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This book can be used in courses on mathematical modeling at the senior undergraduate or graduate level, or used as a reference for in-service scientists and engineers. The book aims to provide an overview of mathematical modeling through a panoramic view of applications of mathematics in science and technology. In each chapter, mathematical models are chosen from the physical, biological, social, economic, management, and engineering sciences. The models deal with different concepts, but have a common mathematical structure and bring out the unifying influence of mathematical modeling in different disciplines.
Each subsequent chapter deals with mathematical modeling through one or more specific techniques. Thus, we consider mathematical modeling through ordinary differential equations of first and second order systems of ordinary differential equations difference equations functional equations integral, integro-differential, differential-difference, delay-differential, and partial differential equations graph theory concepts linear and nonlinear programming dynamic programming, through calculus of variations maximum principle and the maximum entropy principle.
Features
Provides a balance between theory and applications
Features models from the physical, biological, social, economic, management, and engineering sciences
Preface
Chapter 1: Mathematical Modeling: Need, Techniques, Classifications, and Simple Illustrations
Chapter 2: Mathematical Modeling through Ordinary Differential Equations of the First Order
Chapter 3: Mathematical Modeling through Systems of Ordinary Differential Equations of the First Order
Chapter 4: Mathematical Modeling through Ordinary Differential Equations of the Second Order
Chapter 5: Mathematical Modeling through Difference Equations
Chapter 6: Mathematical Modeling through Partial Differential Equations
Chapter 7: Mathematical Modeling through Graphs
Chapter 8: Mathematical Modeling through Functional, Integral, Delay Differential, and ifferential-Difference Equations
Chapter 9: Mathematical Modeling through Calculus of Variations and Dynamic Programming
Chapter 10: Mathematical Modeling through Mathematical Programming, Maximum Principle, and Maximum-Entropy Principle
Appendix A: Mathematical Models Discussed in the Book
Appendix B: Supplementary Bibliography