series and Fourier analysis after periodicity and almost periodicity An extensive Bibliography with over 550 references that connects the presented concepts to further topical exploration Functional Differential Equations: Advances and Applications is an ideal reference for academics and practitioners in applied mathematics, engineering, economics, and physics. The book is also an appropriate textbook for graduate- and PhD-level courses in applied mathematics, differential and difference equations, differential analysis, and dynamics processes. CONSTANTIN CORDUNEANU, PhD, is Emeritus Professor in the Department of Mathematics at The University of Texas at Arlington, USA. The author of six books and over 200 journal articles, he is currently Associate Editor for seven journals; a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Romanian Academy; and past president of the American Romanian Academy of Arts and Sciences. YIZENG LI, PhD, is Professor in the Department of Mathematics at Tarrant County College, USA. He is a member of the Society for Industrial and Applied Mathematics. MEHRAN MAHDAVI, PhD, is Professor in the Department of Mathematics at Bowie State University, USA. The author of numerous journal articles, he is a member of the American Mathematical Society, Society for Industrial and Applied Mathematics, and the Mathematical Association of America.
(source: Nielsen Book Data)

• Frontmatter
• Table of Contents
• Introduction
• Chapter I. Homogeneous Distributions
• Chapter II. Basic Estimates for Pseudo Differential Operators
• Chapter III. Further Regularity Theorems and Composition of Operators
• Chapter IV. Applications
• Appendix
• References.

The theory of pseudo-differential operators (which originated as singular integral operators) was largely influenced by its application to function theory in one complex variable and regularity properties of solutions of elliptic partial differential equations. Given here is an exposition of some new classes of pseudo-differential operators relevant to several complex variables and certain non-elliptic problems.Originally published in 1979.The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These paperback editions preserve the original texts of these important books while presenting them in durable paperback editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.