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Heinz Stefan. Mathematical modeling

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Heinz Stefan. Mathematical modeling
Heidelberg, Dordrecht, London, New York: Springer-Verlag, — 200 s. — ISBN: 978-3-642-20310-7
Contents:
Deterministic Analysis of Observations
Motivation
Data Transformations: Linear Models
Model Development: Polynomial Models
Model Evaluation: Population Modeling
The Advantage of Modeling: Global Warming Modeling
Summary
Exercises
Stochastic Analysis of Observations
Motivation
Model Errors
Optimal Linear Models
Optimal Quadratic Models
Optimal Power and Exponential Models
Summary
Exercises
Deterministic States
Motivation
Dimensional Analysis and Similarity
Applications of Low-Complexity
Applications of Medium-Complexity: Time Measurement
Applications of High-Complexity: Lift
Summary
Exercises
Stochastic States
Motivation
Probability Density Functions
Models for Probability Density Functions
Data Analysis
Real Distributions
Summary
Exercises
Deterministic Changes
Motivation
Linear Changes
Linear Changes with Delays
Nonlinear Changes
Difference and Differential Equations
Summary
Exercises
Stochastic Changes
Motivation
Linear Stochastic Changes
Diffusion
Brownian Motion
Population Dynamics
Summary
Exercises
Deterministic Evolution
Motivation
Heat and Mass Transfer: Balance
Newton’s Laws of Motion: Oscillations
Population Ecology: Growth and Self-Limitation
Population Ecology: Oscillations and Collapse
Summary
Exercises
Stochastic Evolution
Motivation
PDF Evolution Equations
Solution to the Fokker-Planck Equation
Stochastic Differential Equations
Non-Markovian Stochastic Differential Equations
Summary
Exercises
Deterministic Multivariate Evolution
Motivation
Systems of First-Order Differential Equations
Population Ecology: Species Interactions
Mechanical Motions: The Pendulum
Fluid Dynamics: Lorenz’s Weather
Summary
Exercises
Stochastic Multivariate Evolution
Motivation
Data Analysis Concepts for Joint Random Variables
The Joint Normal Probability Density Function Model
The Fokker-Planck Equation
Molecular and Fluid Motion
Summary
Exercises
References
Author Index
Subject Index
About the Author
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