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| Marsden J., Weinstein A. — Calculus unlimited |
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| Предметный указатель |
Absolute value function 9 56
Acceleration 12
Adapted partition 148
Addition axioms 46
Additive identity 46
Additive inverses 46
Antiderivative 95 176
Archimedes 19
Archimedian property 52
Area of a circle 18
Area of a trapezoid 229
Associativity 46
Asymmetry 48
Axiomatics 45
Axioms addition 46
Axioms completeness 50
Axioms multiplication 46
Axioms order 48
Bisection method of 213
Bishop 45
Bound 38
Boundedness lemma 70
Bow-tie 111
Butterfly catastrophe 91
Catastrophe theory xii 91
Cauchy sequence 193
Chain rule 110 191
Change of sign 1 20
Commutativity 46
Comparability 48
Completeness axiom 50
Concave downward 78
Concave upward 78
Constant multiple rule 37
Continuity 54
Continuity, for functions of a rational variable 73
Continuity, of rational functions 59
Continuity, uniform 193
continuous 54
Convex 30 50
Convex functions 131
Convex, strictly 132
Cosine function definition 114
Cosine function derivative of 117
Cosine function graph of 115
Cotangent function derivative of 118
Cubic graph of 83
Cubic symmetry of 91
Cubic three types 85
Cusp 89 90
Decreasing 63
Decreasing at a point 63
Decreasing, on an interval 68
definitions 17
Derivative 6
Derivative definition 6
Derivative in terms of limits 84
Derivative in terms of rapidly vanishing functions 33
Derivative in terms of transitions 27
Details of proofs 201
Difference quotients 184
Differentiability and continuity 57
Differentiable 7
Differentiation 7
Differentiation rules 10
Distributivity 46
Double root 38
Endpoints 155
Exponential function 128
Exponential function, derivative of 138
Exponents laws of 124
Extreme Value Theorem 70 71
Function absolute value 9 56
Function bounded above 70
Function composite 109
Function continuous 54
Function convex 131
Function cosine 114
Function decreasing 63
Function exponential 128
Function greatest integer 169
Function increasing 63
Function integrable 155
Function inverse 100
Function linear 24
Function locally bounded 44
Function logarithm 129
Function piecewise constant 147
Function piecewise linear 223
Function rapidly vanishing 31
Function rational 59
Function sine 114
Function square root 108
Function step 55 148
Fundamental theorem of calculus 171
Fundamental theorem of calculus, alternative version 176
General cubic 83
General quartic 86
General quintic 91
Global property 66
Greatest integer function 169
Heyting 45
Horserace theorem 97
Increasing 63
Increasing, at a point 63
Increasing, on an interval 68
Infinitesimal 49
Inflection point 81
Instantaneous velocity 4
Integrability 155
Integrability, of continuous functions 159
Integrability, of piecewise constant functions 158
Integrable 155
integral 155
Integral sign 150
Integral, of piecewise constant function 149
Integral, properties of 163
integrand 150
Intermediate Value Theorem 62
Intermediate value theorem, alternative version 61
| Intermediate value theorem, for derivatives 99
Interval which works 21
Inverse derivative of 105
Inverse function 100
Inverse function theorem 106
Inverse sine function 119
Inverse sine function, derivative of 120
Invertibility test for 103
Invertible 100
Irrational numbers 49
Kasner 213
Keisler 49
Laws of exponents 124
Least upper bound 53
Lies above 78
LIMIT 180 187
Limit inferior 231
Limit superior 231
Limits of integration 150
Linear approximation error 33 79
Linear function rule 11
Linear functions 24
Local maximum point 75
Local minimum point 75
Local property 66
Locally bounded 44
Logarithm function 129
Logarithm function, derivative of 143
Logarithm function, natural 141
Logarithmic derivative 144
Lower sum 153
Maximum point 75
Mean value theorem 93
Minimum point 75
Monotonic 68
Multiplication axioms 46
Multiplicative identity 46
Multiplicative inverses 46
Natural logarithms 141
Nested intervals 52
Newman 213
Order axioms 48
Organizing center 89
Overtaking functions 21
Overtaking graphs 25
Partition 147
Partition adapted 148
piecewise constant function 147
Piecewise constant function, integral of 149
Piecewise linear function 223
Poston 91
Powers of a number 123
Product rule 40
Quadratic function rule 10
Quartic graph of 86
Quartic nine types 89
Quintic graph of 91
Quotient rule 43
RADIANS 114
Rapidly vanishing functions 31
Rate of change 8
Rational function 59
Rational power of a function rule 112
Reflexivity 48
Renz 131
Riemann Sums 188
Rivlin 91
Rolle’s Theorem 96
Root 31
Root double 38
Rule chain 110 191
Rule constant multiple 37
Rule linear function 11
Rule product 40
Rule quadratic function 10
Rule quotient 43
Rule rational power of a function 112
Rule sum 37
Rules of differentiation 10
Samelson 131
Secant line 93
Second derivative 12
Second Derivative Test 76
Sequence Cauchy 193
Sequence limit of 187
Sign change of 1
Sine function definition 114
Sine function derivative of 117
Sine function graph of 115
Solutions to solved exercises 194
Spivak 53
Square root 108
Step function 55 148
Stewart 91
Sum rule 37
Swallowtail catastrophe 91
Tangency 7
Tangent function derivative of 118
Tangent line 8 28
Test for invertibility 103
Theorem extreme value 71
Theorem fundamental 171 176
Theorem horserace 97
Theorem intermediate value 61
Theorem Inverse Function 106
Theorem mean value 93
Theorem Rolle’s 96
Transition period 17
Transition point 16
Transitions uniqueness of 30
Transitivity 48
Turning point 74
Uniform motion 4
Uniformly continuous 193
Upper sum 153
Vanishes 31
Vanishes rapidly 31
Variable of integration 155
Velocity 4 8
Velocity instantaneous 4
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