Bluman G.W. — Problem Book for First Year Calculus :: Электронная библиотека попечительского совета мехмата МГУ

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

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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:

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

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Предметный указатель

Motion      35 95 96 99-101 (11.11 14 19-32; 35; [11.32-35 45 46 48-87; 13 14 17-23 48 49 53 55 59]
Newton’s Law of Cooling      123 124 140 (III.30) [III.50-52]
Newton’s law of motion      133 140 [III.7 49]
Newton’s method (Newton-Raphson)      195 196 227 (1.10; [VI.17-23 32 33]
Normal line      (VII.3.8) [VIIL3.14-3.18 8.10]
Numerical integration      196 233 (IV.20; 9 22 23) [IV.25; 31 38-44 50 51;
Odd function      3 221 268 5 7; 22; 7.12) [1.7 13 16;
Optics      (III.33) [III.56]
Order of convergence      227 (VII.18)
Output      (VIII.12.7)
Pappus, theorems of      99 (III.
parabola      (II.7 8 III.6 20 33; 4 VIII.1.4 3.9 7.1 8.3 8.6) [11.72 89 94; 56; 3.3 7.3-7.5 7.7 7.8 7.29 7.36 9.4 13.3]
Parabola, equations      (III.6 20 33; 8.4 8.6) [VIII.1.16]
Parabola, focus      (III.33) [III.56]
Parabola, reflection property      (III.33) [III.56]
Parabola, vertex      (II.7 13;
Parabolic interpolation      197 233 [VII.33]
Parabolic lens      [11.89]
Parabolic mirror      (III.33) [III.56]
Parallel lines      (VIII.3.6) [VIII.1.11 3.11]
Parametric equations      (III.6 7 9; [VIII.8.1—8.17]
Parametric equations, and derivatives      (VIII.8.5—8.11) [VIII.8.4—8.17]
Parametric equations, of a circle      (VIII.8.2 8.6) [VIII.8.4 8.12]
Parametric equations, of a cycloid      (VIII.8.5) [VIII.8.17]
Parametric equations, of a hyperbola      [VIII.8.3 8.12]
Parametric equations, of a line      (VIII.8.1)
Parametric equations, of a parabola      (III.6 7 9; 8.4 8.6)
Parametric equations, of an astroid      (VIII.8.10)
Parametric equations, of an ellipse      (VIII.8.11) [VIII.8.1 8.2]
Parametric equations, second derivatives      (VIII.8.7) [VIII.8.7-8.9]
Partial fractions      (VIII.2.4 3.8 3.16) [1.12; (see
Partial sum      198 (VI.14 20 21; [VI.34 35 46; 10.6 10.8]
Pascal’s principle      100 (III.19-21) [III.32-34]
Pearl-Verhulst curve      173 (V.8)
Pendulum, simple      125 (III.32)
Period      (1.13; VIII.9.3 9.5 [VIIL1.7]
Periodic function      (1.13; VII.3; VIII.9.3 9.5) [1.21;
periodicity      1 (VI.5; 5.7 9.5
Phase displacement      [VIII.1.17]
Point of inflection      see Inflection point
Polar coordinates      (III.31; VIII.9.1-9.8) [VIII.9.1-9.17]
Polar coordinates, area      (III.31; VIII.9.5-9.7) [VIII.9.5-9.16]
Polar coordinates, graphs      (VIII.9.3-9.7) [VIII.9.2-9.4 9.12 9.16]
Polar coordinates, length      (VIII.9.8)
Polar equation of a cardioid      (VIII.9.4 9.6 9.7) [VIII.9.6 9.9 9.15]
Polar equation of a circle      (III.31; VIII.9.2 9.6) [VIII.9.2 9.11 9.14 9.15]
Polar equation of a hyperbola      (VIII.9.3)
Polar equation of a lemniscate      (VIII.9.7) [VIII.9.13]
Polar equation of a line      (VIII.9.1) [VIII.9.14]
Polar equation of a parabola      [VIII.9.4]
Polar equation of an ellipse      [VIII.9.3 9.16]
Population size      171 (V.1 9) [V.1 3-9 11 15-18 21]
Position vector      96 (III.9)
potential energy      99
Power series      (V.10; VI. 12 23; [VI.33-35 37-45;
Power series, differentiation of      289 (VIII.10.15 [VIII.10.16
Power series, integration of      290 (VI.17-19 23; [VI.38-45; 11.29]
Power series, interval of convergence of      (VIII.10.15) [VIII.10.21]
Power series, radius of convergence of      (VIII.10.15 10.17) [VI.44]
Present value      144 (IV.9) [IV.18 20]
Pressure      100 (III.19-21) [III.18 32-34]
Principal      143 (IV.6-8) [IV.17-23]
prism      [III.40]
Producer’s surplus      145 (IV.10) [IV.24 25 37]
Production rate      (IV.II)
Profit      146 (IV.3 [IV.8-11 23 26 27 31 35 36]
Projectile      (III.5-7) [III.8 10 14]
Pyramid      (11.34) [11.91 92]
Qualitative features of a graph      (1.16 5) [1.23-26;
Radioactive decay      175 176 (V.3) [V.2]
Radius of convergence      (VIII. 10.15 [VI.44]
Range of a function      (1.2 4 5; 1.10) [VIII.1.22 2.17]
Rate of change      (11.29) (see also Related rates)
Rate of convergence      196 (see also Order of convergence)
Rate of formation      190 [V.20]
Rate of interest      see Interest rate
Ratio Test      (VIII.10.1 [VIII.10.11]
Reactant      184-186 (V.10 11)
Reaction rate      191 [V.22]
Reaction time      132 (III.35)
Reflector      (III.33) [III.56]
Region of Type (i)      98 99 (III.15)
Region of Type (ii)      98 99 (III.18)
Related rates      35 (H.19-28 30-32; 8 11; [11.45-87; 22 25]
Relative maximum/minimum      see Maxima and minima
Remainder in Taylor’s formula      197 (VI.11 14 15; [VI.32-43;
Removable discontinuity      (VII.2) [VII.2 3]
Restricted growth      173 174 (V.5-11) [V.16-22]
Revenue      (IV.4 20) [IV.12-14 28 30]
Revenue, function      146 (IV.3 4 13 15 16 19 20) [IV.8-15 30 46]

