Главная    Ex Libris    Книги    Журналы    Статьи    Серии    Каталог    Wanted    Загрузка    ХудЛит    Справка    Поиск по индексам    Поиск    Форум   
blank
Авторизация

       
blank
Поиск по указателям

blank
blank
blank
Красота
blank
Bluman G.W. — Problem Book for First Year Calculus
Bluman G.W. — Problem Book for First Year Calculus



Обсудите книгу на научном форуме



Нашли опечатку?
Выделите ее мышкой и нажмите Ctrl+Enter


Название: Problem Book for First Year Calculus

Автор: Bluman G.W.

Аннотация:

This book focuses on the application of one-variable calculus to problems connected with physics, engineering, business, economics, biology, and chemistry. It is intended for the student who wants to "learn by doing."


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 385

Добавлена в каталог: 16.04.2010

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
blank
Предметный указатель
$n!$, estimation of      217 [VI.48]
$\pi$ (Pi), estimation of      214 [VI.24]
Absolute convergence      (VIII.10.17) [VIII.10.1]
Absolute value      4 96 (1.3 15; 6 9; 2.3 5.5-5.7 6.2 6.4 7.12 9.8 10.11) [VIII.1.1 3.35 5.5-5.7 7.33 11.7 11.8]
Acceleration      95 96 [III.1-9 13) [III.2-10 49]
Acceleration, due to gravity      (III.5-7 32) [III.5-8 10]
Acceleration, of automobile      (III.1 2) [III.2]
Alternating series      see Series
Amplitude      [III.55; VIII.1.17]
Angle between curves      (VIII.1.5) [VIII.1.10 3.19]
Angular velocity      100 (11.32; 14) [11.48 82 84-87; 53]
Anti-derivative      [VII.20; VIII.4.2 13.5] indefinite)
Approximation, by differentials      see Differential approximation
Approximation, errors in      see Error
Approximation, linear      see Linear approximation
Approximation, of definite integrals      see Power series Simpson’s Trapezoidal
Approximation, to root $f(x) = 0$      see Newton’s method
Arc length      see Length
Area      35 36 (II.3 4 7-9 13 18 25 27 29; 10) [II.1 2 8-13 15 17 20 25 30 31 42 44-47 63 64 76]
Area, as integral      see Integration and area
Area, by parametrization      (VIII.8.8) [VIII.8.1 8.17]
Area, in polar coordinates      (VII.31; VIII.9.1-9.8) [VIII.9.1-9.17]
Area, of surfaces      (VIII.7.16) [11.21 67; 7.43 9.17]
Astroid      (VIII.3.4 8.10) [VIII.3.9 13.4]
Asymptote      3 (1.2 4 6-8 11.18; 6 8-10; 6.6) [1.11 15 18 20; 21 22 24; 22]
Asymptotic behaviour of a function      see Asymptote
Average cost      (IV.12 14) [IV.29 33 40]
Average interest rate      (IV.8)
Average rate of change      [V.3]
Bacteria growth      (V.9) [V.1 10 21]
balance      143 (IV.6 7 9) [IV.21 22]
Ballistics      (III.5-7) [III.8 10 14]
BASEBALL      (III.6) [11.60]
Beer mug      [III.30]
Bessel functions      (VII.22)
Binomial series      (VI.16 18; [VI.37 39]
Birth-rate      178 (V.5 8) [V.15]
Bounded sequence      (VIII.10.10)
Braking distance      132 (III.1 35)
Cable      see Catenary
Capacity of a bridge      129 (III.35)
Carbon dating      175 176 (V.3)
