Mathematical Modeling for System Analysis in Agricultural Research

453 Pages·2003·15.43 MB·English

by  K. Vohnout

MATHEMATICAL MODELING
FOR SYSTEM ANALYSIS IN
AGRICULTURAL RESEARCH
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MATHEMATICAL MODELING
FOR SYSTEM ANALYSIS IN
AGRICULTURAL RESEARCH
Karel D. Vohnout
Former Research Specialist
Inter-American institute for
Cooperation in Agriculture
2003
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First edition 2003
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To my wife Cecilia
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CONTENTS
PREFACE xi
...
ACKNOWLEDGMENTS Xlll
1
THE SCOPE OF SYSTEM
ANALYSIS
1.1 The Mathematical Concept of a System 2
1.2 Classification of Agricultural Systems 7
I .3 Using Linear Models in Agricultural Research 18
2
CHARACTERISTIC
VALUES
2.1 Systems of Linear Equations 36
2.2 Solving Linear Systems 44
2.3 Characteristic Equation, Roots Vectors 55
and
3
CALCULUS FOUNDATION OF MODELING
THE
3.1 Series 66
3.2 Finite Differences 71
3.3 Differentials 79
3.4 Difference Equations 82
3.5 Differential Equations 96
4
SELECTED TRANSFORM PROCEDURES
4.1 Partial Fraction Expansions I09
4.2 Complex Numbers 114
4.3 The Laplace Transform 119
4.4 The Z Transform 130
...
Vlll Contents
5
CURVE FITTING AND EVALUATION
5.1 Theoretical Basis of Nonlinear Curve Fitting 140
5.2 Computation of the Model Parameters 149
5.3 Evaluation of the Mathematical Model and System Behavior 166
6
FRAMEWORK FOR MODELING AGRICULTURAL SYSTEMS
6.1 The system Variables 179
6.2 System Dynamics 186
6.3 Response Functions 195
6.4 Transfer Functions 202
6.5 Structural Properties of Systems 210
7
STOCHASTIC MODELS OF SYSTEMS
7.1 Modeling of Stochastic Agricultural Systems 222
7.2 The Powers of a Probability Matrix 230
7.3 Markov Processes in Agricultural Research 236
7.4 Relationship Between Stochastic and Deterministic Models 252
8
DETERMINISTIC MODELS OF DISCRETE SYSTEMS
8.1 Relationship Between Order and Dimension 259
8.2 Single Input Linear Models 263
8.3 Multidimensional First Order Linear Models 274
8.4 Fitting Models to Data of Discrete Systems 287
9
DETERMINISTIC MODELS OF CONTINUOUS SYSTEMS
9.1 Relationship Between Order and Dimension 295
9.2 Single Input Linear Models 300
9.3 Multidimensional Non Compartmental First Order Linear Models 316
9.4 Compartmental First Order Linear Models 327
9.5 Fitting Models to Data of Continuous Systems 337
Contents
1x
10
EXPERIMENTAL TESTS FOR A SYSTEM ANALYSIS
PROBLEM
10.1 The experimental Hypothesis 344
10.2 Mathematical Models of the Response Functions 350
10.3 Generation of Equations by Geometric Analysis 359
10.4 Assignment and Arrangement of Treatments 369
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APPENDIX A Miscellaneous Matrix Concepts and Procedures 3 86
APPENDIX B - Basal Concepts and Procedures in Calculus 394
APPENDIX C - Probability Defrnitions and Formulas 40 1
APPENDIX D - Rules of Counting 408
APPENDIX E - Probability Distributions 410
APPENDIX F - Most Frequently Used Statistical Formulas 419
-
APPENDIX G Table of Laplace Transforms 422
-
APPENDIX H Table of Z Transforms 427
APPENDIX I - The Delta Function 430
REFERENCES 43 1
S W C TI NDEX 43 3