|
|
 |
| Авторизация |
|
|
|
| Поиск по указателям |
|
|
|
|
|
|
|
 |
|
|
|
| Marsden J., Weinstein A. — Calculus 1 |
|
|
|
| Предметный указатель |
Abel, Nils Hendrik 172
Absolute value 22
Absolute value function 42 72
Absolute value, properties of 23
Accelerating 160
Acceleration 102 131
Addition formulas 259
Air resistance 136
Algebraic rules 16
Antiderivative 128
Antiderivative of  323
Antiderivative of 1/x 323
Antiderivative of constant multiple 130
Antiderivative of polynomial 130
Antiderivative of power 130
Antiderivative of sum 130
Antiderivative of trigonometric functions 269
Applications of integral 240
Approaches 58
Approximation, first-order see "Linear approximation"
Archimedes 3 5 6
Area 4 251
Area between graphs 211 241
Area between intersecting graphs 242
Area of a sector 252
Area under a graph 208 212 229
Area under graph of step function 210
Area, signed 215
Argument 40
Arithmetic mean 188
Astroid 198
Astronomy 9
Asymptote 165
Asymptote, horizontal 165
Asymptote, vertical 164
Asymptotic 164
Average 3
Average, rate of change 100
Average, velocity 50
axes 29
Bascom, Willard 306fn
Base of logarithm 313
Beckman, P. 251fn
Berkeley, Bishop George 6fn
Bernoulli, Jacques 252fn
Bisection, method of 142 145
Boyer, C. 7fn 252fn
Burton, Robert 8
Bus, motion of 49 202 207 225
Calculator discussion 49 112 166 255 257 265 277 309 327 330
Calculator symbol 29
Calculus Unlimited iii 7fn
Calculus, differential 1
Calculus, Fundamental Theorem of 4 225 237
Calculus, integral 1 3
Cardano, Girolamo 172
Cardioid 198
Cartesian coordinates 255
Catastrophe cusp 176
Catastrophe theory 176
Cauchy, Augustin-Louis 6
Cavalieri, Bonaventura 8
Chain rule 112
Chain rule, physical model 116
Change of sign 146
Change, average rate of 100
Change, instantaneous rate of 10
Change, linear or proportional 100
Change, proportional 95
Change, rate of 2 100 101 247
Change, total 244
circle 34 44 120 251
Circle, equation of 37
Circumference 251
City, Fat 116
City, Thin 115
Climate 180
Closed interval 21
Closed interval test 181
Common sense 61 193
Completing the square 16 17
Composition of functions 112 113
Composition of functions, derivative of 113
Compound interest 331
Concave downward 158
Concave upward 158
Concavity, second derivative test for 159
Constant function 41 192
Constant function rule, for limits 62
Constant function, derivative of 54
Constant multiple rule for antiderivatives 130
Constant multiple rule for derivatives 77
Constant multiple rule for limits 62
Consumer's surplus 248
Continuity 63 72
Continuity of rational functions 140
continuous 139
Continuous function 63
Continuous function, integrability of 219
Continuously compounded interest 331
Convex function 199
coordinates 29
Coordinates, Cartesian 255
Coordinates, polar 253 255
Cosecant 256
Cosecant, inverse 285
Cosine 254
Cosine, derivative of 266
Cosine, inverse 283
Cosine, law of 258
Cost, marginal 106
Cotangent 256
Cotangent, inverse 285
Critical points 151
Cubic function 168
Cubic function, general, roots of 172
Cubic function, graphing 172
Curve 31fn
Curve, parametric 124 298
Cusp 170
Cusp, catastrophe 176
Days, length of 30 302
Days, shortening of 303
de Fermat, Pierre 8
Decelerating 160
Decrease, rate of 101
Decreasing function 146
Definite integral 232
Definite integral, properties of 234
Degree as angular measure 252
Degree of polynominal and rational functions 97
Delta 50fn
Demand curve 248
Depreciation 109
Derivative 3 53 70
Derivative as a limit 69
Derivative of 318
Derivative of  71
Derivative of 1/x 71
Derivative of composition 113
Derivative of constant multiple 77
Derivative of cosine 266
Derivative of implicitly defined function 122
Derivative of integer power 87
Derivative of integral with respect to endpoint 236
Derivative of integral, endpoint a given function 236
Derivative of inverse function 278
Derivative of inverse trigonometric functions 285
Derivative of linear function 54
Derivative of logarithmic function 321
| Derivative of polynomial 75 79
Derivative of power 75 119
