Concise handbook of mathematics and physics:
Gespeichert in:
| Hauptverfasser: | , , |
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| Format: | Buch |
| Sprache: | English Russian |
| Veröffentlicht: |
Boca Raton [u.a.]
CRC Press [u.a.]
1997
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | 499 S. Ill., graph. Darst. |
| ISBN: | 0849377455 |
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| 100 | 1 | |a Alenitsyn, Alexander G. |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Concise handbook of mathematics and physics |c Alexander G. Alenitsyn ; Eugene I. Butikov ; Alexander S. Kondratyev |
| 264 | 1 | |a Boca Raton [u.a.] |b CRC Press [u.a.] |c 1997 | |
| 300 | |a 499 S. |b Ill., graph. Darst. | ||
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| 650 | 4 | |a Mathématiques - Guides, manuels, etc | |
| 650 | 4 | |a Physique - Guides, manuels, etc | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Mathematics |v Handbooks, manuals, etc | |
| 650 | 4 | |a Physics |v Handbooks, manuals, etc | |
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| 700 | 1 | |a Kondratyev, Alexander S. |e Verfasser |4 aut | |
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| adam_text | CONCISE HANDBOOK -OF MATHEMATICS AND PHYSICS ALEXANDER G.AIENITSYN
EUGENE I. BUTIKOV ALEXANDER S. KONDRATYEV CRC PRESS NAUKA PUBLISHERS
BOCA RATON NEW YORK FIZMATLIT, MOSCOW CONTENTS I MATHEMATICS 1 1 BASIC
NOTATIONS, FORMULAS, AND CONCEPTS 3 1.1 GENERAL RULES 3 1.1.1 SOME
NOTATIONS 3 1.1.2 THE RULES TO REMOVE BRACKETS 3 1.1.3 SHORT METHODS OF
MULTIPLICATION 4 1.1.4 FRACTIONS 5 1.1.5 THE RULES OF HANDLING WITH
FRACTIONS 5 1.1.6 FRACTIONAL EXPRESSIONS 7 1.1.7 PROPORTIONS 7 1.1.8
PERCENTAGE 8 1.2 DECIMAL FRACTIONS 8 1.2.1 INTRODUCTION 8 1.2.2 HANDLING
WITH DECIMAL FRACTIONS 8 1.2.3 NORMALIZED FORM OF NUMBERS 10 1.2.4
REPEATING DECIMALS . . . . 10 1.3 ROUNDING OFF NUMBERS. APPROXIMATE
NUMBERS 11 1.3.1 ROUNDING OFF 11 -- 1.3.2 APPROXIMATE NUMBERS 12 1.4 THE
MATHEMATICAL INDUCTION METHOD 13 2 SETS. REAL NUMBERS. FUNCTIONS 15 2.1
SETS 15 2.1.1 CONCEPT OF A SET 15 2.1.2 SUBSETS 16 2.1.3 INTERVALS 16
2.2 REAL NUMBERS 17 2.2.1 NATURAL NUMBERS 17 2.2.2 RATIONAL NUMBERS 19
2.2.3 IRRATIONAL NUMBERS 19 2.2.4 PROPERTIES OF ARITHMETIC OPERATIONS 19
2.3 FUNCTIONS 20 2.3.1 CONCEPT OF A FUNCTION 20 CONTENTS 2.3.2 VARIABLES
. , 20 2.3.3 GRAPH 21 2.4 BASIC CHARACTERISTICS OF FUNCTIONS 21 2.4.1
MONOTONICITY 21 2.4.2 PERIODICITY 23 2.4.3 EVENNESS AND ODDNESS 23 2.4.4
BOUNDEDNESS 24 2.5 INVERSE FUNCTIONS 24 2.5.1 DEFINITION 24 2.5.2
INVERSE FUNCTION FOR A MONOTONIC ONE 25 2.5.3 GRAPH OF THE INVERSE
FUNCTION 25 2.6 LINEAR AND QUADRATIC FUNCTIONS. MODULUS 25 2.6.1 LINEAR
