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Marsden J., Weinstein A. — Calculus 1
Marsden J., Weinstein A. — Calculus 1

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Название: Calculus 1

Авторы: Marsden J., Weinstein A.

Аннотация:

The goal of this lext is to help students learn lo use calculus intelligently for solving a wide variety of mathematical and physical problems.
This book is an outgrowth of our teaching of calculus at Berkeley, and the present edition incorporates many improvements based on our use of the first edition. We list below some of the key features of the book.


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Издание: 2-nd edition

Год издания: 1985

Количество страниц: 399

Добавлена в каталог: 03.01.2014

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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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 $b^{x}$      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 $b^{x}$      318
Derivative of $\sqrt{}x$      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
1 2 3
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