Электронная библиотека Попечительского советамеханико-математического факультета Московского государственного университета
 Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум Авторизация Поиск по указателям     Marsden J., Weinstein A. — Calculus 1 Обсудите книгу на научном форуме Нашли опечатку?Выделите ее мышкой и нажмите Ctrl+Enter 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: 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 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
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