FUNCTION 25 2.6.2 QUADRATIC FUNCTION 26 2.6.3 MODULUS 28 2.7 DEGREE
FUNCTION 29 2.8 EXPONENTIAL AND LOGARITHMIC FUNCTIONS 31 2.8.1
EXPONENTIAL FUNCTION 31 2.8.2 HYPERBOLIC FUNCTIONS 31 2.8.3 LOGARITHMIC
FUNCTION 32 EQUATIONS AND SYSTEMS OF EQUATIONS. INEQUALITIES 35 3.1
GENERAL CONCEPTS 35 3.1.1 CONCEPT OF THE EQUATION 35 3.1.2 MULTIPLICITY
OF A ROOT 36 3.1.3 EQUIVALENT EQUATIONS 36 3.1.4 EXTRANEOUS ROOTS 37 3.2
LINEAR AND QUADRATIC EQUATIONS 37 3.2.1 LINEAR EQUATION 37 3.2.2
QUADRATIC EQUATION 37 - 3.2.3 BIQUADRATIC EQUATION 39 3.3 POLYNOMIALS 39
3.3.1 DEFINITIONS 39 3.3.2 HORNER S METHOD 39 3.3.3 POLYNOMIAL ALGEBRA
40 3.3.4 FACTORIZATION OF A POLYNOMIAL 42 3.4 ALGEBRAIC EQUATIONS 43
3.4.1 ROOTS OF AN ALGEBRAIC EQUATION 43 3.4.2 ON GENERAL FORMULAS FOR
THE ROOTS 43 3.4.3 REDUCTION OF THE DEGREE OF A POLYNOMIAL 44 3.4.4
BINOMIAL ALGEBRAIC EQUATION 44 3.4.5 RATIONAL EQUATIONS 45 3.5
IRRATIONAL AND MODULUS EQUATIONS 45 3.5.1 IRRATIONAL EQUATIONS 45 3.5.2
MODULUS EQUATIONS 47 CONTENTS 3.6 SYSTEMS OF EQUATIONS 48 3.6.1 LINEAR
SYSTEM, TWO EQUATIONS 48 3.6.2 LINEAR SYSTEM, THREE EQUATIONS 49 3R6.3
^NONLINEAR SYSTEM 51 3.7 INEQUALITIES 52 3.7.1 DEFINITIONS 52 3.7.2
BASIC PROPERTIES OF INEQUALITIES 53 3.7.3 PROBLEMS RELATED WITH
INEQUALITIES . 54 3.7.4 DOMAIN OF DEFINITION 55 3.7.5 ALGEBRAIC
INEQUALITIES 55 3.7.6 IRRATIONAL INEQUALITIES 56 3.7.7 TRANSCENDENTAL
INEQUALITIES 57 3.7.8 INEQUALITIES WITH MODULUS SYMBOL 58 4 TRIGONOMETRY
59 4.1 TRIGONOMETRIC FUNCTIONS 59 4.1.1 TRIGONOMETRIC FUNCTIONS OF AN
ACUTE ANGLE 59 4.1.2 TRIGONOMETRIC FUNCTIONS OF ARBITRARY VALUES OF AR-
GUMENT 60 4.1.3 PROPERTIES OF THE TRIGONOMETRIC FUNCTIONS 62 4.2
FORMULAS OF TRIGONOMETRY 64 4.2.1 REDUCTION FORMULAS . 64 4.2.2 THE
BASIC FORMULAS OF TRIGONOMETRY 65 4.3 INVERSE TRIGONOMETRIC FUNCTIONS 66
4.3.1 ARCSINE 66 4.3.2 ARCCOSINE 67 4.3.3 ARCTANGENT 67 4.3.4
ARCCOTANGENT 67 4.3.5 FORMULAS FOR INVERSE TRIGONOMETRIC FUNCTIONS . .
. . 68 4.4 TRIGONOMETRIC EQUATIONS AND INEQUALITIES 69 4.4.1 SIMPLEST
TRIGONOMETRIC EQUATIONS 69 4.4.2 EQUATION REDUCIBLE TO THE SIMPLEST ONE
69 4.4.3 EQUATION A SIN X + B COS X = C 70 4.4.4 TRIGONOMETRIC
INEQUALITIES 71 5 ELEMENTS OF CALCULUS 73 5.1 SEQUENCES 73 5.1.1 CONCEPT
OF A SEQUENCE . 73 5.1.2 LIMIT OF A SEQUENCE 73 5.1.3 MONOTONIC AND
BOUNDED SEQUENCES. INFINITESIMAL SEQUENCES 75 5.1.4 INFINITE LIMIT 76
5.1.5 ARITHMETIC PROGRESSION AND SERIES 76 5.1.6 GEOMETRIC PROGRESSION
AND SERIES 77 5.1.7 INFINITELY DECREASING GEOMETRIC PROGRESSION 78
CONTENTS 5.1.8 THE NUMBER E - 80 5.2 LIMIT OF FUNCTION 80 5.2.1
DEFINITION AND THEOREMS 80 5.2.2 ONE-SIDE LIMITS , 82 5.2.3 INFINITE
LIMIT 82 5.2.4 LIMIT AT INFINITY 84 5.2.5 RULES TO CALCULATE THE LIMITS
OF FUNCTIONS 85 5.3 CONTINUITY OF FUNCTION. DISCONTINUITIES 88 5.3.1