Revenue, marginal      146 (IV.19 20) [IV.41 42 45]
Riemann sum (Riemann integral)      97 (VII.14; [VII.26;
Rocket motion      (III.13) [III.6 7 9 17]
Rolle’s Theorem      222 (VI.17; 12 22)
Root(s) of a function      1 (1.4-8 10 11 13; 16; 12 17 22) [I.9 11 14 20; 39;
Round-off error      (VI.18)
Rumour      [V.18]
Secant line      (VI.24)
Second derivative      1 2 95 96 144 145 174 195-197 (1.11; 5-9 V.5 7 6-13 VII.18 23; 2.5 8.7 12.5 [1.5 7 20 25; 8-10 49; 30 32 33; 2.13 8.9 8.16 12.7-12.10]
Second derivative, sign of      2 (1.9)
Second derivative, test for concavity      2 (1.2 4-7 14 16 17; [1.6 8 9 11 15 16 19 25;
Second derivative, test for max/min      2 (1.6-9 12; 10 12-14; 12 V.5 9) [IV.16]
Separation of variables      see Differential equation separable
SEQUENCE      97 173 227 228 (IV.6 9; 18 20; [IV.21 22; 32 33; 34; 11.23 11.27 13.1]
Series      198 227 228 (V.10; 23; 10.11 10.19) [VI.33-47 50; 10.16-10.24 11.29]
Series, absolutely convergent      (VIII.10.17) [VIII.10.1]
Series, alternating      198 (VI.14-18 20 23; 10.4) [VI.38-40 44 46; 10.3]
Series, binomial      (VI.16 VIII.10.17) [VI.37 39]
Series, comparison test      (VII.20; VIII.10.2-10.4) [VIII.10.3]
Series, convergent      (VIII.10.1-10.4 [VIII.10.1-10.4 10.9-10.11]
Series, differentiation of      see Power series
Series, divergent      (VII.20; VIII.10.4 10.11) [VIII.10.3 10.4 10.9 10.10]
Series, geometric      see Geometric series
Series, integration of      see Power series
Series, Maclaurin      see Maclaurin series
Series, partial sums of      see Partial sum
Series, power      see Power series
Series, Taylor      see Taylor series
Series, with telescoping property      (VIII.10.6) [VIII.10.5]
Signed areas      (1.17)
Similar triangles      (II.3 26-28 31 34 35) [11.15 73-80 91 92]
simple harmonic motion      [III.55]
Simple interest      143 [IV.21]
simple pendulum      125 [11.32]
Simpson’s rule      197 233 (IV.20; 22) [IV.25;
Singular points      (1.7 10; 6.6) [1.11-14 21; 6.5 6.6 6.9 6.10]
Slope of a curve      (III.33; VIII.8.5 [III.56; 3.20 8.4 12.5 12.6]
Slope of a line      (11.18; VIII.1.5 3.4 3.6 9.4) [VIII.3.3 3.17 3.33]
Specific rate of reaction      191
Speed      96 (III.6-8 35) [III.1 5 59]
Spring      (III.29) [III.45-47]
State of equilibrium      191 [V.21 22 24]
Static equilibrium      (III.34)
Stationary point      see Critical point
Step function      (VIII.12.7) [VII.4]
Supply      144 145
Supply curve      144 145 (IV.10) [IV.25]
Supply equation      144 (IV.10) [IV.37]
Supply function      145 [IV.24]
Surface area      (VIII.7.16) [11.21 67; 7.43 9.17]