Cardioid      (VIII.9.4 9.6 9.8) [VIII.9.6 9.8 9.15]
Catenary      127-129 (III.34) [III.58;
Centre of gravity      96 97 [III.29 30]
Centre of mass      96 97 (III.22 23) [III.28]
Centring errors      196 198 (VI.6-9 11 23) [VI.24 25 30 37 43 46 47 50;
Centroid      97-101 (III.15-17 19-21 24 27) [III.24-27]
Chain rule      (1.2; 11.25; III.1; VIII.2.1 2.7) [VII.11; 3.35]
Chemical concentration      (V.11) [V.12-14 19 20 24]
Chemical mixture      [V.12-14]
Chemical reaction      184-187 (V.10 11) [V.19 20 22-24]
circle      (1.1 15; 8.2 8.6 9.2) [1.1; 1.13 3.20 7.11 9.2 9.14 9.15]
Comparison tests for convergence of improper integrals      (VIII.6.3 6.5 6.6) [VIII.6.4 6.8-6.10]
Comparison tests for convergence of series      (VII.20; VIII.10.2-10.4) [VIII.10.3]
Completing the square      (1.1; VIII.1.6 5.10 9.2) [1.1; 1.14 1.16]
Components of a vector      96 (III.6-9)
Composite function      (1.2) [VII.20; 4.6 5.8]
Compound interest      143 144 (IV.6-9) [IV.17 20-22]
Concavity      2 144 (1.2 4-7 10 12-14 16 II [1.4-21; 41;
Cone      (11.26 35 38; [11.16 18 73 75 76; 7.43]
Conic sections      (LI) [1.1;
Consumer’s surplus      145 (IV.10) [IV.25 31 37]
Continuity      (1.3 16; 9 10; [1.25 26; 3 8-10 13 15 19 20 24 32 36-38 VIII.13.6]
Continuously compounded interest      144 (IV.8) [IV.18 19 21 23]
Convergence, absolute      see Series
Convergence, of a sequence      97 (VII.18; [VII.34;
Convergence, of alternating series      see Series
Convergence, of improper integrals      see Integral
Convergence, of power series      see Series
Convergence, of series      see Series
Convergence, tests for      see Comparison tests for convergence Estimation Integral Ratio
Coordinates, polar      see Polar coordinates
Cosines, Law of      (III.14) [III.21]
Cost, average      (IV.12 14) [IV.29 33 40]
Cost, function      146 (IV.1 3 5) [IV.1 2 4-8 10 16 26 27 31 34 36]
Cost, marginal      see Marginal cost
Cost, total      145 (IV.2 5 12 15 17) [IV.3 15 32 35 39 43 44]
Critical point(s)      2 35 (1.2 4-14 17; 35; 9 14-16; 9; VII.12 22; 3.11 3.13 3.14 9.4) [1.4-12 14-21 23-25; 12-15 59; 26-31 33 35 36 41; 21; 27; 7.19 8.6 13.4]
Cross-sectional area      35 36 (II.9 27 28 33-40; 20 27) [11.88-100;
Current value      see Present value
Curve(s), demand      see Demand curve
Curve(s), length of      see Length
Curve(s), parametrization of      see Parametric equations
Cusp      16 (1.11)
Cycloid      (VIII.8.5) [VIII.8.17]
Cylinder      (II.2) [II.7 8 21 70 71; 34 37]
Death-rate      (V.5) [V.16]
Deceleration      (III.1 2 35) [III.3]
Decreasing function      1 (1.2 4-6 16 17; [1.6 8-10 24; 59 68 69; 41;
Definite integral      see Integral
demand      144-146 (IV.14) [IV.33]
Demand, curve      144 145 (IV.10) [IV.25]
Demand, elasticity of      146 (IV.16) [IV.37 38]
Demand, equation      144 (IV.10 15 18 19) [IV.28 29 31 35-38 41 45]
Demand, function      144 (IV.13 15 16 19) [IV.24 27]
Demand, rate      (IV.II)
density      (III.3 35)
Derivative      1 2 Differentiation Second