CONTINUITY 88 5.3.2 DISCONTINUITIES 89 5.4 DERIVATIVE. DIFFERENTIATION
RULES 91 5.4.1 DERIVATIVE 91 5.4.2 DERIVATIVES OF HIGHER ORDER 92 5.4.3
APPLICATION OF DERIVATIVES 92 5.4.4 INFLECTION 93 5.4.5 DIFFERENTIATION
RULES 94 5.5 SOME DIFFERENTIAL EQUATIONS 95 5.5.1 INTRODUCTION 95 5.5.2
SOME SIMPLE DIFFERENTIAL EQUATIONS 96 5.5.3 SOME PROBLEMS RELATED TO
DIFFERENTIAL EQUATIONS . . 97 5.6 ANTIDERIVATIVE. INDEFINITE INTEGRAL 98
5.6.1 ANTIDERIVATIVE 98 5.6.2 INDEFINITE INTEGRAL 99 5.7 DEFINITE
INTEGRAL AND ITS APPLICATIONS 101 5.7.1 DEFINITION 101 5.7.2 PROPERTIES
OF THE DEFINITE INTEGRAL 103 5.7.3 IMPROPER INTEGRALS: INFINITE INTERVAL
104 5.7.4 IMPROPER INTEGRALS: DISCONTINUOUS FUNCTION 105 5.7.5 SOME
APPLICATIONS OF THE DEFINITE INTEGRAL 106 5.8 SOME INFORMATION ABOUT
SERIES 107 5.8.1 CONVERGENCE OF A SERIES 107 5.8.2 TESTS FOR CONVERGENCE
OF SERIES 108 5.8.3 SERIES WHOSE MEMBERS ARE OF ARBITRARY SIGN .... 109
5.8.4 POWER SERIES 109 COMBINATORICS 111 6.1 PERMUTATIONS. ARRANGEMENTS.
COMBINATIONS ILL 6.1.1 PERMUTATIONS ILL 6.1.2 FACTORIAL ILL 6.1.3
STIRLING FORMULA 112 6.1.4 SEMI-FACTORIAL 112 6.1.5 ARRANGEMENTS 112
6.1.6 COMBINATIONS 113 6.2 BINOMIAL FORMULA AND APPLICATIONS 113 6.2.1
BINOMIAL FORMULA 113 CONTENTS 6.2.2 PROPERTIES OF THE BINOMIAL
COEFFICIENTS 114 6.2.3 PASCAL TRIANGLE 114 6.2.4 SUM OF NATURAL NUMBERS
IN A CERTAIN POWER . . . . 115 7 COMPLEX NUMBERS 117 7.1 BASIC CONCEPTS
117 7.1.1 NOTATIONS 117 7.1.2 RULES TO OPERATE WITH COMPLEX NUMBERS 117
7.1.3 CONJUGATE NUMBERS 118 7.2 ALGEBRAIC FORM OF COMPLEX NUMBER 118 7.3
TRIGONOMETRIC AND EXPONENTIAL FORMS 119 7.3.1 VECTOR INTERPRETATION 119
7.3.2 MODULUS AND ARGUMENT OF A COMPLEX NUMBER . . . 120 7.3.3
TRIGONOMETRIC FORM 120 7.3.4 EXPONENTIAL FORM 122 7.3.5 EULER FORMULAS
122 7.3.6 DE MOIVRE FORMULA 123 7.3.7 ROOTS OF COMPLEX NUMBERS 124 7.4
LOGARITHMS OF COMPLEX NUMBERS 125 7.5 COMPLEX ROOTS OF EQUATIONS 125 8
VECTORS. COORDINATES. SYMMETRIES 127 8.1 VECTORS. PROJECTIONS 127 8.1.1
VECTORS 127 8.1.2 PROJECTIONS 130 8.1.3 EXPANSION IN UNIT VECTORS 131
8.2 SCALAR AND VECTOR PRODUCTS 132 8.2.1 SCALAR PRODUCT 132 8.2.2
VECTOR PRODUCT 133 8.3 COORDINATE SYSTEMS 135 8.3.1 COORDINATE AXIS 135
8.3.2 COORDINATE SYSTEM IN A PLANE 135 8.3.3 COORDINATE SYSTEMS IN SPACE
136 8.3.4 POLAR COORDINATES 138 8.4 DISPLACEMENT. SYMMETRY. SIMILARITY
139 8.4.1 DISPLACEMENT ., 139 8.4.2 SYMMETRY 140 8.4.3 SPATIAL SYMMETRY
. 142 8.4.4 SIMILARITY 143 9 GEOMETRY. STEREOMETRY 145 9.1 POINTS,
STRAIGHT LINES AND ANGLES IN A PLANE 145 9.1.1 POINTS AND STRAIGHT LINES
145 9.1.2 SEGMENT 146 9.1.3 ANGLE 146 CONTENTS 9.1.4 DEGREE 147 9.1.5
RADIAN 147 9.1.6 INTERSECTION OF STRAIGHT LINES 148 9.2 TRIANGLES.
