- of a holomorphic function 277
direct image 24
disjoint sets 12
distance 57
- in a metric space 304
- uniform convergence 218
doubly periodic (function) 179
dual numbers 250
element (of a set) 7
equality relation 7
equicontinuity 207
equipotent 25
equivalence class 19
equivalence relation 19
- quotient set 19
Euler's relation e ix = cos x + i sin x
162,372,383
everywhere dense 215
expansion
- decimal 28
exponential function 124,336
- addition formula 169,337,370
- and logarithm 107,195,345
- and trigonometric functions 372
- complex 124, 169
- derivative 339
- functional equation 337
- limit of (1 + x/n)n 104,368
- periodicity 377
- series 124,345
exterior 188
family of numbers, sets 21
- union, intersection of a family 22
fluents 247
fluxions 248
formula
- Leibniz' 255
- MacLaurin 151
- Taylor's (power series) 151
function 19
- analytic 81, 148
- bounded 217
- characteristic 21
- composed 24
- constant to within r 64,193
- continuous at a point 64,192
- elliptic 179
- exponential of base a 330
- holomorphic 153
- hyperbolic 388
- identity 25
Index
427
- implicit 290
- injective, surjective, bijective 23
- inverse 25
- linear tangent 245
- logarithm 73, 105, 195
- monotone 197
- multiform 415
- power X S 333
- regulated 112,241
- step 111
- trigonometric 372
functional determinant 292
functional equation 337
graph of a function 19
holomorphic
- function 153,278,292,295
image 20
image of A by 1 24
implicit
- function 290
increasing (function) 197
index 21
induction proof 16
inequalities in JR, properties 55
inequality
- of the mean 263
- triangle 56,303
infinite limits 138
infinite product 80, 394, 395
- and partitions 409
- and series 403
- for sin z 165,401
- of Jacobi 409
- of the Dedekind function 411
- of the Riemann series 395
infinity
- symbol 58
injection, injective 24
integral 110
- of l/x, xn 113
intersection 12
interval 58,201,225
- closed 58
- compact 58
- open 58
inverse image 1-1 (B) 24
isolated point of a subset of C 160
Jacobian
- determinant 292
- matrix 275
direct image 24
disjoint sets 12
distance 57
- in a metric space 304
- uniform convergence 218
doubly periodic (function) 179
dual numbers 250
element (of a set) 7
equality relation 7
equicontinuity 207
equipotent 25
equivalence class 19
equivalence relation 19
- quotient set 19
Euler's relation e ix = cos x + i sin x
162,372,383
everywhere dense 215
expansion
- decimal 28
exponential function 124,336
- addition formula 169,337,370
- and logarithm 107,195,345
- and trigonometric functions 372
- complex 124, 169
- derivative 339
- functional equation 337
- limit of (1 + x/n)n 104,368
- periodicity 377
- series 124,345
exterior 188
family of numbers, sets 21
- union, intersection of a family 22
fluents 247
fluxions 248
formula
- Leibniz' 255
- MacLaurin 151
- Taylor's (power series) 151
function 19
- analytic 81, 148
- bounded 217
- characteristic 21
- composed 24
- constant to within r 64,193
- continuous at a point 64,192
- elliptic 179
- exponential of base a 330
- holomorphic 153
- hyperbolic 388
- identity 25
Index
427
- implicit 290
- injective, surjective, bijective 23
- inverse 25
- linear tangent 245
- logarithm 73, 105, 195
- monotone 197
- multiform 415
- power X S 333
- regulated 112,241
- step 111
- trigonometric 372
functional determinant 292
functional equation 337
graph of a function 19
holomorphic
- function 153,278,292,295
image 20
image of A by 1 24
implicit
- function 290
increasing (function) 197
index 21
induction proof 16
inequalities in JR, properties 55
inequality
- of the mean 263
- triangle 56,303
infinite limits 138
infinite product 80, 394, 395
- and partitions 409
- and series 403
- for sin z 165,401
- of Jacobi 409
- of the Dedekind function 411
- of the Riemann series 395
infinity
- symbol 58
injection, injective 24
integral 110
- of l/x, xn 113
intersection 12
interval 58,201,225
- closed 58
- compact 58
- open 58
inverse image 1-1 (B) 24
isolated point of a subset of C 160
Jacobian
- determinant 292
- matrix 275