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