POLYGONS 149 9.2.1 TRIANGLE 149 9.2.2 ELEMENTS OF A TRIANGLE 150 9.2.3
EQUAL TRIANGLES 151 9.2.4 SIMILAR TRIANGLES 153 9.2.5 FORMULAS FOR A
TRIANGLE 154 9.2.6 POLYGONS 155 9.2.7 PARALLELOGRAM 157 9.2.8 RHOMBUS
158 9.2.9 RECTANGLE 158 9.2.10 SQUARE 158 9.2.11 TRAPEZOID 159 9.3
CIRCLE, ELLIPSE, HYPERBOLA, PARABOLA 159 9.3.1 CIRCLE 159 9.3.2 ELLIPSE
161 9.3.3 HYPERBOLA 163 9.3.4 PARABOLA 164 9.3.5 CURVATURE OF A CURVE
164 9.4 PLANES AND STRAIGHT LINES IN SPACE 165 9.4.1 PARALLELISM OF
PLANES AND LINES 165 9.4.2 SKEW-LINES 165 9.4.3 PERPENDICULAR 166 9.4.4
ANGLE BETWEEN TWO PLANES 167 9.4.5 DIHEDRAL ANGLE 168 9.4.6 PROJECTION
OF A FIGURE ON A PLANE 168 9.5 POLYHEDRONS 169 _.- 9.5.1 POLYHEDRAL
SURFACE 169 9.5.2 POLYHEDRON 169 9.5.3 PRISM 169 9.5.4 PARALLELEPIPED
170 9.5.5 PYRAMID 171 9.5.6 FRUSTUM OF A PYRAMID 171 9.5.7 REGULAR
POLYHEDRONS 172 9.6 BODIES OF REVOLUTION 173 9.6.1 SURFACE OF REVOLUTION
173 9.6.2 CYLINDER 173 9.6.3 CONE . . 173 9.6.4 SPHERE 175 9.6.5
SPHERICAL SEGMENT 176 9.6.6 SPHERICAL SECTOR 176 9.6.7 SPHERICAL LAYER
177 CONTENTS 9.6.8 TORUS ****. 177 9.7 CURVATURE OF A SURFACE 178 10
NUMERICAL ANALYSIS 181 10.1 ROUNDING OFF AND ERRORS 181 10.2
APPROXIMATION OF FUNCTIONS 183 10.2.1 APPROXIMATE FORMULAS 183 10.2.2
FUNCTION GIVEN BY A TABLE 185 10.2.3 METHOD OF LEAST SQUARES 188 10.3
NUMERICAL INTEGRATION 189 10.3.1 TRAPEZOID RULE 190 10.3.2 FORMULA OF
RECTANGLES 191 10.3.3 SIMPSON S FORMULA 191 10.3.4 TAYLOR APPROXIMATION
193 10.3.5 IMPROPER INTEGRALS 193 10.4 APPROXIMATE SOLUTION OF EQUATIONS
194 10.4.1 BISECTION METHOD 194 10.4.2 ITERATION METHOD 194 10.4.3
NEWTON S METHOD 195 10.5 APPROXIMATE SOLUTION OF DIFFERENTIAL EQUATIONS
197 10.5.1 EULER S METHOD 197 10.5.2 RUNGE-KUTTA METHOD 198 11
PROBABILITY THEORY 199 11.1 RANDOM EVENTS AND PROBABILITIES 199 11.1.1
RANDOM EVENT 199 11.1.2 PROBABILITY 200 11.1.3 BERNOULLI FORMULA . . .
