Mathematical Analysis and Analytical Modeling

176 Pages·2019·4.824 MB·English

by  Ivan Stanimirović

MATHEMATICAL ANALYSIS AND
ANALYTICAL MODELING

MATHEMATICAL ANALYSIS AND
ANALYTICAL MODELING
Ivan Stanimirović
ARCLER
P r e ss
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Mathematical Analysis and Analytical Modeling
Ivan Stanimirović
Arcler Press
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e-book Edition 2020
ISBN: 978-1-77407-407-7 (e-book)
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ABOUT THE AUTHOR
Ivan Stanimirovic gained his PhD from University of Niš, Serbia in 2013.
His work spans from multi-objective optimization methods to applications of
generalized matrix inverses in areas such as image processing and computer
graphics and visualisations. He is currently working as an Assistant professor
at Faculty of Sciences and Mathematics at University of Niš on computing
generalized matrix inverses and its applications.

TABLE OF CONTENTS
List of Figures ........................................................................................................ix
List of Tables .........................................................................................................xi
Preface........................................................................ .......................................xiii
Chapter 1 Preliminaries .............................................................................................1
1.1. Metric Spaces .....................................................................................1
1.2. Complex Variable ...............................................................................5
1.3. Complex Functions .............................................................................9
1.4. Singularities Classes And Classes Of Functions .................................13
1.5. Curves, Contours, And Simple-Minded Domains Related ..................14
Chapter 2 Normal Families ......................................................................................17
2.1. Sequence Of Functions .....................................................................17
2.2. Compactness And Convergence In The Space Of
Analytical Functions .......................................................................18
2.3. Arsela-Ascoli Theorem And Montel ...................................................20
Chapter 3 Iteration Functions, Fixed Points And
Fatou And Julia Sets ................................................................................27
3.1. Iteration Of Functions And Points......................................................27
3.2. Fatou And Julia Set ............................................................................31
3.3. Fatou Assembly Components ............................................................32
3.4. Classification Of Periodic Components For Functions .......................33
Chapter 4 Baker Theorem For Completely Invariant Components In
The Set Of Fatou .....................................................................................37
4.1. Definitions And Results .....................................................................37
4.2. Demonstration Of Baker’s Theorem ...................................................38
Chapter 5 Mathematical Analysis Of Significant Transformations Of
The Transverse Projects ...........................................................................41
Chapter 6 Theoretical Framework ...........................................................................55
6.1. Theoretical Background ....................................................................55
6.2. Conceptual Framework .....................................................................64
6.3. Regulatory Framework ......................................................................76
6.4. Developed Method ...........................................................................80
6.5. Recommendations And Limitations .................................................110
Chapter 7 Applying Analytical Functions In
Educational Research ............................................................................113
7.1. Approach And Problem Formulation ...............................................114
7.2. Background To The Problem Under Study .......................................118
7.3. Vie Model Overview .......................................................................126
7.4. Variability Model Of Educational Research Or Model Vie ...............128
7.5. The Extra-Framework Component ...................................................129
7.6. Encompassing Theoretical Empirical Result .....................................136
7.7. Patterns Methodology .....................................................................138
7.8. Contrasting Operations And Validation ...........................................139
7.9. Balancing The Components Which Are Logical-Structural ...............141
7.10. Base Epistemological Predominant ...............................................142
Chapter 8 Methodological Framework ..................................................................143
8.1. Level Or Stage Of Research ............................................................143
8.2. Design Chosen For Data Collection ................................................143
8.3. Study Units .....................................................................................143
8.4. Techniques And Instruments For Data Collection ............................144
8.5. Technical Data Analysis ..................................................................144
8.6. Technical Reliability Of Life And
Employee Instrument ....................................................................144
8.7. Process ...........................................................................................144
Chapter 9 Conclusions And Recommendations .....................................................147
9.1. Recommendations For The Study ....................................................148
Bibliography ..........................................................................................151
Index .....................................................................................................157
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