Schinazi R.B. From Calculus to Analysis

250 Index

Inverse

function, 29

power function, 30

trigonometric functions, 79

Irrationality

of e,91

of π , 131

of

√

2, 13

L

Lagrange Mean Value Theorem, 163

Least upper bound, 15

Limit

of a function, 147

of a sequence, 33

Limit point, 157

Lipschitz functions, 204

Logarithmic function, 87

M

Maximum

of a function, 161

of a set, 15

Mean Value Theorems

Cauchy, 162

Lagrange, 163

Minimum

of a function, 161

of a set, 6

Monotone sequences, 40

O

One-to-one function, 235

Onto functions, 235

Open

intervals, 150

set, 45

P

Partial sum, 46

Partition, 177

Peano axioms, 1

π

deﬁnition, 71

estimation, 95

Pointwise convergence, 207

Power

functions, 30

series, 65

sets, 242

R

Radius of convergence, 66

Rational powers, 27

Ratio Test, 56

Real power, 89

Riemann

integrability, 179

integral, 183

Rolle’s Theorem, 163

Root Test, 59

S

Sequences, 33

Series, 45

Sine function, 67

Squeezing Principle, 36

Stirling’s formula, 114

Subsequences, 36

T

Transcendental numbers, 131

Triangle inequality, 3

U

Uncountability of the reals, 241

Uniform continuity, 202

Uniform convergence, 209

Upper bound, 14

W

Wallis’ inﬁnite product, 111

Wallis’ integrals, 109

Well Ordering Principle, 6