. 202 11.1.4 LARGE NUMBERS LAW 203 11.2 RANDOM VARIABLES AND
DISTRIBUTIONS 204 11.2.1 RANDOM VARIABLE 204 11.2.2 MEAN VALUE AND
DISPERSION 205 11 PHYSICS 207 12 PHYSICAL QUANTITIES AND SYSTEMS OF
UNITS 209 12.1 BASIC CONCEPTS. LAWS OF PHYSICS 209 12.1.1 PHYSICAL
QUANTITIES AND MEASUREMENTS 209 12.1.2 EQUATIONS IN PHYSICS 210 12.1.3
PHYSICAL-MODELS 210 12.2 SYSTEMS OF UNITS 211 12.2.1 BASE AND DERIVED
UNITS . . . 211 12.2.2 DIMENSIONS OF PHYSICAL QUANTITIES 211 12.2.3
STANDARDS OF BASE UNITS 213 CONTENTS 12.2 A UNITS OF MAGNETIC QUANTITIES
IN GAUSSIAN SYSTEM OF UNITS 214 12.2.5 UNITS OF MAGNETIC QUANTITIES IN
SI 215 12.2.6 RELATIONSHIP BETWEEN SI AND GAUSSIAN UNITS . . . . 217
12.3 THE METHOD OF DIMENSIONAL ANALYSIS 219 12.3.1 DIMENSIONLESS AND
DIMENSIONAL UNITS 219 12.3.2 EXAMPLE: VELOCITY IN FREE FALL 219 12.3.3
EXAMPLE: FLIGHT RANGE 220 12.3.4 EXAMPLE: VISCOUS FLOW 221 12.3.5
EXAMPLE: SPEED OF SOUND 222 12.3.6 EXAMPLE: VELOCITY OF WAVES 223 12.3.7
EXAMPLE: MICROSCOPIC MODEL OF A REAL GAS 224 12.3.8 EXAMPLE: TIME OF
RELAXATION IN A GAS 224 12.3.9 EXAMPLE: TIME OF RELAXATION IN PLASMA 225
12.3.10EXAMPLE: TEMPERATURE DEPENDENCE OF BLACK-BODY RADIATION 226 13
MECHANICS 227 13.1 KINEMATICS 228 13.1.1 KINEMATICS OF A PARTICLE 228
13.1.2 EXAMPLE: MOTION ALONG AN ELLIPSE 229 13.1.3 VELOCITY AND
ACCELERATION 229 13.1.4 TANGENTIAL AND RADIAL ACCELERATION 231 13.1.5
RECTILINEAR MOTION 231 13.1.6 CIRCULAR UNIFORM MOTION 233 13.1.7
KINEMATICS OF A RIGID BODY 233 13.1.8 ROTATION ABOUT A FIXED AXIS 234
13.1.9 PLANE MOTION OF A SOLID 234 13.L.LOROTATION ABOUT A FIXED POINT
236 13.2 DYNAMICS 236 * *- 13.2.1 BASIC CONCEPTS OF CLASSICAL DYNAMICS
236 13.2.2 MOMENTUM 239 13.2.3 DETERMINATION OF FORCE ON THE BASIS OF
GIVEN MOTION 240 13.2.4 MOTION CAUSED BY GIVEN FORCES 240 13.2.5
RESTRICTED MOTION 242 13.3 FORCES OF GRAVITATION, FRICTION, AND
ELASTICITY 243 13.3.1 THE LAW OF GRAVITATION 244 13.3.2 FRICTION AND
ELASTICITY 245 13.4 CONSERVATION LAWS 248 13.4.1 CONSERVATION OF
MOMENTUM 248 13.4.2 THE CENTER OF MASS 249 13.4.3 THE LAW OF MOTION OF
THE CENTER OF MASS 250 13.4.4 JET PROPULSION 251 13.4.5 WORK AND KINETIC
ENERGY 251 13.4.6 POTENTIAL ENERGY 252 CONTENTS 13.4.7 CONSERVATION OF
MECHANICAL ENERGY 254 13.4.8 COLLISIONS 255 13.5 MOTION IN A CENTRAL
GRAVITATIONAL FIELD 257 1-3.5.1_ KEPLER S LAWS OF PLANETARY MOTION 257
13.5.2 COSMIC VELOCITIES 258 13.5.3 EXAMPLE: ELLIPTIC ORBIT OF A
SATELLITE 259 13.6 MECHANICAL EQUILIBRIUM 260 13.6.1 CONDITIONS OF
EQUILIBRIUM 260 13.6.2 PLANE SYSTEM OF FORCES 261 13.6.3 EXAMPLE:
DETERMINATION OF FORCES OF REACTION . . . 261 13.6.4 STATICS AND ENERGY
CONSERVATION 263 13.6.5 THE STABILITY OF EQUILIBRIUM 263 13.7 DYNAMICS
OF A SOLID 264 13.7.1 THE PRINCIPAL LAWS 264 13.7.2 MOMENT OF INERTIA
265 13.7.3 ENERGY OF ROTATION 267 13.7.4 A GYROSCOPE 267 13.8
HYDROSTATICS 269 13.8.1 PRESSURE IN A LIQUID 269 13.8.2 HYDROSTATIC
PRESSURE 270 13.8.3 ARCHIMEDES PRINCIPLE AND BUOYANT FORCE 271 13.8.4
MEASUREMENT OF DENSITY 271 13.8.5 FLOATING ON THE SURFACE 272 13.9
