Sensitivity & Uncertainty Analysis, Volume 1: Theory Book

I	Concepts of Matrix and Operator Theory for Sensitivity and Uncertainty Analysis	1
A	Matrices: Basic Definitions and Properties	1
B	Operators in Vector Spaces: Basic Definitions and Properties	12
C	Adjoint Operators: Basic Definitions and Properties	27
D	Elements of Differential Calculus in Normed Spaces	33
II	Concepts of Probability Theory for Sensitivity and Uncertainty Analysis	39
A	Introduction and Terminology	39
B	Interpretation of Probability	48
C	Multivariate Probability Distributions	51
D	Fundamental Parameters of Probability Functions	55
E	Characteristic and Moment Generating Functions	65
F	Commonly Encountered Probability Distributions	69
G	Central Limit Theorem	85
H	Basic Concepts of Statistical Estimation	88
I	Error and Uncertainty	100
J	Presentation of Results of Measurements: Rules for Rounding Off	101
III	Measurement Errors and Uncertainties: Basic Concepts	105
A	Measurements: Basic Concepts and Terminology	105
B	Classification of Measurement Errors	109
C	Natural Precision Limits of Macroscopic Measurements	114
D	Direct Measurements	116
E	Indirect Measurements	119
F	Propagation of Moments (Errors)	120
IV	Local Sensitivity and Uncertainty Analysis of Linear Systems	129
A	The Forward Sensitivity Analysis Procedure (FSAP)	132
B	The Adjoint Sensitivity Analysis Procedure (ASAP)	134
C	Illustrative Example: Sensitivity Analysis of Linear Algebraic Models	142
D	Illustrative Example: Local Sensitivity Analysis of a Linear Neutron Diffusion Problem	146
E	Illustrative Example: Sensitivity Analysis of Euler's One-Step Method Applied to a First-Order Linear Ode	154
F	Illustrative Example: Sensitivity and Uncertainty Analysis of a Simple Markov Chain System	165
G	Illustrative Example: Sensitivity and Uncertainty Analysis of Neutron and Gamma Radiation Transport	182
V	Local Sensitivity and Uncertainty Analysis of Nonlinear Systems	199
A	Sensitivity Analysis of Nonlinear Systems with Feedback and Operator-Type Responses	199
B	Example: A Paradigm Climate Model with Feedback	205
C	Sensitivity Analysis of Nonlinear Algebraic Models: The Discrete Adjoint Sensitivity Analysis Procedure (DASAP)	209
D	Illustrative Example: A Transient Nonlinear Reactor Thermal Hydraulics Problem	217
E	Illustrative Example: Sensitivity Analysis of the Two-Step Runge-Kutta Method for Nonlinear Differential Equations	231
F	Illustrative Example: Sensitivity Analysis of a Scalar Nonlinear Hyperbolic Problem	238
VI	Global Optimization and Sensitivity Analysis	245
A	Mathematical Framework	247
B	Critical Points and Global Optimization	249
C	Sensitivity Analysis	252
D	Global Computation of Fixed Points	256
E	A Constrained Optimization Problem for Testing the Global Computational Algorithm	263
F	Illustrative Example: Global Analysis of a Nonlinear Lumped-Parameter Model of a Boiling Water Reactor	264
	References	267
	Index	273