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[null,"1.","Record Nr.",null,"UNINA9910960571603321"]
[null,null,"Autore",null,"Haghighi Aliakbar Montazer"]
[null,null,"Titolo",null,"Advanced mathematics for engineers with applications in stochastic processes / / Aliakbar Montazer Haghighi, Jian-ao Lian, and Dimitar P. Mishev"]
[null,null,"Pubbl/distr/stampa",null,"New York, : Nova Science Publishers, Inc., 2011, c2010"]
[null,null,"ISBN",null,"1-62417-681-X"]
[null,null,"Edizione",null,"[Rev. ed.]"]
[null,null,"Descrizione fisica",null,"1 online resource (568 p.)"]
[null,null,"Collana",null,"Mathematics research developments"]
[null,null,"Disciplina",null,"510"]
[null,null,"Soggetti",null,"Functions of several complex variables"]
[{"$nulls":4},"Stochastic analysis"]
[null,null,"Lingua di pubblicazione",null,"Inglese"]
[null,null,"Formato",null,"Materiale a stampa"]
[null,null,null,"Livello bibliografico","Monografia"]
[null,null,null,"Note generali","Description based upon print version of record."]
[null,null,null,"Nota di bibliografia","Includes bibliographical references (p. [535]-541) and index."]
[null,null,"Nota di contenuto",null,"Intro -- ADVANCED MATHEMATICSFOR ENGINEERS WITH APPLICATIONSIN STOCHASTIC PROCESSES -- ADVANCED MATHEMATICSFOR ENGINEERS WITH APPLICATIONSIN STOCHASTIC PROCESSES -- LIBRARY OF CONGRESS CATALOGING-IN-PUBLICATION DATA -- CONTENTS -- PREFACE -- Chapter 1: INTRODUCTION -- 1.1. FUNCTIONS OF SEVERAL VARIABLES -- Definition 1.1.1. -- Example 1.1.1. -- Definition 1.1.2. -- Definition 1.1.3. -- Definition 1.1.4. -- Definition 1.1.5. -- Example 1.1.2. -- Definition 1.1.6. -- Definition 1.1.7. -- 1.2. PARTIAL DERIVATIVES, GRADIENT, AND DIVERGENCE -- Definition 1.2.1. -- Theorem 1.2.1 (Clairaut's1 Theorem or Schwarz's2 Theorem) -- Example 1.2.1. -- Definition 1.2.2. -- Example 1.2.3. -- Definition 1.2.3. -- Definition 1.2.4. -- Definition 1.2.5. -- Example 1.2.4. -- Definition 1.2.6. -- Definition 1.2.7. -- Example 1.2.5. -- Definition 1.2.8. -- Theorem 1.2.2. -- Example 1.2.6. -- 1.3. FUNCTIONS OF A COMPLEX VARIABLE -- Definition 1.3.1. -- 1.4. POWER SERIES AND THEIR CONVERGENT BEHAVIOR -- Definition 1.4.1. -- Definition 1.4.2. -- 1.5. REAL-VALUED TAYLOR SERIES AND MACLAURIN SERIES -- Definition 1.5.1. -- Definition 1.5.2. -- 1.6. POWER SERIES REPRESENTATION OF ANALYTIC FUNCTIONS -- 1.6.1. Derivative and Analytic Functions -- Definition 1.6.1. -- Definition 1.6.2 -- Theorem 1.6.1 (Cauchy-Riemann10 Equations and Analytic Functions) -- 1.6.2. Line Integral in the Complex Plane -- Definition 1.6.3. -- Definition 1.6.4. -- Definition 1.6.5. -- Theorem 1.6.2. -- 1.6.3. Cauchy's Integral Theorem for Simply Connected Domains -- Theorem 1.6.3 (Cauchy's Integral Theorem) -- 1.6.4. Cauchy's Integral "]
[{"$nulls":4},"Theorem for Multiple Connected Domains -- Theorem 1.6.4. (Cauchy's Integral Theorem for Multiple ConnectedDomains) -- 1.6.5. Cauchy's Integral Formula -- Theorem 1.6.5. (Cauchy's Integral Formula) -- 1.6.6. Cauchy's Integral Formula for Derivatives."]