HYDRODYNAMICS 273 13.9.1 EQUATION OF CONTINUITY 273 13.9.2 BERNOULLI S
PRINCIPLE 274 13.9.3 MOTION OF A VISCOUS FLUID 276 13.9.4 TURBULENT FLOW
OF VISCOUS FLUID 279 14 MOLECULAR PHYSICS 281 *14.1 PRINCIPLES OF
THERMODYNAMICS 282 14.1.1 THERMAL EQUILIBRIUM 282 14.1.2 PARAMETERS OF
THE EQUILIBRIUM STATE 283 14.1.3 EQUATION OF STATE FOR THE IDEAL GAS 284
14.1.4 GAS THERMOMETER 286 14.1.5 COMPONENTS AND PHASES * 286 14.1.6
REVERSIBLE AND IRREVERSIBLE PROCESSES 287 14.1.7 INTERNAL ENERGY 287
14.1.8 HEAT CAPACITY 288 14.1.9 ISOPROCESSES IN THE IDEAL GAS 289
14.1.10 EFFICIENCYOF A HEAT ENGINE 290 14.1.11 THE SECOND LAW OF
THERMODYNAMICS 291 14.1.12 A REFRIGERATOR MACHINE 293
14.1.13THERMODYNAMIC TEMPERATURE 293 14.1.14 ENTHROPY 294 CONTENTS 14.2
THE PRINCIPLES OF STATISTICAL MECHANICS 295 14.2.1 THERMAL MOTION 295
14.2.2 MOLECULAR INTERACTION 296 14.2.3 AMOUNT OF SUBSTANCE 297 14.2.4
KINETIC THEORY OF AN IDEAL GAS 297 14.3 STATISTICAL DISTRIBUTIONS 299
14.3.1 DISTRIBUTIONS OF DIFFERENT QUANTITIES 299 14.3.2 MAXWELL
DISTRIBUTION 300 14.3.3 PROBABILITIES 301 14.3.4 CALCULATION OF MEAN
VALUES 301 14.3.5 BOLTZMANN DISTRIBUTION 302 14.3.6 FLUCTUATIONS 303
14.3.7 PHYSICAL REASONS FOR IRREVERSIBILITY 304 14.3.8 STATISTICAL
MEANING OF ENTHROPY 304 14.4 REAL GASES 305 14.4.1 VAN DER VAALS
EQUATION 305 14.4.2 EXPERIMENTAL ISOTHERMS AND PHASE TRANSITIONS . . .
306 14.4.3 PHASE TRANSITIONS 307 14.4.4 HUMIDITY OF AIR 308 14.4.5
EQUILIBRIUM OF PHASES 309 14.5 LIQUIDS 310 14.5.1 SURFACE TENSION 310
14.5.2 CAPILLARY PHENOMENA 311 14.6 SOLIDS 313 14.6.1 CRYSTALS AND
AMORPHOUS BODIES 313 14.6.2 ELASTIC DEFORMATIONS 313 14.6.3 THERMAL
EXPANSION 316 14.7 HEAT EXCHANGE. PHASE TRANSITIONS 318 14.7.1 THERMAL
CAPACITY 318 * - 14.7.2 HEAT OF COMBUSTION 319 14.7.3 LATENT HEAT OF
PHASE TRANSITIONS 319 15 ELECTRICITY AND MAGNETISM 321 15.1
ELECTROSTATICS : 321 15.1.1 INTERACTION OF ELECTRIC CHARGES 321 15.1.2
ELECTROSTATIC FIELD 322 15.1.3 ELECTROSTATIC FIELD IN DIELECTRICS 326
15.1.4 ELECTRIC FIELD NEAR CONDUCTORS 326 15.1.5 CAPACITORS 327 15.1.6
CONNECTION OF CAPACITORS 328 15.1.7 ENERGY OF ELECTRIC FIELD 329 15.2
ELECTRIC CURRENT 330 15.2.1 OHM S LAW 330 15.2.2 SERIES AND PARALLEL
CONNECTION OF RESISTORS 332 15.2.3 MEASUREMENTS IN DIRECT CURRENT
CIRCUITS 333 CONTENTS 15.2.4 CIRCUIT WITH A SOURCE 335 15.2.5
KIRCHHOFF S RULES 336 15.2.6 THE WORK OF ELECTRIC CURRENT 338 15.2.7 A
POWER SOURCE IN A CIRCUIT 339 15.2.8 FARADAY S LAWS OF ELECTROLYSIS 341
15.3 MAGNETIC FIELD 341 15.3.1 INDUCTION OF MAGNETIC FIELD 341 15.3.2
AMPERE S FORCE AND LORENTZ FORCE 343 15.3.3 MAGNETIC FIELD ENERGY 344
15.3.4 MAGNETIC FIELD IN SUBSTANCES 345 15.4 ELECTROMAGNETIC INDUCTION
345 15.4.1 FARADAY S LAW 345 15.4.2 INDUCTANCE 346 15.5 ALTERNATING
ELECTRIC CURRENT (AC) 347 15.5.1 AC IN CIRCUITS WITH ONE ELEMENT 347
15.5.2 SERIES HLC-CIRCUIT 349 15.5.3 PARALLEL FLLC-CIRCUIT 350 15.5.4
IMPEDANCE OF A CIRCUIT 351 15.5.5 RESONANCE OF VOLTAGES AND RESONANCE OF
CURRENTS . 353 15.5.6 POWER OF ALTERNATING CURRENT 353 15.5.7