Derivative, chain rule      see Chain rule
Derivative, definition of      (VII.4 5 7 8 19) [1.19; 15 16]
Differentiability      194 (1.3; 6 9) [VII.7-9 17 25]
Differential      146 173 (III.1 2 22 25 30 34; V.9; 4.10 4.12 5.3 5.8 7.8 7.11 7.12 8.9 12.1 12.3 12.4 12.7]
Differential equation(s)      171 (III.33;
Differential equation(s), first order linear      (IV.8; VIII.12.7) [VIII.13.5]
Differential equation(s), general solution      (VII.23; VIII.12.1 [VIII.12.7]
Differential equation(s), periodic solution      298-300 (VIII.12.7)
Differential equation(s), second order linear      (VII.23; VIII.12.5) [VII.35;
Differential equation(s), separable      (III.30; IV.8 V.2 6 8-11; 12.4 [IV.34; 12 20-24;
Differential, approximation      146 147 195 (III.32; [IV.30 38 43 44; 49]
Differential, element of area      97-100 (III.16-18 21)
Differentiation, implicit      see Implicit differentiation
Differentiation, of integrals      (1.17; VI.5; VII.15; VIII.2.7-2.9) [VI.15; 3.35]
Differentiation, of power series      289 (VIII.10.15 [VIII.10.16
Discontinuity      (1.3; VII.2 3) [1.26; 37 38]
Discontinuity, essential      [VII.3]
Discontinuity, jump      (VIII.12.7)
Discontinuity, removable      (VII.2) [VII.2 3]
Distance      96
Distance, as definite integral      96 (III.3 4) [III.1-3 11]
Distance, between point and curve      34 [11.43]
Distance, between point and line      (III. 12)
Distance, between points      (11.12 22-24 28; [11.41 52 54 55 59 62 79; 15 17 20 23]
Divergent improper integral      (VIII.6.6 6.7) [VIII.6.3-6.6 6.9 6.10]
Divergent sequence      (VII.20) [VII.34; 10.9 10.10]
Divergent series      (VII.20; VIII.10.4 [VIII.10.3 10.4 10.9 10.10]
Domain of a function      1 35 (1.2 4 5; 22 38; 5 9; 10; 2.6) [II.1-44; 2.14 2.17 3.23-3.29 13.2]
Doubling time      172 (V.6) [V.1 8-10]
Dynamics      see Motion
Effective annual interest rate      144 [IV.21]
Elasticity of demand      146 (IV.16) [IV.37 38]
Electrostatic force      122 (III.28) [III.44]
ellipse      (11.33; VIIL8.11) [1.1; 7.21 7.27 8.1 8.2 9.3 9.17]
Ellipsoid      (11.33) [VIII.7.20 7.21 7.27]
Energy      [III.49 57]
Epidemic      173 (V.7) [V.17]
Equilibrium concentration      (V.24)
Equilibrium demand      145 (IV.10) [IV.24]
Equilibrium point      145 (IV.10) [IV.25 37]
Equilibrium price      145 (IV.10) [IV.24]
Equilibrium state of      [V.21 22 24]
Equilibrium static      (III.34)
Erfx      320 [VIII.10.21]
Error      see also Centring errors
Error, effect of step size      197 (VI.10 22) [VI.25 30]
Error, for Newton’s method      196 227 (VI.6-8; [VI. 23 32 33]
Error, for series approximation      198 (VI.11 14-18 20 21 23) [VI.33-35 37-47;
Error, for Simpson’s rule      197 233 (VI.10 22; [VI.28-30]
Error, for Taylor’s formula      197 (VI.11 19; [VI.32 36;
Error, for Trapezoidal rule      197 (VI.9) [VI.25 29 30]
Error, in measurement      195 (VI.4) [VI.14]
Error, in modelling      (V.4; VI.35)
Error, round-off      (VI. 18)
