Mathematical Modeling for System Analysis in Agricultural Research

Abstract

Contents. Preface. Acknowledgements. 1. The scope of system analysis. The mathematical concept of a system. Classification of agricultural systems. Using linear models in agricultural research. 2. Characteristic values. Systems of linear equations. Solving linear systems. Characteristic equation, roots and vectors. 3. The calculus foundation of modeling. Series. Finite differences. Differentials. Difference equations. Differential equations. 4. Selected transform procedures. Partial fraction expansions. Complex numbers. The laplace transform. The Z Transform. 5. Curve fitting and evaluation. Theoretical basis of nonlinear curve fitting. Computation of the model parameters. Evaluation of the mathematical model and system behavior. 6. Framework for modeling agricultural systems. The system variables. System dynamics. Response functions. Transfer functions. Structural properties of systems. 7. Stochastic models of systems. Modeling of stochastic agricultural systems. The powers of a probability matrix. Markov processes in agricultural research. Relationship between stochastic and deterministic models. 8. Deterministic models of discrete systems. Relationship between order and dimension. Single input linear models. Multidimensional first order linear models. Fitting models to data of discrete systems. 9. Deterministic models of continuous systems. Relationship between order and dimension. Single input linear models. Multidimensional non compartmental first order linear models. Compartmental first order linear models. Fitting models to data of continuous systems. 10. Experimental tests for a system analysis problem. The experimental hypothesis. Mathematical models of the response functions. Generation of equations by geometric analysis. Assignment and arrangement of treatments. Appendix A - Miscellaneous matrix concepts and procedures. Appendix B - Basal concepts and procedures in calculus. Appendix C - Probability definitions and formulas. Appendix D - Rules of counting. Appendix E - Probability distributions. Appendix F - Most frequently used statistical formulas. Appendix G - Table of laplace transforms. Appendix H - Table of Z transforms. Appendix I - The delta function. References. Subject Index.