TRANSFORMER 354 15.6 ELECTROMAGNETIC FIELD 355 15.6.1 RELATIVE CHARACTER
OF ELECTRIC AND MAGNETIC FIELDS . 355 15.6.2 INVARIANTS OF
ELECTROMAGNETIC FIELD 356 15.6.3 MAXWELL S EQUATIONS 356 16 OSCILLATIONS
AND WAVES ( 359 16.1 CLASSIFICATION OF OSCILLATIONS 359 16.2 HARMONIC
OSCILLATIONS 361 16.2.1 KINEMATICS OF SIMPLE HARMONIC MOTION 361 16.2.2
VECTOR DIAGRAMS FOR HARMONIC OSCILLATIONS 362 16.3 NATURAL OSCILLATIONS
OF SIMPLE SYSTEMS 363 16.3.1 DIFFERENTIAL EQUATION OF HARMONIC
OSCILLATOR . . . . 363 16.3.2 INITIAL CONDITIONS 364 16.3.3
TRANSFORMATIONS OF ENERGY IN OSCILLATIONS 365 16.3.4 NONLINEAR FREE
OSCILLATIONS 366 16.3.5 DAMPED NATURAL OSCILLATIONS 367 16.3.6 DAMPING
BY DRY FRICTION 370 16.4 FORCED OSCILLATIONS. RESONANCE 370 16.4.1
STEADY-STATE FORCED OSCILLATIONS 370 16.4.2 RESONANCE, CURVES OF LINEAR
OSCILLATOR 372 16.4.3 RESONANCE OF VELOCITY 374 16.4.4 ENERGY IN FORCED
OSCILLATIONS 374 16.4.5 TRANSIENT PROCESSES 375 16.4.6 NON-SINUSOIDAL
EXTERNAL FORCE 375 CONTENTS 16.5 PARAMETRIC RESONANCE. SELF-EXCITED
OSCILLATIONS 376 16.5.1 PARAMETRIC EXCITATION OF OSCILLATIONS 376 16.5.2
SELF-EXCITED OSCILLATIONS 378 16.6 OSCILLATIONS OF COMPLEX SYSTEMS.
COMPOSITION OF OSCILLA- TIONS 380 16.6.1 DEGENERATE OSCILLATORY SYSTEMS
380 16.6.2 NORMAL OSCILLATIONS (MODES) 381 16.6.3 COUPLED PENDULUMS 382
16.6.4 FORCED OSCILLATIONS OF COUPLED PENDULUMS 384 16.6.5 COUPLED
ELECTROMAGNETIC CIRCUITS 386 16.6.6 STANDING WAVES AS NORMAL
OSCILLATIONS 386 16.7 WAVES 388 16.7.1 WAVES OF DIFFERENT PHYSICAL
NATURE 388 16.7.2 POLARIZATION OF WAVES 388 16.7.3 KINEMATICS OF WAVE
MOTION 389 16.7.4 THE SPEED OF WAVES 391 16.7.5 ENERGY TRANSFERRED BY
WAVES 393 16.7.6 PLANE, SPHERICAL, AND CYLINDRICAL WAVES 394 16.7.7
REFLECTION AND REFRACTION OF WAVES 395 16.7.8 INTERFERENCE OF WAVES 395
16.7.9 STANDING WAVES 397 16.7.10 DIFFRACTION OF WAVES 398 16.7.11
DOPPLER EFFECT 398 16.7.12 ELECTROMAGNETIC WAVES 401 16.7.13WAVESON THE
WATER 404 16.7.14SPEED OF WAVE PACKETS 406 17 OPTICS 409 17.1
GEOMETRICAL OPTICS 409 17.1.1 THE PRINCIPAL LAWS 409 17.1.2 PLANE
MIRRORS 413 17.1.3 PARAXIAL APPROXIMATION AND OPTICAL IMAGES . . . . 414
17.1.4 SPHERICAL MIRRORS 415 17.1.5 LENSES 417 17.2 OPTICAL INSTRUMENTS
420 17.2.1 CAMERA 420 17.2.2 DIASCOPE 421 17.2.3 MAGNIFYING GLASS 422
17.2.4 MICROSCOPE 423 17.2.5 TELESCOPE 425 17.3 INTERFERENCE OF LIGHT
426 17.3.1 INTERFERENCE AND COHERENT LIGHT 426 17.3.2 INTERFERENCE
FRINGES 427 17.3.3 YOUNG S DOUBLE-SLIT EXPERIMENT 428 17.3.4 LOCALIZED
INTERFERENCE PATTERNS 430 CONTENTS 17.3.5 MULTIPLE-RAY INTERFERENCE 433
17.3.6 THE ENLIGHTENMENT OF OPTICAL SYSTEMS 434 17.4 DIFFRACTION OF
LIGHT 434 17.4.1 THE HUYGENS-FRESNEL PRINCIPLE 434 17.4.2 DIFFRACTION
SPREADING OF A PARALLEL LIGHT BEAM . . . 434 17.4.3 FRESNEL DIFFRACTION
437 17.4.4 FRAUNHOFER DIFFRACTION 438 17.4.5 DIFFRACTION GRATING 439
17.4.6 DISPERSION SPECTROMETER 441 17.4.7 HOLOGRAPHY 442 17.4.8
PHOTOMETRY 444 18 RELATIVISTIC AND QUANTUM PHYSICS 447 18.1 THE THEORY
OF RELATIVITY 447 18.2 RELATIVISTIC KINEMATICS 448 18.2.1 GALILEAN