[{"$nulls":4},"Theorem 1.6.6. (Cauchy's Integral Formula for Derivatives) -- 1.6.7. Taylor and Maclaurin Series of Complex-Valued Functions -- Definition 1.6.6. -- Definition 1.6.7. -- Theorem 1.6.7. (Taylor Theorem) -- Definition 1.6.8. -- 1.6.8. Taylor Polynomials and their Applications -- Definition 1.6.9. -- EXERCISES -- 1.1. Functions of Several Variables -- 1.2. Partial Derivatives, Gradient, and Divergence -- 1.3. Functions of a Complex Variable -- 1.4. Power Series and their Convergent Behavior -- 1.5. Real-Valued Taylor Series and Maclaurin Series -- 1.6. Power Series Representation of Analytic Functions -- Chapter 2: FOURIER AND WAVELET ANALYSIS -- 2.1. VECTOR SPACES AND ORTHOGONALITY -- Definition 2.1.1. -- Definition 2.1.2. -- Definition 2.1.3. -- Definition 2.1.4. -- Definition 2.1.5. -- Definition 2.1.6. -- Definition 2.1.7. -- Definition 2.1.8. -- Definition 2.1.9. -- Definition 2.1.10. -- Definition 2.1.11. -- 2.2. FOURIER SERIES AND ITS CONVERGENT BEHAVIOR -- Definition 2.2.1. -- Definition 2.2.2. -- Definition 2.2.3. -- Theorem 2.2.1. (Uniform Convergence) -- Theorem 2.2.2. (Fourier Series of Piecewise Smooth Functions) -- 2.3. FOURIER COSINE AND SINE SERIESAND HALF-RANGE EXPANSIONS -- Definition 2.3.1. -- Definition 2.3.2. -- 2.4. FOURIER SERIES AND PDES -- Definition 2.4.1. -- 2.5. FOURIER TRANSFORM AND INVERSE FOURIER TRANSFORM -- Definition 2.5.1. -- Definition 2.5.2. -- 2.6. PROPERTIES OF FOURIER TRANSFORMAND CONVOLUTION THEOREM -- Definition 2.6.1. -- 2.7. DISCRETE FOURIER TRANSFORMAND FAST FOURIER TRANSFORM -- Definition 2.7.1. -- Definition 2.7.2. -- Definition 2.7.3. -- Definition 2.7.4. -- 2.8. CLASSICAL HAAR SCALING FUNCTION AND HAAR WAVELETS -- Definition 2.8.1. -- 2.9. DAUBECHIES7 ORTHONORMALSCALING FUNCTIONS ANDWAVELETS -- Definition 2.9.1. -- Definition 2.9.2. -- 2.10.MULTIRESOLUTION ANALYSIS IN GENERAL -- Definition 2.10.1."]