Derivative of power of a function 110 119
Derivative of product 82
Derivative of quadratic function 54
Derivative of quotient 85
Derivative of rational power 119
Derivative of rational power of a function 119
Derivative of reciprocal 85
Derivative of sum 78
Derivative, formal definition 70
Derivative, Leibniz notation 73
Derivative, logarithmic 117 322 329
Derivative, second 99 104 157
Derivative, summary of rules 88
Dido 182
Diferentiation 3 53 122 201
Diferentiation, implicit 120
Diferentiation, logarithmic 117 322 329
Difference quotient 53
Difference quotient, limit of 70
Differentiable 70
Differential calculus 1
Diminishing returns, law of 106
Discriminant 17
Displacement 230
Distance formula in the plane 30
Distance formula on the line 23
Domain 41
Double-angle formulas 259
Drag 136
Dummy index 203
e 319 325
e as a limit 330
Ear popping 116
Earth's axis, inclination of 301
Economics 105
Element 21
Endpoints 181
Endpoints of integration 217
Energy 201
Equations of circles and parabolas 37
Equations of straight lines 32
Equations of tangent lines 90
Equations, parametric 124 298
Equations, simultaneous 37
Eudoxus 4
Euler, Leonhard 251fn 252fn
evaluating 40
Even function 164 175
Exhaustion, method of 5 7
Existence theorem 180 219
Exponent, zero 23
Exponential and logarithmic functions, graphing problems 236
Exponential functions 307
Exponential functions, derivative of 320
Exponential functions, limiting behavior 328
Exponential growth 332
Exponential spiral 310 333
exponentiation 23
Exponents, integer 23
Exponents, laws of 25
Exponents, negative 26
Exponents, rational 27 118
Exponents, real 308
Extended product rule for limits 62
Extended sum rule for limits 62 69
Extreme Value Theorem 180
Factoring 16
First Derivative Test 153
First-order approximation see "Linear approximation"
Focusing property of parabolas 36
Fractional exponents see "Rational exponents"
Fractional exponents powers see "Rational powers"
frequency 259
Function 1 39
Function, absolute value 42 72 73
Function, composition 112 113
Function, constant 41 192
Function, continuous 63
Function, convex 199
Function, cubic 168
Function, definition of 41
Function, differentiation of 268
Function, even 164 175
Function, exponential 307
Function, graph of 41 44
Function, greatest integer 224
Function, identity 40 277
Function, inverse 272 274
Function, inverse trigonometric 281 285
Function, linear 192
Function, odd 164 175
Function, power 307
Function, rational 63
Function, squaring 41
Function, step 140 209 210
Function, trigonometric, antiderivatives 269
Function, trigonometric, graphs of 260
Function, zero 41
Fundamental integration method 226
Fundamental theorem of calculus 4 225 237
Fundamental theorem of calculus: alternative version 236
Galileo 8
Gauss, Carl Friedrich 205
Geometric mean 188
global 141 177
Goldstein, Larry 172
Gould, S.H. 6fn
Graphing in polar coordinates 296
Graphing in polar coordinates, procedure 163
Graphing problems, exponential and logarithmic functions 236
Graphing problems, trigonometric functions 292
graphs 41 163
Graphs of functions 41 44
Graphs, area between 241
Graphs, area under 212 229
Greatest integer function 224
Growth, exponential 332
Herring 156
Hipparchus 256fn
Hooke's law 99 295
Horizontal asymptote 165
Horizontal asymptote, tangent 193
Horserace theorem 193
Identity function 40 277
Identity function rule, for limits 60
Identity, trigonometric 257
Illumination 183
imaginary numbers 18
Implicit differentiation 120 122
Inclination of the earth's axis 301
Increase, rate of 101
Increasing function 146
Increasing function on an interval 149
Increasing function, function theorem 195
Increasing-decreasing test 148
Indefinite integral see "Antiderivative"
Indefinite integral test 233
Independent variable 40
Index, dummy 203
Index, substitution of 205
Induction, Principle of 69
Inequalities 18
Inequalities, properties of 19
Inequality, arithmetic-geometric mean 188
Infinite limit 66
Infinitesimal 73
Infinitesimals, method of 6 8
infinity 21
|
|
|
| Реклама |
|
|
|
|
|
О проекте