Estimation by Taylor’s formula      197 (VI.II) [VI.32 36] Taylor Taylor
Estimation of tails of infinite series      198 (VI.20 21; [VI.34 35 46 47;
Even function      3 20 217 221 222 (1.2 5 13 17; 7; 9.6 9.7) [1.19; VII.37]
Exponential decay      171-173 (V.2 3) [V.2 4]
Exponential functions      144 (III.30; 7-11; 2.6 [IV.42; 20-22 24; 22; 2.16 11.25 11.30]
Exponential functions, derivatives of      (1.9 10; 22; 19; [1.15 16; 28; 2.21 2.24 3.33 7.19 8.5 8.8 12.10]
Exponential functions, graphs of      (1.9 10; 7.6 12.7) [1.15 IV.28; 7.19 7.23 7.34]
Exponential functions, integrals of      (IV.19; VI.17 20 22; 7.13 10.8 11.4) [III.42 48; 38; 6.2 6.9 6.10 7.19 7.30 7.34 7.35 10.21]
Exponential functions, power series for      (V.II; VI.11 17; [VI.34 38; 10.21 11.29]
Exponential growth      171 (V.1 4 6) [V.1 3 5-8]
Extrapolation      (V.4)
Extremal point      see Critical point
Extremum      see Critical point
Fluid pressure      100 (III.19-21) [III.18 32-34]
Flux of cars      129 (III.35)
Focal point      126 141 (III.33) [III.56;
Focus      see Focal point
force      100 (III.19-29 34) [III.32-49]
Frustum of a cone      (11.38)
Function(s), asymptotic behaviour      see Asymptote
Function(s), composite      see Composite function
Function(s), continuous      see Continuity
Function(s), cost      see Cost function
Function(s), demand      see Demand function
Function(s), derivative of      see Differentiability Differentiation Second
Function(s), domain of      see Domain
Function(s), even      see Even function
Function(s), exponential      see Exponential function
Function(s), hyperbolic      see Hyperbolic function
Function(s), implicit      see Implicit function
Function(s), increasing      see Increasing function
Function(s), inverse      see Inverse function
Function(s), limit of      see Limit
Function(s), logarithmic      see Logarithmic function
Function(s), monotonic      see Monotonic function
Function(s), odd      see Odd function
Function(s), periodic      see Periodic function
Function(s), range of      see Range
Function(s), roots of      see Root
Function(s), symmetry of      see Symmetry
Function(s), trigonometric      see Trigonometric function
Fundamental theorem of calculus      (II.4; 5; VII.15 VIII.2.7-2.9) [VI.15; 3.35]
Geometric sequence      173
Geometric series      198 (VI.14; [VIII.10.19 10.24]
Geometrical rate of convergence      196
Graph(s)      1 2 98-101 195-197 (1.1—17; 6-18 22 25 33 35-40; 5 8 9 25 27 31 33-35; 20; 5 8-11; 8 20 24; 13; 2.6 3.7 3.9 5.10 7.1-7.15 8.1-8.6 8.10 9.3-9.7 [1.1-26; 72 94; 21 27 29 43 56 58; 39; 2.17 2.18 7.8 7.17 7.36 7.39 7.42 8.3 8.12 8.17 9.2 9.3 9.12 9.13 13.2 13.4]
Gravity, centre of      96 97 [III.29 30]
Half-life      172 (V.3) [V.2 22]
Hanging cable      127-129 (III.34) [III.58]
Headway      130 (III.35)
Heat flow      123 (III.30) [III.15 50-52]
Hooke’s law      123 (III.29) [III.45-47]
Hyperbola      (1.3 15; [1.12; 8.12]