Symmetry      1 9 (1.5 7 II.3 6-28 31 34-40; 20 21 24 25 31 33 34; VI.5 8; 6 7 8 VIII.2.6 5.1 5.6 5.7 5.10 6.2 7.8-7.16 9.5) [1.3 22 23; 73-80 88-100; 32 34 36-40 43 56; 29 35 37; 5.2 5.15 7.17 7.20-7.36 7.40-7.43 9.18]
Tail of an infinite series      198 (VI.20 21; [VI.34 35 46 47;
Tangent line      194 (11.18; 2; 8.4 8.6 9.4 12.4 [III.23; 27; 3.16 3.17 3.19 3.33 8.10 8.16 12.8 13.4]
Tangent line, approximation      146 (IV.18; [IV.43 44;
Tangent vector      (VIII.8.6)
Tax      (IV.14 15) [IV.31 35 36 46]
Taylor polynomial      197 (VI.13 10.12) [VI.43;
Taylor series      198 (VI.11 12 14 15; 10.17 10.18) [VI.33 38-40; 10.17 10.21] Power
Taylor’s Formula      197 (VI.II; [VI.32 36; 10.15]
Taylor’s Theorem      [VIII.10.14]
Telescoping series      (VIII.10.6) [VIII.10.5]
Tension      (III.34)
Total cost      145 (IV.2 5 12 15 17) [IV.3 15 32 35 39 43 44]
traffic flow      129-132 (III.35) [III.59]
Trajectory      (III.6 8;
Translation of axes      (1.1 15 17; 8; 8.2 8.4 9.2) [1.1 12 23; 1.14 1.16 8.2]
trapezoid      (III.27)
Trapezoidal rule      196 (IV.20; 18) [IV.25; 29-31]
Trigonometric functions      (1.13 11.11; 34; 23; 6.5 8.2 9.1 9.2 [1.22; 4.6 8.1 8.2 9.1 9.3 11.19 11.22 11.26 11.28]
Trigonometric functions, differentiation of      (II.4 9 III.9 11 VI.2 4 8; 9; 3.11-3.13 8.5 8.6 8.10 8.11 9.3-9.5) [1.21; 21; 6 9 22; 2.16 2.20 2.25 3.1 8.4 8.5 8.9 8.11 8.15 8.17 9.4 12.9]
Trigonometric functions, graphs of      (II.9 14 15; [1.21;
Trigonometric functions, integration of      (III.31; VI.5 VII.16; 4.13 5.1-5.4 5.6 5.7 7.4 7.10 8.10 8.11 9.5-9.8) [VI.44 45; 4.16-4.18 5.1-5.4 7.9 8.11 8.17 9.5-9.17
Trigonometric functions, inverses of      (11.11 III.28; 12; 23; 4.2 4.9 4.10 7.8 10.17 11.7 12.1) [VII.31; 2.8 2.16 3.6 4.5 4.8-4.12 5.9 7.11 13.5]
Trigonometric functions, series for      (VI.13 VIII.11.15) [VI.35 42-44; 11.29]
Trigonometric identities      (II.4 9 III.1 33; 23; 4.5 4.6 4.13 5.1-5.4 5.7 7.8 8.10 9.3-9.6 9.8 11.16) [VI.44; 1.18 4.3 9.2]
Unit elasticity      146 160 (IV.16)
Unrestricted growth or decay      171 (V.2 9) Law
Vector acceleration      96 (III.6 8 9)
Vector components of      96 (III.6-9)
Vector velocity      96 (III.7 8)
Vector, position      96 (III.9)
Vector, tangent      (VIII.8.6)
Velocity      95 96 (III.1-9) [III.3 4 6-11 49]
Velocity, angular      see Angular velocity
Verhulst equation      173 (V.8)
Volume of a solid of revolution      99 (11.33 38-40; 17; [VIII.7.20-7.36 7.41-7.43]
Volume of a solid with known cross-sections      35 36 (II.33-40) [11.88—100]
Weber Fechner law      [VIII.12.4]
Work      101 (III.22-29) [III.35-49]
Zero      see Root

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