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| Marsden J., Weinstein A. — Calculus 1 |
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| Предметный указатель |
Inflection point 159
Inflection point, test for 160
Instantaneous velocity 50 51
Integer power rule for derivatives 87
Integers 15
Integers, sum of the first n 204
Integrability of continuous function 219
Integrable 217
integral 217
Integral calculus 1
Integral, calculated "by hand" 212
Integral, definite 232
Integral, definition of 217
Integral, indefinite 129 see
Integral, Leibniz notation 132
Integral, mean value theorem 239
Integral, Riemann 220
Integral, sign 129 132 217
Integral, wrong-way 235
integrand 129
Integration 33 129 201
Integration method, fundamental 226
Integration, endpoint of 217
Integration, limit of 217
Interest, compound 244 331
Intermediate Value Theorem 141 142
Intersecting graphs, area between 242
Intersection points 39
interval 21
Interval, closed 21
Interval, open 19
Inverse cosine 283
Inverse cotangent 285
Inverse Function Rule 278
Inverse function test 276
Inverse functions 272 274
Inverse secant 285
Inverse sine 281
Inverse tangent 283
Inverse trigonometric function 281 285
Invertibility, test for 275 276
Irrational numbers 16
Keisler, H.J. 7fn 73fn
Kendrew, W.G. 180
Kepler, Johannes 8
Kline, Morris 182
Labor 106
LADDER 190
Lambert, Johann Heinrich 251fn
Latitude 300
Law of reflection 290
Legendre, Adrien Marie 251fn
Leibniz notation 73 104 132 217
Leibniz notation for derivative 73
Leibniz notation for integral 132
Leibniz, Gottfried 3 73 193fn
Lemniscate 136
Length of days 300 302
Limacon 298
LIMIT 6 57 59
Limit at infinity 65
Limit method 6
Limit of (cos x - 1)/x 265
Limit of (sin x)/x 265
Limit of integration 217
Limit properties 60
Limit, derivative as a 69
Limit, derived properties of 62
Limit, infinite 66
Limit, one-sided 65
Line 31fn
Line, equation of 32
Line, perpendicular 33
Line, point-point form 32
Line, point-slope form 32
Line, real-number 18
Line, secant 51 191
Line, slope of 52
Line, slope-intercept form 32
Line, straight 31fn 125
Line, tangent 2 191
Linear approximation 90 91 92 158 159
Linear function 192
Linear function, derivative of 54
Linear or proportional change 100
local 141 151 177
Local maximum point 151 157
Local minimum point 151 157
Logarithm 313
Logarithm and exponential functions, word problems 326
Logarithm function, derivative of 321
Logarithm, base of 313
Logarithm, defined as integral 326
Logarithm, laws of 314
Logarithm, limiting behavior 328
Logarithm, natural 319
Logarithm, properties of 314
Logarithmic differentiation 117 322 329
Logistic model for population 335
Lower sum 210
Lucan 8fn
Majorize 199
Marginal cost 106
Marginal productivity 106
Marginal profit 106
Marginal revenue 106
Maxima and minima, tests for 153 157 181
Maximum, global 177
Maximum, point 151
Maximum, value 177
Maximum-minimum problems 177
Mean value theorem 191
Mean Value Theorem for Integrals 239
Mean value theorem, consequences 192
Meech, L.W. 9
Midnight sun 301fn
Minimum points 177
Minimum value 177
Natural logarithms 319
Natural numbers 15
Newton, Isaac 3fn 8fn 193fn 253fn
Noon 301fn
Northern hemisphere 301
Notation, Leibniz 73 104 132 217
Notation, summation 203 204
Number, imaginary 18
Number, irrational 16
Number, natural 15
Number, rational 15
Number, real 15 16
Odd function 164 175
One-sided limit 65
Open interval 21
Optical focusing property of parabolas 95
Order 18
Orientation quizzes 13
Origin 29
oscillations 294
parabola 34
Parabola, equations of 37
Parabola, focusing property of 36
Parabola, optical focusing property 97
Parabola, vertex of 55
Parametric curve 124 287
Partition 209
Period 259
