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Schiffer M.M. — The role of mathematics in science
Schiffer M.M. — The role of mathematics in science

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Название: The role of mathematics in science

Автор: Schiffer M.M.

Аннотация:

Our primary aim is to illustrate the power and elegance of mathematical reasoning in science; our secondary aim, to show also that science egenders mathematics.
We start with Archimedes work on the lever, which, based on our common experience of carrying ladders, confirms our bone borne intuition. We finish with the work of Einstein, which , as we have no experience of "unaccustomed dimensions" such as intergalatic travel at nearly the speed of light, disconcertingly discomforts us with situations beyond our intuitive grasp. Here mathematics comes into its own; to give brain borne counsel where bone borne guidance fails; to give such comforting assurance that scientists justifiably call it a sixth sense.
Our ultimate aim is to help develop this sixth sense in as wide a readership as possible; we have restricted technical mathematics to minimum, just algebra and some calculus. therefore let none be deterred!


Язык: en

Рубрика: Математика/

Статус предметного указателя: Готов указатель с номерами страниц

ed2k: ed2k stats

Год издания: 1984

Количество страниц: 215

Добавлена в каталог: 21.11.2013

Операции: Положить на полку | Скопировать ссылку для форума | Скопировать ID
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Предметный указатель
$\pi$ (pie)      25 59
$\pi$ (pie), Cusanus' calculation of      59
$\pi$ (pie), recursive formula for      59
Aaboe, Asger      15
Abraham      189
Absorption factor      30
Addition of velocities      160
Addition of velocities, relativistic      152 163 166
Addition, formulas      119 159 191
Addition, formulas for hyperbolIc functions      191
Addition, formulas of trigonometry      119 123 157
Additive function      173
Additive property      112 116
Admissible energy functions      178
Affine maps      112
Algebra      104 131
Algebra of matrices      119 123
Algebra of vectors      107 108
Algebra, factor theorem of      143
Algebra, rules of      123
Algebraization of geometry      105
Allgaier — Hamppe      1
Analytic geometry      104
Angle of deflection      188
Angle of incidence      76 77 80 81 82
Angle of reflection      76 77 80
Angle of refraction      82
Angle of rotation      145 156
Apothem      64
Archimedes      1 3 4 6—9 11 12 15 16 24 59 169 199
Archimedes, "mechanical method" of      15 16
Archimedes, axiom of      4
Archimedes, law of the lever      3 8 169
Archimedes, symmetry proof      80
Arithmetic, average      34
Arithmetic, mean      44 69—74
Arithmetic, progression      46
Arithmetic-geometric mean      44
Arithmetic-geometric mean, inequality      25 69—74
Associative      115 118 164
Associative, binary operation      164 167
Associative, property      164
Attractors      52 56
Average      see "Arithmetic mean"
Beam(s) of light      94 100
Beam(s) of light, interfering      94
Bernoulli, James      33
Binary operation      164 165 166
Binary operation, infinitesimal      167
Binomial coefficients      32
Binomial theorem      32
Bohr, Niels      181
Bucherer      189
Calculus      91 99 162
Calculus of variations      91
Calculus, differential      87 98
Cartesian coordinates      110
Cassegrain      101—103
Cauchy      70
Cavalieri      15
Center of gravity      12 14 19 20
Centroid      10 12 14 16
Clock readings      137
Collision, elastic      174
Collision, symmetric      170 174
Commutative      107 110 118 119 194
Commute      112 194
Component(s)      109 110 113 117 129
Component(s), transformation      130
Composite      117 123—126
Composition of linear maps      115
Composition of maps      115 118 123
Compound interest      30 31
Compounding, continuously      33
Compounding, instantaneously      33
Congruence      124 125
Conics      99
Conie section      12 101—103
Conservation law      183
Conservation of energy      170 172 174 189
Conservation of momentum      172
Continuous, additive      174
Continuous, compounding      33
Continuous, function      144 173
Converge      52 56 67
Convergence      32 66 68
Coordinate(s)      105 129
Coordinate(s), axes      129
Coordinate(s), cartesian      110
Coordinate(s), geometry      108
Coordinate(s), system      130 145
Coordinate(s), transformation      128
Copernicus      136
Corpuscular, nature of light      95
Corpuscular, theory of light      91 94
Correspondence principle      181 183—185 188 196
Cosines, Law of      110
Crooked lever      16 18—20
Curie      190
Cusanus      25 59 66
Cycle, stable      55 56
Cycle, steady      52 53
Cycle, steady, of period      2 52
Cyclotron      150
Darwin      46
Decimal fraction      21
density      22
Descartes      66 91 108
Differential calculus      87 98
Differential equation(s)      44 45 58 175 178
Differential equation(s), partial      196
Differentiate      99 165 177 183
Displacement      105 106 124—126
Distance      124—127 130
Distance, preserving map      124—126 130 144
Distributive      107 110 112
Dot product      107 108 110 111 113 118 127 128
e (Euler's number)      32 33 73 74
Einstein's formula      163 189
Einstein's law for relativistic addition of velocities      160 161
Einstein's principle of relativity      171
Einstein's space-time transformation problem      132 138
Einstein's special theory of relativity      147
Einstein's theory of relativity      94
