1  20
Next
 Buono, PietroLuciano, author.
 Berlin ; Boston : De Gruyter, [2016]
 Description
 Book — 1 online resource (313 p). Digital: text file; PDF.
 Summary

 Frontmatter
 Contents
 Preface
 1. Introduction
 2. Calculus of Vector Functions
 3. Tangent Spaces and 1forms
 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
(source: Nielsen Book Data)
2. Single Variable Calculus : A First Step [2018]
 Zou, Yunzhi, author.
 Berlin ; Boston : De Gruyter, [2018]
 Description
 Book — 1 online resource (424 p). Digital: text file; PDF.
 Summary

 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
(source: Nielsen Book Data)
 Fernández, Oscar, author. Author http://id.loc.gov/vocabulary/relators/aut
 Princeton, NJ : Princeton University Press, [2017]
 Description
 Book — 1 online resource (168 p.) : 47 line illus. 1 table Digital: text file; PDF.
 Summary

 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 17
 Notes
 Index
 Xue, Dingyü author.
 Berlin ; Boston : De Gruyter, [2017]
 Description
 Book — 1 online resource (388 p). Digital: text file; PDF.
 Summary

 Frontmatter
 Foreword
 Preface
 Contents
 1. Introduction to fractional calculus and fractionalorder control
 2. Mathematical prerequisites
 3. Definitions and computation algorithms of fractionalorder derivatives and integrals
 4. Solutions of linear fractionalorder differential equations
 5. Approximation of fractionalorder operators
 6. Modelling and analysis of multivariable fractionalorder transfer function matrices
 7. State space modelling and analysis of linear fractionalorder systems
 8. Numerical solutions of nonlinear fractionalorder differential equations
 9. Design of fractionalorder PID controllers
 10. Frequency domain controller design for multivariable fractionalorder systems
 A. Inverse Laplace transforms involving fractional and irrational operations
 B. FOTF Toolbox functions and models
 C. Benchmark problems for the assessment of fractionalorder differential equation algorithms
 Bibliography
 Index
(source: Nielsen Book Data)
 Borrelli, Vincent.
 [Place of publication not identified] : Fondation Maison des Sciences de l'Homme  Diffusion, 2015.
 Description
 Book — 1 online resource.
6. Calculus I [2016]
 Kelley, W. Michael, author.
 First American edition.  Indianapolis, Indiana : Alpha, a member of Penguin Random House LLC, 2016.
 Description
 Book — 1 online resource : illustrations.
 Summary

 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 xIntercepts 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
 DoubleAngle 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
 OneSided 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 BuiltIn Equation Solver 166
 The EquationFunction 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
 uSubstitution 236
 Tricky uSubstitution 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.
 Baily, Walter L., author. Author http://id.loc.gov/vocabulary/relators/aut
 Princeton, NJ : Princeton University Press, [2015]
 Description
 Book — 1 online resource (280 p). Digital: text file; PDF.
 Summary

 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 semisimple Lie group
 Chapter 6. Examples for algebraic groups
 Chapter 7. Algebraic groups
 Chapter 8. Representations of compact groups
 Chapter 9. Some work of HarishChandra
 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
 Artés, Joan C., 1961 author.
 Cham, Switzerland : Birkhäuser, 2018.
 Description
 Book — 1 online resource (vi, 267 pages) : illustrations (some color)
9. Fourier analysis [2017]
 Ceschi, Roger.
 London, UK : ISTE, Ltd. ; Hoboken, NJ : Wiley, 2017.
 Description
 Book — 1 online resource
 Summary

 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)
(source: Nielsen Book Data)
 New York : Nova Science Publishers, Inc., 2017.
 Description
 Book — 1 online resource.
11. Foundations of isodifferential calculus. Volume 6, Theory of isofunctions of a real isovariable [2016]
 Georgiev, Svetlin author.
 New York : Nova Science Publishers, [2016]
 Description
 Book — 1 online resource. Digital: data file.
12. Elementary analysis [1965]
 Snell, K. S. (Kenneth Scotchburn), author.
 First edition.  Oxford ; New York : Pergamon Press [1965]
 Description
 Book — 1 online resource (249 pages)
 Summary