Periodic 259
Perpendicular lines 33
Ph 317
plotting 29 43 163
| Point, critical 151
Point, inflection 159
Point, intersection 39
Point, local maximum 151 157
Point, local minimum 151 157
Point-point form 32
Polar coordinates 253 255
Polar coordinates, graphing in 296
Polar coordinates, tangents in 299
Polya, George 182
Polynomial, antiderivative of 130
Polynomial, derivative of 75 79
Pond 74
Population 117 175 189 195 335
POSITION 131
Positive velocity 149
Poston, Tim 176
Power of a function, rule for derivatives 110
Power rule for antiderivatives 130
Power rule for derivatives 76 119
Power rule for limits 62
Power, function 307
Power, integer 23
Power, negative 26
Power, rational 18 27 169
Power, real 308
Producer's surplus 248
Product rule, for derivatives 82
Product rule, for derivatives for limits 60
Productivity of labor 106
Productivity, marginal 106
Profit 329
Profit, marginal 106
PROGRAM 40
Projectile 295
Proportional change 95
Ptolemy 256fn
Pythagoras, Theorem of 30
Quadratic formula 16 17
Quadratic function, derivative of 54
Quartic function, general, graphing 176
Quizzes, orientation 13
Quotient rule, for limits 62
Quotient, derivative of 85
Quotient, difference 53
Radian 252
RADIUS 34
Rate of change 2 101 247
Rate of change, relative 329
Rate of decrease 101
Rate of increase 101
Rates, related 124
Rational exponents 118
Rational functions, continuity of 63 140
Rational numbers 15
Rational power rule, for derivatives of a function 119
Rational powers 118 169
rationalizing 28
Real number line 18
Real number line, exponents 308
Real number line, numbers 15 16
Real number line, powers 308
Reciprocal rule for derivatives 86
Reciprocal rule for limits 60
Reflection, law of 290
Region between graphs 240
Related rates 124
Related rates, word problems 125
Relative rate of change 329
Relativity 80fn
Replacement rule, for limits 60
Revenue, marginal 106
Richter scale 317
Riemann integral 220
Riemann Sums 220 221
Riemann, Bernhard 220fn
Rivlin's equation 199
Robinson, Abraham 7 73fn
Rolle's theorem 193
Rolle, Michel 193fn
rose 297
Ruffini, Paolo 172
Schelin, C.W. 257fn
School year 303
Secant 256
Secant line 52 191
Secant, inverse 285
Second derivative 99 104 157
Second derivative test for concavity 159
Second derivative test for maxima and minima 157
Sector, area of 252
Set 21
Shifting rule, for derivatives 115
sigma 203
Sign, change of 146
Signed area 215
Similar triangles 254
Simultaneous equations 37
Sine 254
Sine, derivative of 266
Sine, inverse 281
Sines, law of 263
slope 2 31
Slope of tangent line 52
Slope-intercept form 32
Smith, D.E. 193fn
Snell's law 305
Solar energy 8 107 179 180 221
Speed 103
Speedometer 95
Spiral, exponential 310 333
Spivak, Mike 251fn
Square root function, continuity of 64
Square, completing the 16 17
Squaring function 41
Step function 5 140 209 210
Step function, area under graph 210
Straight line 31fn 125 see
Stretching rule, for derivatives 117
Strict local minimum 151
Stuart, Ian 176
Substitution of index 205
SUM 203
Sum of the first n integers 204
Sum rule for antiderivatives 130
Sum rule for derivatives 78
Sum rule for limits 60
Sum rule, physical model 80
Sum, collapsing 206
Sum, lower 210
Sum, Riemann 220 221
Sum, telescoping 206
Sum, upper 210
Summation notation 201 203 204
Summation, properties of 204 208
Sun 300
Supply curve 248
Symmetry 163 296
Tangent function 256
Tangent function, inverse 284
Tangent line 2 191
Tangent line in polar coordinates 299
Tangent line, horizontal 193
Tangent line, slope of 52
Tangent line, vertical 169
Tartaglia, Niccolo 172
Telescoping sum 206
Third derivative test 160
Time of day 301
Time of year 301
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