A concrete approach to mathematical modelling

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作者：Michael Mesterton-Gibbons

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ISBN：9780201129106

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简介

简介

A textbook that teaches both critical and creative modeling skills, primarily for a senior-level course that gives equal weight to deterministic and probabilistic modeling. It emphasizes both the validation of mathematical models and the rationale behind improving them. The approach embodies the belief that the three most fundamental ideas in mathematical modeling are transience, permanence, and optimality. The minimal mathematical prerequisites are the standard calculus sequence and first courses in linear algebra, ordinary differential equations, and probability and statistics. Probability and statistics are reviewed in an appendix. Annotation c. by Book News, Inc., Portland, Or.

The Deterministic View
Growth and Decay: Dynamical Systems
Equilibrium
Optimal Control and Utility
Validating A Model
Validation: Accept, Improve, or Reject
The Probabilistic View
Birth and Death: Probabilistic Dynamics
Stationary Distributions
Optimal Decision and Reward
The Art of Application
Using a Model: Choice and Estimation
Building a Model: Adapting, Extending, and Combining
Toward More Advanced Models
Further Dynamical Systems
Further Flow and Diffusion
Further Optimization
Epilogue
Appendices
Solutions to Selected Exercises
References
Index

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