Hyperbolic function(s)      129 233 275 315 (III.34; [1.17; 2.18 7.39 8.12
Implicit differentiation      35 (II.9 24-28 30-32; IV.17; VII.23; 2.6 3.3 3.4) [H.45-87; 2.16-2.18 3.16 3.19 13.2]
Implicit function      35 (III.10 33-35; [VII.35 39; 12.5-12.8]
Improper integral      see Integral
Increasing function      1 (1.2 4 6 11.19 20 25 29; 3.12) [1.6 8 9 24; 46 52 59 61-65 67 72 75 76; 28 39 41; 3.21]
Indefinite integral      see Integral
Indeterminate forms      144 294 (1.10; 35; 5 7 8 20; 6.6 6.7 11.1-11.15) [1.15 19; 50; 21 22; 11.1-11.30 13.2]
Induction      (VIII.10.9) [VIII.5.14]
Inelastic demand      see Elasticity of demand
Inequalities      (1.15; IV.7; VII.9 11 13; 3.12 7.5 [1.22; 21 22 31 32 39; 3.5 7.9 13.4 13.6]
Infinite series      see Series
Inflection point      2 (1.4-6 8-13 5 7; [1.4-12 25;
Initial condition(s)      95 96 298-300 (11.22 24; 5-7 13 33; 7-11; 12.3-12.5 [III.5-8 V.1-24; 13.5]
Integral(s)      see also Integration
Integral(s), definite      196 (III.1-5; 9 11 19; 5.5-5.7) [IV.23; 26;
Integral(s), improper      (VIII.6.1-6.7 7.14) [V.26; 7.34 7.35]
Integral(s), indefinite      95 96 (III.6) [VIII.4.1 13.5]
Integral(s), Riemann      97 (VII.14; [VII.26;
Integral(s), rules for approximating      see Simpson’s Integral(s) rule Trapezoidal
Integral(s), test      (VIII.10.7) [VIII.10.6]
Integration      see also Centre of gravity Centre of Centroid Length Moment of Surface Work
Integration, and area      97-100 145 197 (1.17; 15; 31; 20; 21; 5.10 7.1-7.7 7.15 8.8 9.7) [1.23; 7.1-7.19 7.33 7.35 7.42 8.11 8.17 9.5-9.17 13.3]
Integration, and distance      96 (III.3 4) [III.1 3
Integration, and volume      35 (11.33-40; [11.88-100; 7.41-7.43]
Integration, by partial fractions      (VII.16; VIII.4.3 4.12 5.9) [VIII.4.7-4.18 5.9-5.11]
Integration, by parts      (VIII.7.8 7.10) [VIII.5.8 5.14 5.16]
Integration, by substitution      (11.34 35 38; 4.8 4.12 4.13 5.4 5.7 5.8 7.12 7.13 8.9 8.10 12.1) [VII.28 29]
Integration, by trigonometric substitution      (VIII.4.7 7.8)
Integration, of rational functions of the sine and cosine      (VII.16; VIII.4.13) [VIII.4.16-4.18 5.11]
Integration, of series      (VI.14 23; [VI.38-45;
Interest      143 144
Interest, compound      143 (IV.6-9) [IV.17 20-22]
Interest, continuously compounded      144 (IV.8) [IV.18 19 21 23]
Interest, rate      143 144 (IV.6-9) [IV.17-23]
Interest, rate, effective annual      144 [IV.21]
Interest, rule      144 (IV.9)
Interest, simple      143 [IV.21]
Intermediate Value Theorem      232 [VII.25]
Interpolation      see Linear interpolation
Inventory      (IV.11 14) [IV.32 33]
Inverse function(s)      144 (VIII.1.9 1.10 2.6 7.8) [VII.35; 2.18 13.2]
Inverse hyperbolic function(s)      233 302 [VII.35;
Inverse square law      (III.28) [III.44]
Inverse trigonometric function(s)      (11.11; 3 VII.15 23; 4.2 4.9 5.8 7.7 7.8 [III.28; 2.8 2.17 3.6 4.5 4.8-4.12 4.14 5.9 9.16 13.5]
Isosceles triangle      (II.9 27) [11.15 42;
Jump discontinuity      (VIII.12.7)
