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Marsden J., Weinstein A. — Calculus unlimited
Marsden J., Weinstein A. — Calculus unlimited

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Название: Calculus unlimited

Авторы: Marsden J., Weinstein A.

Язык: en

Рубрика: Математика/Анализ/Учебники по элементарному анализу/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1981

Количество страниц: 245

Добавлена в каталог: 13.04.2005

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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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