Principles of Mathematics in Operations Research

294 Index

differential equations, 60, 62-63, 65,

191-196, 201, 202, 228, 290

dodecahedron, 100, 244

eigen value, 54-65, 74-76, 81, 82, 84-89,

195, 230, 234-240

eigen vector, 54-65, 84-89, 234-240

example, 3

Fibonacci, 60, 61, 202, 292
field, 13, 28, 123-129
complex, 125, 127-128, 176, 180-186
dense, 125, 143
ordered, 124-129, 133, 134, 266-269
rational, 122, 124, 130, 133, 143, 267
real, 125-128, 131, 133, 134, 143, 268
function
beta, 185
bounded, 137-139, 159, 164
class Cr, 172
continuous, 157-166, 169, 170, 279
derivative, 169-173, 280-283
differentiable, 169-170, 173
directional derivative, 280
discontinuities, 162-164, 171
exponential, 180-183, 195
gamma, 183, 185-186
generating, 187, 285-289
Intermediate Value Theorem, 162,
279
L'Hospital's Rule, 171
local maximum, 170
local minimum, 170, 173, 281, 283
logarithm, 181-182, 187, 289
Mean Value Theorem, 170-173, 280
metric, 138
monotonic, 164-166, 173
optima, 159, 173, 281
saltus, 165
semi-continuous, 166, 279
sequence, 178-179
Taylor's approximation, 172, 173,
180, 280-281
trigonometric, 182-184
uniform continuity, 160-161
Fundamental Theorem of Linear
Algebra, 27, 35, 215

Gaussian elimination, 20, 52, 107

graph, 28, 116, 210, 257

Heine-Barel, 150

hull

affine, 16

convex, 16, 94

linear, 16

hyperplane, 95-98, 113

inner product, 35, 40

integer, 129, 133, 266-269

irrational, 126

isomorphism, 17, 125

kernel, 24-28, 44, 54, 57, 211-215

Laplace transforms, 192-196, 199, 201,

202, 290

law of cosines, 37

Least Squares Approximation, 38-47,

218

lemma, 4

linear

combination, 15, 95

dependence, 15

equation systems, 20, 24, 38, 42,

44-47, 81-86, 105, 220, 234-240

hull, 16

independence, 15, 55

transformation, 18

variety, 95

Linear Programming, 103-119, 246-265

bfs, 105, 246, 250

bounded simplex method, 116,

253-255

canonical form, 103

column generation, 116, 262

complementary slackness, 112, 256

decomposition, 116, 257-265

degeneracy, 106

duality, 111-119, 250, 256

Farkas Lemma, 113-115

minimum ratio, 106, 116, 254

optimality, 105, 116, 253, 255

revised simplex method, 110, 115,

248-250

simplex method, 105, 115, 246

simplex tableau, 107, 115, 248

standard form, 103