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About this book
About this book
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.
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.