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Index

Algorithm

Fibonacci Search, 113 Golden Section Search, 109 method of steepest ascent, 147 modified Newton’s method, 156 attracting fixed point, 59

balancing chemical equations, 230 Battle of Normandy, Operation Overlord, 308

Battle of the Bismarck Sea, 300

Cobb-Douglas function, 173 competitive hunter model, 75 convex multivariable function, 123 correlation, 236

correlation coefficient, 237 linearity likelihood for math, science, and engineering data, table, 240 linearity likelihood for

non-math, non-science, and non-engineering data, table, 240

cubic splines, 219

dark money network, 329 definiteness of a matrix, 130 indefinite, 131 negative definite, 131 negative semi-definite, 131 positive definite, 131 positive semi-definite, 131 summary using Hessians, table, 132

discrete dynamical system, 35 first order, 35 homogeneous, 38 initial condition(s), 35 linear, 38

linear nonhomogeneous table of behaviors, 62 nonhomogeneous, 38 nonlinear, 38, 66 paradigm, 37 domain, 34 dynamical solution

numerical solution, 34 dynamical system definition of, 34

equilibrium value, 53

fixed point, 53 function, 34

game theory

classical two-player games, table, 286 extensive form, 285 mixed strategy solution, 287 movement diagram, 288 Nash equilibrium, 284 normative form, 285 partial conflict game, 285 perfect information, 285 pure strategy solution, 284 sequential game, 284 simultaneous game, 284 strategies per player, 284 total conflict game, 285 zero-sum game, 285

Hessian matrix, 124

Krackhardt’s Kite Network, 356

Lagrange multipliers, 163

graphical interpretation, 165 necessary conditions, 163 regular point, 164 leading principal minor, 125 least squares curve fitting

as a system of linear equations, 217

least squares regression line. 141 normal equations, 142 Leontief Input-Output Economic Model, 215 linear regression, 236

multiple linear regression, 243 local and global extrema, 96 Lotka-Volterra model, 81 continuous, 82 discrete, 82

Maple

Builtin Algebraic Functions, 11 Help System, 9

Maple Applications Center, 30 plot, 26

plots package, 28 proc, 15 Procedure, 15 with, 8 Worksheet, 6

mathematical modeling process, 1 method of joints, 206 methods of choosing weights entropy method, 383 pairwise comparisons, 382 rank order centroid (ROC), 381 ratio method, 382

nonlinear regression

exponential decay, 244

logistic regression (logit regression), 256 Poisson regression, 256 sine regression, 250 Numerical Technique

Fibonacci Search, 112 Golden Section Search, 106 Modified Newton’s Method, 115

Problem solving

five-step method, 1

range, 34 relation, 34

sequence, 34

converge, 64 diverge, 64 limit of, 63 stable equilibrium, 59

Theorem

Extended Derivative Test, 97 Extreme Value Theorem, 96 First Derivative Test, 97 Interval Endpoints Test, 97 Lagrange multipliers, 164 Multivariable Local Extremum Characterization, 123 multivariate optimal solution necessary conditions, 180 sufficient conditions, 180 Nash Arbitration Theorem, 299 Nondifferentiable Point Test, 97 Second Derivative Test, 96 Tower of Hanoi puzzle, 38

Unimodal Function, 105

Warren truss, 205

 
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