796 Index
eigenvalue, 79
eigenvector, 79
ellipse, 212
ellipsoid, 219
Euclid’s algorithm, 271
Euclid’s theorem, 1, 254
Euler’s formula, 235, 289
for homogeneous functions, 168
Euler’s substitutions, 217
Euler’s theorem, 266
Euler’s totient function, 265
exact differential equation, 192
Fermat’s infinite descent principle, 248
Fermat’s little theorem, 4, 261
Fibonacci sequence, 8
flux, 180
focus, 212
Fourier series, 164
Fubini’s theorem, 177
function
concave, 142
continuous, 128
contractive, 110
convex, 142
differentiable, 134
harmonic, 169
Gauss–Ostrogradski theorem, 180
Gaussian integral, 177
generalized mean inequality, 147
generating function, 298
gradient, 183
graph, 282
greatest integer function, 250
Green’s theorem, 179
group, 90
Abelian, 91
Klein, 91
special linear, 272
Hölder’s inequality, 142
for integrals, 157
holomorphic function, 182
hyperbola, 212
hyperboloid
of one sheet, 219
of two sheets, 220
identity element, 87
identity matrix, 61
inclusion–exclusion principle, 308
induction, 3
strong, 7
inductively,seeinduction
infinite descent,seeFermat’s infinite descent
principle
integral
Fresnel, 175
Gaussian, 175
integrals
computed recursively, 151
definite, 150
indefinite, 147
multivariable, 174
integrating factor, 193
intermediate value property, 131
inverse, 88
modulon, 258
of a matrix, 69
invertible matrix,seeinverse of a matrix
irreducible polynomial, 56Jacobian, 174
Jensen’s inequality, 146
Lagrange multipliers, 171
Leibniz formula, 151
L’Hôpital’s rule,seeL’Hôpital’s theorem
L’Hôpital’s theorem, 137
limit
of a function, 126
of a sequence, 104
linear
combination, 77
dependence, 77
independence, 77
linear Diophantine equation, 270
linear map,seelinear transformation
linear transformation, 79
matrix, 61
circulant, 66