[{"$nulls":4},"2.11.WAVELET TRANSFORM AND INVERSE WAVELET TRANSFORM -- Definition 2.11.1. -- Definition 2.11.2. -- 2.12. OTHER WAVELETS -- 2.12.1. Compactly Supported Spline Wavelets -- Definition 2.12.1. -- Definition 2.12.2. -- 2.12.2. Morlet Wavelets -- 2.12.3. Gaussian Wavelets -- 2.12.4. Biorthogonal Wavelets -- 2.12.5. CDF 5/3 Wavelets -- 2.12.6. CDF 9/7 Wavelets -- EXERCISES -- 2.1. Vector Spaces and Orthogonality -- 2.2. Fourier Series and its Convergent Behavior -- 2.3. Fourier Cosine and Sine Series and Half-Range Expansions -- 2.4. Fourier Series and PDEs -- 2.5. Fourier Transform and Inverse Fourier Transform -- 2.6. Properties of Fourier Transform and Convolution Theorem -- 2.8. Classical Haar Scaling Function and Haar Wavelets -- 2.9. Daubechies Orthonormal Scaling Functions and Wavelets -- 2.12. Other Wavelets -- Chapter 3: LAPLACE TRANSFORM -- 3.1. DEFINITIONS OF LAPLACE TRANSFORM ANDINVERSE LAPLACE TRANSFORM -- Definition 3.1.1. -- Theorem 3.1.1. (Existence of Laplace Transform) -- 3.2. FIRST SHIFTING THEOREM -- Theorem 3.2.1. (First Shifting or s-Shifting Theorem) -- 3.3. LAPLACE TRANSFORM OF DERIVATIVES -- Theorem 3.3.1. (Laplace Transform of First Order Derivative) . -- Theorem 3.3.2. (Laplace Transform of High Order Derivatives) -- 3.4. SOLVING INITIAL-VALUE PROBLEMS BY LAPLACE TRANSFORM -- 3.5. HEAVISIDE FUNCTION AND SECOND SHIFTING THEOREM -- Definition 3.5.1. -- Theorem 3.5.1. (The Second Shifting or t-Shifting Theorem) -- 3.6. SOLVING INITIAL-VALUE PROBLEMSWITH DISCONTINUOUS INPUTS -- 3.7. SHORT IMPULSE AND DIRAC'S DELTA FUNCTIONS -- 3.8. SOLVING INITIAL-VALUE "]
[{"$nulls":4},"PROBLEMSWITH IMPULSE INPUTS -- 3.9. APPLICATION OF LAPLACE TRANSFORMTO ELECTRIC CIRCUITS -- 3.10. TABLE OF LAPLACE TRANSFORMS -- EXERCISES -- 3.1. Definitions of Laplace Transform and Inverse Laplace Transform -- 3.2. First Shifting Theorem -- 3.3. Laplace Transform of Derivatives."]
[{"$nulls":4},"3.4. Solving Initial-Value Problems by Laplace Transform -- 3.5. Heaviside Function and Second Shifting Theorem -- 3.6. Solving Initial-Value Problems with Discontinuous Inputs -- 3.8. Solving Initial-Value Problems with Impulse Inputs -- 3.9. Application of Laplace Transform to Electric Circuits -- Chapter 4: PROBABILITY -- 4.1. INTRODUCTION -- Definition 4.1.1. -- Definition 4.1.2. -- Definition 4.1.3. -- Definition 4.1.4. -- Definition 4.1.5. -- Definition 4.1.6. -- Definition 4.1.7. -- Definition 4.1.8. -- Definition 4.1.9. -- 4.2. COUNTING TECHNIQUES -- Definition 4.2.1. -- Rule 4.2.1. The Fundamental Principle of Counting -- Definition 4.2.2. -- Theorem 4.2.1. -- Definition 4.2.3. -- Definition 4.2.4. -- Theorem 4.2.3. -- 4.3. TREE DIAGRAMS -- 4.4. CONDITIONAL PROBABILITY AND INDEPENDENCE -- Definition 4.4.1. -- Definition 4.4.2. -- Theorem 4.4.1. -- Definition 4.4.3. -- 4.5. THE LAW OF TOTAL PROBABILITY -- Theorem 4.5.1. (The Multiplicative Law) -- Theorem 4.5.2. (The Multiplicative Law)Let 1 -- Theorem 4.5.3. (The Law of Total Probability) -- Theorem 4.5.4. (Bayes' Formula) -- 4.6. DISCRETE RANDOM VARIABLES -- Definition 4.6.1. -- Definition 4.6.2. -- Definition 4.6.3. -- 4.7. DISCRETE PROBABILITY DISTRIBUTIONS -- Definition 4.7.1. -- Definition 4.7.2. -- Definition 4.7.3. -- Definition 4.7.4. -- Definition 4.7.5. -- Definition 4.7.6. -- Definition 4.7.7. -- Definition 4.7.8. -- Definition 4.7.9. -- Theorem 4.7.2. -- 4.8. RANDOM VECTORS -- Definition 4.8.1. -- Definition 4.8.2. -- Definition 4.8.3. -- Theorem 4.8.1. Multinomial Theorem -- Definition 4.8.4. -- 4.9. CONDITIONAL DISTRIBUTION AND INDEPENDENCE -- Theorem 4.9.1. (The Law of Total Probability) -- Definition 4.9.1. -- Definition 4.9.2. -- Definition 4.9.3. -- Theorem 4.9.2. -- Theorem 4.9.3 -- Theorem 4.9.4. -- 4.10. DISCRETE MOMENTS -- Definition 4.10.1. -- Definition 4.10.2."]
