Elsevier S & T

Mathematical Modeling for System Analysis in Agricultural Research

Vohnout, K.

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Table of contents
  • Cover
  • Contentsvii
  • Prefacexi
  • Acknowledgmentsxiii
  • Chapter 1. The Scope of System Analysis1
  • 1.1 The Mathematical Concept of a System2
  • 1.2 Classification of Agricultural Systems7
  • 1.3 Using Linear Models in Agricultural Research18
  • Chapter 2. Characteristic Values36
  • 2.1 Systems of Linear Equations36
  • 2.2 Solving Linear Systems44
  • 2.3 Characteristic Equation, Roots and Vectors55
  • Chapter 3. The Calculus Foundation of Modeling66
  • 3.1 Series66
  • 3.2 Finite Differences71
  • 3.3 Differentials79
  • 3.4 Difference Equations82
  • 3.5 Differential Equations96
  • Chapter 4. Selected Transform Procedures109
  • 4.1 Partial Fraction Expansions109
  • 4.2 Complex Numbers114
  • 4.3 The Laplace Transform119
  • 4.4 The Z Transform130
  • Chapter 5. Curve Fitting and Evaluation140
  • 5.1 Theoretical Basis of Nonlinear Curve Fitting140
  • 5.2 Computation of the Model Parameters149
  • 5.3 Evaluation of the Mathematical Model and System Behavior166
  • Chapter 6. Framework for Modeling Agricultural Systems179
  • 6.1 The system Variables179
  • 6.2 System Dynamics186
  • 6.3 Response Functions195
  • 6.4 Transfer Functions202
  • 6.5 Structural Properties of Systems210
  • Chapter 7. Stochastic Models of Systems222
  • 7.1 Modeling of Stochastic Agricultural Systems222
  • 7.2 The Powers of a Probability Matrix230
  • 7.3 Markov Processes in Agricultural Research236
  • 7.4 Relationship Between Stochastic and Deterministic Models252
  • Chapter 8. Deterministic Models of Discrete Systems259
  • 8.1 Relationship Between Order and Dimension259
  • 8.2 Single Input Linear Models263
  • 8.3 Multidimensional First Order Linear Models274
  • 8.4 Fitting Models to Data of Discrete Systems287
  • Chapter 9. Deterministic Models of Continuous Systems295
  • 9.1 Relationship Between Order and Dimension295
  • 9.2 Single Input Linear Models300
  • 9.3 Multidimensional Non Compartmental First Order Linear Models316
  • 9.4 Compartmental First Order Linear Models327
  • 9.5 Fitting Models to Data of Continuous Systems337
  • Chapter 10. Experimental Tests for a System Analysis Problem344
  • 10.1 The experimental Hypothesis344
  • 10.2 Mathematical Models of the Response Functions350
  • 10.3 Generation of Equations by Geometric Analysis359
  • 10.4 Assignment and Arrangement of Treatments369
  • Appendix A - Miscellaneous Matrix Concepts and Procedures386
  • Appendix B - Basal Concepts and Procedures in Calculus394
  • Appendix C - Probability Definitions and Formulas401
  • Appendix D - Rules of Counting408
  • Appendix E - Probability Distributions410
  • Appendix F - Most Frequently Used Statistical Formulas419
  • Appendix G - Table of Laplace Transforms422
  • Appendix H - Table of Z Transforms427
  • Appendix I - The Delta Function430
  • References431
  • Subject Index433
Book details
  • Vendor Elsevier S & T
  • SKU 9780444512680
  • ISBN-13 9780080535883
  • Author Vohnout, K.
  • Category Reference
  • Subject Research

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Description eBook delivery & access Reviews
This book provides a clear picture of the use of applied mathematics as a tool for improving the accuracy of agricultural research. For decades, statistics has been regarded as the fundamental tool of the scientific method. With new breakthroughs in computers and computer software, it has become feasible and necessary to improve the traditional approach in agricultural research by including additional mathematical modeling procedures.


The difficulty with the use of mathematics for agricultural scientists is that most courses in applied mathematics have been designed for engineering students. This publication is written by a professional in animal science targeting professionals in the biological, namely agricultural and animal scientists and graduate students in agricultural and animal sciences. The only prerequisite for the reader to understand the topics of this book is an introduction to college algebra, calculus and statistics. This is a manual of procedures for the mathematical modeling of agricultural systems and for the design and analyses of experimental data and experimental tests. It is a step-by-step guide for mathematical modeling of agricultural systems, starting with the statement of the research problem and up to implementing the project and running system experiments.