Abstract, Course Outline and References

Description:

• The course introduces the fundamental concepts for sensitivity and uncertainty analysis of mathematical models of physical, engineering, biological, etc, processes. Being self-contained, the course also provides a review of the mathematical tools needed for sensitivity and uncertainty analysis, assembled from linear algebra, differential and integral equations, numerical methods, operators and differential calculus in vector spaces.

Topics:

1. conceptual mathematical modelling of physical, engineering, biological, econometric, etc., systems;
2. review of selected concepts underlying the analysis of random processes: probability, measurement errors, uncertainties in experiments;
3. fundamental concepts of perturbation theory;
4. fundamental concepts of system sensitivity and uncertainty analysis: system response sensitivities to parameter perturbations, propagation of parameter uncertainties, system response uncertainties;
5. sensitivity analysis of systems of algebraic equations;
6. sensitivity analysis of ordinary and differential equations;
7. sensitivity analysis of integral and integro-differential equations.

Prerequisites:

• Graduate standing or consent of instructor.

Textbook:

• No textbook required