[{"$nulls":4},"Theorem 4.10.1. -- Theorem 4.10.2. -- Theorem 4.10.3. -- Definition 4.10.3. -- Definition 4.10.4. -- Definition 4.10.5. -- Theorem 4.10.4. -- Definition 4.10.6. -- Theorem 4.10.5. -- Definition 4.10.7. -- Theorem 4.10.6. -- Theorem 4.10.7. -- Theorem 4.10.8. -- Theorem 4.10.9. -- Theorem 4.10.10. -- Theorem 4.10.11. -- Definition 4.10.8. -- Definition 4.10.8. -- 4.11. CONTINUOUS RANDOM VARIABLES AND DISTRIBUTIONS -- Definition 4.11.1. -- Definition 4.11.2. -- Definition 4.11.3. -- Definition 4.11.4. -- Definition 4.11.5. -- Definition 4.11.6. -- Definition 4.11.7 -- Definition 4.11.8 -- Definition 4.11.9. -- Definition 4.11.10 -- Definition 4.11.11. -- Definition 4.11.12. -- Definition 4.11.13. -- Definition 4.11.14 -- Definition 4.11.15. -- Definition 4.11.16 -- Remark 4.11.1. -- 4.12. CONTINUOUS RANDOM VECTOR -- Definition 4.12.1. -- Definition 4.12.2 -- 4.13. FUNCTIONS OF A RANDOM VARIABLE -- Definition 4.13.1. -- Definition 4.13.2. -- Theorem 4.13.1. -- Definition 4.13.3. -- Theorem 4.13.2. -- Definition 4.13.4. -- Theorem 4.13.3. Central Limit Theorem -- EXERCISES -- 4.1. Introduction -- 4.2. Counting Techniques -- 4.3. Tree Diagrams -- 4.4. Conditional Probability and Independence -- 4.5. The Law of Total Probability -- 4.6. Discrete Random Variables -- 4.7. Discrete Probability Distributions -- 4.8. Random Vectors -- 4.9. Conditional Distribution and Independence -- 4.10. Discrete Moments -- 4.11. Continuous Random Variables and Distributions -- 4.12. Continuous Random Vector -- 4.13. Functions of a Random Variable -- Chapter 5: STATISTICS -- PART ONE: DESCRIPTIVE STATISTICS -- 5.1. BASIC STATISTICAL CONCEPTS -- Definition 5.1.1. -- Definition 5.1.2. -- "]
[{"$nulls":4},"5.1.1. Measures of Central Tendency -- Definition 5.1.3. -- Definition 5.1.4. -- Definition 5.1.5. -- Definition 5.1.6. -- 5.1.2. Organization of Data -- Definition 5.1.7. -- Definition 5.1.8."]
[{"$nulls":4},"Definition 5.1.9."]
[null,null,null,"Sommario/riassunto","The contents of this work cover Fourier and wavelet analysis, Laplace transform, probability, statistics, difference and differential-difference equations, stochastic processes and their applications, and much more."]