Index

absolute convergence, 34, 71, 114, 117

absolute value, 11, 22, 25

additive inverse, 3

angle, 44

Archimedean property, 10, 12

argument principle, 143

Bernoulli numbers, 72, 78

beta function, 133

biholomorphic, 150

Binet’s formula, 76

birational isomorphism, 147

bounded, 8

bounded set, 8

branch cut, 46

calculus, 31

Cardano, 29

Cauchy integral formula, 112, 113, 115,

117

Cauchy sequence, 11, 22, 26, 30, 33

Cauchy’s theorem, 89, 105, 111, 117,

128

Cauchy-Riemann equations, 18, 83

characteristic equation, 76

circle of convergence, 69, 70

clock arithmetic, 6

cohomology, 105

commutative ring, 1, 20

completeness axiom, 8, 10, 11, 14, 109,

138, 139

complex analytic, 31

complex analytic function, 116

complex manifold, 63

conformal, 95, 150

connected, 22, 23, 114

conservative, 106

continuously diﬀerentiable, 36, 87

cosine, 41, 42

cross product, 155

cubic equation, 29

curl, 98, 108

de Moivre’s formula, 42

deﬁning equation, 49

determinant, 56, 60, 61, 94, 97, 155

dilation, 44, 61

directrix, 53

Dirichlet problem, 94

disk, 51

distance, 27

divergence of a vector ﬁeld, 98, 108

divergence theorem, 109

division algorithm, 20

dot product, 89, 101, 155

eccentricity, 53

eigenvalues, 57

ellipse, 52

ellipsoid, 53

empty set, 22, 51

equivalence class, 2, 20, 21

equivalence relation, 7, 19, 20

essential singularity, 120

Euclid’s postulates, 152

exact, 106

exponential function, 41

exterior derivative, 104, 107

161