Kinematics      95 96 99 (III.1-9 13) [III.1-10 49]
kinetic energy      100 140 [III.49]
Law of Cosines      (III.14) [III.21]
Law of natural decay      171 (III.3) [III.2]
Least squares method      (III.4)
Lemniscate      (VIII.9.7) [VIII.9.13 9.17]
Length of a curve      141 232 233 (IIL34; 8.9-8.11 9.8) [III.58; 7.41 7.42 8.13-8.17 13.4]
Limit Comparison Test      227 (VII.20)
Limit, infinite      (1.10 11.15 18; 6.6 6.7 9.4 [1.19;
Limit, left-hand      (1.10; 11.15; VII.1; VIII.3.16) [VII.2 3 37 38; 11.7 11.8 11.28]
Limit, of a function      144 (1.9 16; 35; 8-10; 5 7 8 VIIL4.9-4.12 6.1 6.3 6.7 7.14 9.4 [1.15 26; 20-22 24; 8 9 17 21 22 36; 7.35 11.1-11.22
Limit, of a sequence      97 (VII.14 20; 10.4 10.5 10.8 10.10 10.11) [IV.21; 34; 10.10 10.22 11.23 11.27]
Limit, right-hand      (1.10 14; 18; 3.16 6.2 6.4 6.6 11.9 11.16 [VII.2-5 37 38; 11.14 11.21 11.25 11.26 11.28]
Linear approximation      146 (IV.18 1-5) [IV.43 44;
Linear interpolation      195 (VI.24) [VI.
Linear momentum      99
Lions Gate Bridge      129 131 (III.35)
Lipschitz condition      231 [VII.19]
Local maximum/minimum      see Maxima and minima
Logarithmic functions      172 (IV.19; VIII.4.3 4.4 4.13 5.9 6.7 7.5 [IV.2; 22 31 36; 4.1 4.8-4.18 5.9 5.13 11.14 11.16 11.26 11.27]
Logarithmic functions, differentiation of      (1.10 IV.17; [1.19 20; 2.3 2.7 3.2 3.17 8.8]
Logarithmic functions, graphs of      (1.10 V.4) [1.19 20]
Logarithmic functions, integration of      (VII.21) [IV.45; 40 48; 6.3 6.9 7.16 7.40]
Logarithmic functions, series for      (VI.14 [VI.36 VIII.10.15]
Logarithms      172 (IV.7 8; 3 6 7; 2.6 7.6 7.13) [III.8; 45; 5 22; 31; 5.9 6.3 7.6 11.26]
Logistic equation      173 174 (V.6-8 10 11) [V.15-22]
Logistic growth curve      173 174 (V.6 10)
L’H$\hat{o}$pital’s rule      (1.9 VIII.9.4 (see
Maclaurin series      198 (VI.19; [VI.37; (see
Malthusian growth law      171 (V.1 4 6 9) [V.1 3 5-8]
Marginal      146 147
Marginal cost      146 (IV.17) [IV.34 39 40 43 44]
Marginal demand      (IV.18) [IV.38]
Marginal profit      146
Marginal revenue      146 (IV.19 20) [IV.41 42 45]
Market equilibrium      145 [IV.25 37]
Market value      145
Mathematical induction      (VIII.10.9) [VIII.5.14]
Maxima and minima      2 34 35 (1.2 9 II.1-18 22; 35; 9 V.5 9; 3.11 3.13-3.16) [1.4-11 20; 59; 59; 20 26-29 31 33 35 36 42; 21 22; 27 39; 3.20-3.35 8.6 13.4 13.6]
Maxima and minima, second derivative test      2 (1.6-9 12; 10 12-14; 12 14 16; 9) [IV.16]
Maxima and minima, strategy for finding      2 34 35
Mean value theorem      232 (VII.9) [1.26; 25 32]
Mean Value Theorem, Cauchy’s      [VII.32]
Mixing problems      [V.12-14]
Moment of inertia      100 (III.18) [III.31]
Monopoly      (IV.15) [IV.25 41 45]
Monotonic function      (III.35)
Monotonic sequence      (VIII.10.4 10.10)
1 2
blank
Реклама
blank
blank
HR
@Mail.ru
       © Электронная библиотека попечительского совета мехмата МГУ, 2004-2019
Электронная библиотека мехмата МГУ | Valid HTML 4.01! | Valid CSS! О проекте