Mathematical Methods of Environmental Risk Modeling

by Crawford-Brown, Douglas J.

• ISBN13: 9780792373926
• ISBN10: 0792373928
• Format: Hardcover
• Copyright: 2001-06-01
• Publisher: Kluwer Academic Pub

Summary

Mathematical Methods of Environmental Risk Modeling provides a working introduction to both the general mathematical methods and specific models used for human health risk assessment. Rather than being purely an applied math book, this book focuses on methods and models that students and professionals are likely to encounter in practice. Examples are given from exposure assessment, pharmacokinetic modeling, and dose-response modeling.

Table of Contents

Preface	p. ix
Fields, Spaces and States	p. 1
The Concept of Fields and States	p. 1
Scalar, Vector and Tensor Fields	p. 5
The Gradient, Divergence and Curl of a Field	p. 6
Translation, Rotation and Superposition of Fields	p. 15
Probability and Statistics	p. 27
Decisions Under Variability and Uncertainty	p. 27
Probability, Frequency, Confidence and Likelihood	p. 29
Long-Term Frequentist and Bayesian Conceptions	p. 32
Histograms and Probability Density Functions	p. 35
Special Probability Density Functions	p. 41
Correlation	p. 46
Parameter Estimation and Measures of Model Quality	p. 49
Error Propagation through Models	p. 56
Systems of Differential Equations	p. 61
A Systems View of the Environment	p. 61
Mass/Energy Balance and Conservation Laws	p. 66
Linear Differential Equations	p. 69
Systems of Differential Equations	p. 71
Applications of Bernoulli's Method	p. 75
Laplace Transforms and Coupled Differential Equations	p. 95
Coupled Systems and Feedback	p. 95
Transforms	p. 97
The Laplace Transform	p. 99
The Inverse Laplace Transform	p. 101
Applications of Laplace Transforms	p. 102
Some Additional Laplace Transforms	p. 122
Matrix Methods and Spectral Analysis	p. 125
Spectra in Environmental Problems	p. 125
Back-elimination	p. 126
Matrices	p. 128
Augmented Matrices and Gauss-Jordan Elimination	p. 134
Determinants Co-Factors, Minors and Inverses	p. 136
Applications	p. 140
Numerical Methods and Exposure-Response	p. 147
Exposure-Response Relationships	p. 147
Numerical Integration	p. 152
Numerical Solutions to Differential Equations: Euler's Method	p. 157
Numerical Solutions to Differential Equations: Runge-Kutta Methods	p. 163
The Stella Modeling Software	p. 167
Monte Carlo Methods	p. 175
Decisions Under Variability and Uncertainty	p. 175
Analytic Methods	p. 176
Monte Carlo Methods	p. 179
Incorporating Model Uncertainty	p. 187
Variability Between Geographic Regions and Subpopulations	p. 194
Nested Variability and Uncertainty Analysis	p. 196
Index	p. 203
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