Mathematical Methods of Environmental Risk Modeling

Preface. 1: Risk, Rationality and Decisions. 1.1. The Concept of Fields and States. 1.2. Scalar, Vector and Tensor Fields. 1.3. The Gradient, Divergence and Curl of a Field. 1.4. Translation, Rotation and Superposition of Fields. 2: Probability and Statistics. 2.1. Decisions Under Variability and Uncertainty. 2.2. Probability, Frequency, Confidence and Likelihood. 2.3. Long-Term Frequentist and Bayesian Conceptions. 2.4. Histograms and Probability Density Functions. 2.5. Special Probability Density Functions. 2.6. Correlation. 2.7. Parameter Estimation and Measures of Model Quality. 2.8. Error Propagation through Models. 3: Systems of Differential Equations. 3.1. A Systems View of the Environment. 3.2. Mass/Energy Balance and Conservation Laws. 3.3. Linear Differential Equations. 3.4. Systems of Differential Equations. 3.5. Applications of Bernoulli's Method. 4: Laplace Transforms and Coupled Differential Equations. 4.1. Coupled Systems and Feedback. 4.2. Transforms. 4.3. The Laplace Transform. 4.4. The Inverse Laplace Transform. 4.5. Applications of Laplace Transforms. 4.6. Some Additional Laplace Transforms. 5: Matrix Methods and Spectral Analysis. 5.1. Spectra in Environmental Problems. 5.2. Back-elimination. 5.3. Matrices. 5.4. Augmented Matrices and Gauss-Jordan Elimination. 5.5. Determinants Co-Factors, Minors en Inverses. 5.6. Applications. 6: Numerical Methods and Exposure-Response. 6.1. Exposure-Response Relationships. 6.2. Numerical Integration. 6.3. Numerical Solutions to Differential Equations: Euler's Method. 6.4. Numerical Solutions to Differential Equations: Runge-Kutta Methods. 6.5. The STELLA Modeling Software. 7: Monte Carlo Methods. 7.1. Decisions Under Variability and Uncertainty. 7.2. Analytic Methods. 7.3. Monte Carlo Methods. 7.4. Incorporating Model Uncertainty. 7.5. Variability Between Geographic Regions and Subpopulations. 7.6. Nested Variability and Uncertainty Analysis. Index.