Einstein's time contraction      150
Einstein's transformation equations      153
Einstein's transformation law      155
Einstein, Albert      1 94 132 137 139 144 148 150 152 189 190 196 197 199
Elastic      170
Elastic collision      173 174
Electrodynamics      196
Electromagnetic theory      197
Electron(s)      188 189
Electron(s), beam      129
ellipse      12 82 95—99 101 103
Ellipse, foci of an      96
Ellipse, reflecting      99
Ellipse, tangent to an      95
Ellipsoidal cupola      99
Elliptical orbit      82
Energy      169 173 174 184—186 189 190
Energy and matter      189
Energy and momentum      181
Energy conservation      170 172 174 189
Energy function      174—181 184 192
Energy function, admissible      174 178 181
Energy function, Newtonian      175
Energy, kinetic      170 189 190
Energy, Newtonian      181
Energy, relativistic      182
Epidemic      29
Equilibrium      3 5—8 10—12 17—21 72
Equilibrium of the lever      3 80
Equiprobable      40
Error(s)      34 35 43
Error(s) in combinations of observations      43
Error(s), actual      35
Error(s), combination of      35
Error(s), Gauss' law of      35 42
Error(s), law of      34 36 42
Ether      94 163 189 196
Euclid      61 75—77 91
Euclid, law of reflection      91
Euclid, optics of      75
Euclidean motions      124
Even function      39 178
Events      38
Events, combined      38
Events, independent      38
Experimentum crucis      93 94
Exponential      25
Exponential function      28 34 42
Exponential, law of growth      25 34
Factor theorem of algebra      143
Feigenbaum, Mitchell J.      55
Fermat      16 84 85 91 93—95 98
Fermat, law of refraction      90 91
Fermat, quickest path principle      84
Fitzgerald — Lorentz contraction      148 149 189
Fixed point      53—55 125 126
Fixed point of a function      53 54
Fixed point, stable      54
Fizeau      163 167 168
Focus (foci)      96 99 101 103
force      18 22 186—188
Force, magnetic      188
Force, moment of a      18
Frank, Philipp      199
Fresnel      163 167 168
Function      25 82 86 140 141
Function, additive      173
Function, continuous      144 173
Function, differentiable      165
Function, energy      174
Function, energy, admissible      174
Function, even      39 178
Function, exponential      28 34 42
Function, growth      25
Function, hyperbolic      157 191
Function, linear      142
Function, momentum      184
Function, vector      196 197
Functional equation      25 27 34 42 45 157 159
Galilei, Galileo      1 6 9 18—20 24 84 196
Gauss, Carl Friedrich      34—36 42 43 72
Gauss, Carl Friedrich, law of errors      42
Gauss, Carl Friedrich, method of least squares      44 72
Geometnc mean      69
Geometric progression      45
Geometry, analytic      104
Geometry, coordinate      108
Gravitational field      169
Group      155 194
Growth      25 57
Growth, exponential law of      25 34
Growth, factor      49
Growth, functions      25
Growth, law of      28 29 42
Growth, population      29 45 47
Growth, rate      45
Half-life      30 150 151
Half-life of muons      150
Half-life of radium      30
Heiberg      16
Heron of Alexandria      76—78 80 81 85 91
Heron of Alexandria, minimum principle      85
Heron of Alexandria, shortest path law of reflection      90
Hexagon      64
Hexagon, regular      64 67
Homogeneity      112
Homogeneous map      114
Huygens, Christian      94 95 170—172
Hyperbola      12 101 103
Hyperbolic cosine      159
Hyperbolic functions      157 190 191
Hyperbolic sine      159
Hyperbolic tangent      159 161
Identity      115 125 126
identity map      115 116
Image      105 106 112 113 117 125 127
Image, mirror-      120 121 125
Image, point      112
impact      170 173
Incident ray      76 91
Inclined plane      18 20—22 35
Independent events      38
Index of refraction      90
Inequality of arithmetic-geometric mean      25 69
Inertia      186
infinity      99
Intensity of light      30
Interest      30 31
Interest, compound      30 31
Interest, rate      30
Interest, simple      30
Interferometer      134
Invariance      196
Invariance of velocity of light      147
Invariance, laws of      169
Invariance, principle of      172
Inverse      106 115—117 119 122 126 154
Inverse of a displacement      106
Inverse of a Lorentz matrix      154
Inverse of a one-to-one onto map      115 116
Isometry      124—128 130 144 145 156 160
Kaufmann      188
Kepler      82 83 90 91
Kepler, third law      84
Kinetic      35
kinetic energy      170 189 190
Kinetic theory of gases      35
Law(s) of (in)sufficient reason      3 4
Law(s) of conservation of energy      170
Law(s) of cosines      110
Law(s) of errors      34—36 42
Law(s) of invariance      169
Law(s) of the lever      3 10 11 14 16 169
Law(s), Verhulst's      47 48 55 58
Least squares      44
Least squares, Gauss' principle of      72
Leibniz      16 91
Lens, refracting      100
Lever      3 5—7 11 14 19
Lever, Archimedes' law of the      3
Lever, crooked      16 19
Lever, weightless      3
Lie, Sophus      167 168
Light, corpuscular theory of      91 94 95
Light, interfering beams of      94
Light, Newton's mechanistic theory of      91
Light, propagation of      81 163
Light, rays      75 81 94 133 134
Light, rays, bending of      81
Light, rectilinear propagation of      91 95
Light, speed of      137 152
LIMIT      15 67 69
Limit, relation      89
Limiting value, tending to a      32
Linear      112 114—116
Linear functions      142 143
1 2
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