162 Index
Fibonacci numbers, viii, 73, 74, 76
field, 2, 4
focus, 53
folium of Descartes, 107
Fourier series, 95
Fourier transform, 129, 130
fundamental theorem of algebra, 15,
138, 140, 141, 146
fundamental theorem of calculus, 38,
45, 103, 106, 109, 144
Gamma function, 131
Gaussian elimination, 61
Gaussian random variable, 130
generalized function, 129
generating function, 73
geodesic, 152
geometric series, 32, 33, 67, 69, 78, 114,
156
golden ratio, 74
Goursat, 89, 109
Green’s theorem, 89, 103, 105, 108, 109,
117
group, 61, 151, 155
Hadamard, 71
Hamilton, 153
harmonic function, 89, 91, 92, 98, 141
Hermitian symmetric, 54–56, 62, 63, 84
Hessian, 94
Hodge star operator, 98
holomorphic, 68
hyperbola, 52
hyperbolic functions, 43, 59
hyperbolic geometry, 152
imaginary part, 25, 90, 93, 100
inductive set, 9
infimum, 9, 13
integers, 1
internet, 11, 33, 72
inverse tangent, 68
inversion, 61
irrational, 14, 15
Laurent series, 120
least upper bound, 8
level set, 59, 89
lim inf, 13
lim sup, 13, 71
limit of a sequence, 11
line integral, 49, 101, 102, 105, 109, 112,
128, 141
linear fractional transformation, 60, 63,
65, 150, 152
Liouville’s theorem, 140
maximum principle, 93
Maxwell’s equations, 109
mean, 130
mean value property, 91, 93
metric space, 27, 51
minimum-maximum theorem, 126, 137,
139
modular arithmetic, 6, 149
modulus, 6
monotone convergence, 12, 30
multiplicative inverse, 3, 16
multiplier effect, 68
neighborhood, 64
open set, 51
ordered field, 7, 9, 11, 12, 17, 109
orthogonal, 59, 89
orthogonal trajectories, 89, 90
parabola, 53
parallel postulate, 152
parametric equation, 49
partial fractions, 72, 75, 77, 148
permutation, 97
Picard’s theorem, 141
piecewise smooth, 100, 101, 103, 111,
112
Poisson integral formula, 95
polar representation, 44
pole, 120, 141
polygonal path, 23
positive elements in ordered field, 7
positively oriented, 103
potential energy, 106
primitive Pythagorean triple, 148
probability, 74
probability density function, 132
Pythagorean triples, 147, 149
quadratic formula, 5, 75
quadratic polynomial, 53
quadrisection, 110, 137
quartic equations, 29
quaternions, 153
quotient space, 19
radius of convergence, 68, 71
random variable, 132
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