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.
 Fikhtengolʹt͡s, G. M. (Grigoriĭ Mikhaĭlovich), 18881959, author.
 Oxford : Pergamon Press, 1965.
 Description
 Book — 1 online resource (521 pages).
 Fikhtengolʹt͡s, G. M. (Grigoriĭ Mikhaĭlovich), 18881959, author.
 London : Pergamon Press, 1965.
 Description
 Book — 1 online resource (541 pages).
15. Ordinary differential equations [1962]
 Pontri͡agin, L. S. (Lev Semenovich), 19081988, author.
 Reading, Massachusetts : AddisonWesley Publishing Company, Inc. ; London : Pergamon Press, 1962.
 Description
 Book — 1 online resource : illustrations.
 Bell, D. J. (David John), 1913
 First edition.  Oxford ; New York : Pergamon Press, [1966]
 Description
 Book — 1 online resource (247 pages)
 Summary

 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.
 Guo, Boling, author.
 Berlin : Walter de Gruyter GmbH., [2018]
 Description
 Book — 1 online resource
 Summary

 Frontmatter
 Preface
 Contents
 1. Attractor and its dimension estimation
 2. Inertial manifold
 3. The approximate inertial manifold
 Bibliography
 Index
 Amato, Francesco, author.
 First edition.  Hoboken, NJ : Wiley, 2018.
 Description
 Book — 1 online resource.
 Summary

 Preface xi List of Acronyms xiii
 1. Introduction 1 1.1 FiniteTime Stability (FTS) 1 1.2 InputOutput FiniteTime Stability 6 1.3 FTS and FiniteTime 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 TimeVarying Systems: IOFTS Analysis 15 2.1 Problem Statement 15 2.2 IOFTS for W2 Exogenous Inputs 16 2.2.1 Preliminaries 16 2.2.2 Necessary and sufficient conditions for IOFTS for W2 exogenous inputs 22 2.2.3 Computational issues 25 2.3 A Sufficient Condition for IOFTS for W Inputs 26 2.4 Summary 29
 3. Linear TimeVarying Systems: Design of IO FiniteTime Stabilizing Controllers 33 3.1 IO FiniteTime Stabilization via State Feedback 34 3.2 IOFiniteTime Stabilization via Output Feedback 36 3.3 Summary 42
 4. IOFTS 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 IOFTSNZIC 52 4.4 Design of IO FiniteTime Stabilizing Controllers NZIC 55 4.4.1 State feedback 56 4.4.2 Output feedback 57 4.5 Summary 58
 5. IOFTS with Constrained Control Inputs 61 5.1 Structured IOFTS and Problem Statement 61 5.2 Structured IOFTS Analysis 63 5.3 State Feedback Design 65 5.4 Design of an Active Suspension Control System Using Structured IOFTS 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 IOFTS with an H bound 73 6.2 Robust and Quadratic IOFTS 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 IOFTS with an H Bound of the Inverted Pendulum 86 6.5 Summary 88
 7. Impulsive Dynamical Linear Systems: IOFTS 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 IOFTS in Presence of W2 Signals 91 7.3 Example and Computational Issues 96 7.4 Main Result: A Sufficient Condition for IOFTS in Presence of W Signals 98 7.4.1 An illustrative example 99 7.5 Summary 100
 8. Impulsive Dynamical Linear Systems: IO FiniteTime Stabilization via Dynamical Controllers 103 8.1 Problem Statement 103 8.2 IO FiniteTime Stabilization of IDLSs: W2 Signals 104 8.2.1 A numerical example 107 8.3 IO FiniteTime 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 FiniteTime 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 TimeVarying 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 IOFTS Control Design to RealWorld Systems 151 References 159 Index 167.
 (source: Nielsen Book Data)
(source: Nielsen Book Data)
 Corduneanu, C., author.
 Hoboken, New Jersey : John Wiley & Sons, Inc., [2016]
 Description
 Book — 1 online resource.
 Summary

 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 SecondOrder 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 FirstOrder 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 APrSpaces 176 4.2 Some Properties of the Spaces APr(R, C) 183 4.3 APrSolutions to Ordinary Differential Equations 190 4.4 APrSolutions 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 FirstOrder Equations 240 5.3 Some Auxiliary Results 243 5.4 A Case Study, I 248 5.5 Another Case Study, II 256 5.6 SecondOrder Causal Neutral Functional Differential Equations, I 261 5.7 SecondOrder 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)
(source: Nielsen Book Data)
 Nagel, Alexander author.
 Princeton, N.J. : Princeton University Press, [2015]
 Description
 Book — 1 online resource(168 p.) : illustrations. Digital: text file; PDF.
 Summary

 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.
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