TRANSFORMATION 448 18.2.2 INSUFFICIENCY OF CLASSICAL CONCEPTS 449 18.2.3
MAIN PRINCIPLES OF THE THEORY OF RELATIVITY 450 18.2.4 THE RELATIVITY OF
SIMULTANEITY. TIME DILATION AND LORENTZ CONTRACTION 451 18.2.5 LORENTZ
TRANSFORMATIONS 452 18.2.6 RELATIVISTIC INTERVAL 453 18.3 RELATIVISTIC
DYNAMICS 454 18.3.1 RELATIVISTIC MOMENTUM AND ENERGY 454 18.3.2 MASS AND
ENERGY 455 18.3.3 RELATIVISTIC KINETIC ENERGY 456 18.3.4 RELATIVISTIC
TRANSFORMATION OF ENERGY AND MO- MENTUM 457 18.3.5 EXAMPLE: ACCELERATION
BY A CONSTANT FORCE 457 18.3.6 EXAMPLE: RELATIVISTIC PARTICLE IN
MAGNETIC FIELD . . 458 18.3.7 TRANSMUTATIONS OF ELEMENTARY PARTICLES 459
18.4 THE PRINCIPLES OF QUANTUM PHYSICS 460 18.4.1 UNCERTAINTY RELATIONS
460 18.4.2 WAVE-PARTICLE DUALTY 462 18.4.3 RANGE OF VALIDITY OF
CLASSICAL THEORY 463 18.4.4 QUANTA OF LIGHT*PHOTONS 463 18.4.5
PHOTOELECTRIC EFFECT 464 18.4.6 LIGHT PRESSURE 465 18.4.7 DOPPLER EFFECT
465 18.4.8 COMPTON EFFECT 465 18.5 THE STRUCTURE OF AN ATOM 466 18.5.1
BOHR S MODEL OF THE HYDROGEN ATOM 466 18.5.2 ELECTRON SHELLS 468 18.5.3
LIGHT RADIATION OF AN ATOM 470 18.5.4 BLACK-BODY RADIATION 470 CONTENTS
18.6 ATOMIC NUCLEUS 471 18.6.1 COMPOSITION OF ATOMIC NUCLEI 471 18.6.2
RADIOACTIVE DECAY 474 18.6.3 NUCLEAR REACTIONS 474 18.7 ELEMENTARY
PARTICLES 476 APPENDIX 479 I FUNDAMENTAL PHYSICAL CONSTANTS 479 II
PHYSICAL QUANTITIES AND THEIR SI UNITS 480 III CONVERSION OF GAUSSIAN
UNITS INTO SI UNITS 483 IV CONVERSION OF NON-SYSTEM UNITS INTO SI UNITS
484 V MAIN FORMULAS OF ELECTRODYMAMICS IN GAUSSIAN UNITS AND IN SI UNITS
485 VI ATOMIC ELEMENTS AND THEIR MASSES 487 VII TABLE OF ELEMENTARY
PARTICLES 488 VIII DECIMA L MULTIPLES TO BE USED WITH SI UNITS 489 IX
RELATIONS BETWEEN FUNDAMENTAL CONSTANTS (IN GAUSSIAN SYSTEM OF UNITS)
489 X TABLE OF MATHEMATICAL SYMBOLS 490 INDEX 491
|
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| author | Alenitsyn, Alexander G. Butikov, Eugene I. Kondratyev, Alexander S. |
| author_facet | Alenitsyn, Alexander G. Butikov, Eugene I. Kondratyev, Alexander S. |
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| building | Verbundindex |
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| callnumber-first | Q - Science |
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| ctrlnum | (OCoLC)37004438 (DE-599)BVBBV011442648 |
| dewey-full | 530 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 530 - Physics |
| dewey-raw | 530 |
| dewey-search | 530 |
| dewey-sort | 3530 |
| dewey-tens | 530 - Physics |
| discipline | Physik Mathematik |
| format | Book |
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| genre_facet | Einführung |
| id | DE-604.BV011442648 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T18:09:51Z |
| institution | BVB |
| isbn | 0849377455 |
| language | English Russian |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-007696206 |
| oclc_num | 37004438 |
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| physical | 499 S. Ill., graph. Darst. |
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| publisher | CRC Press [u.a.] |
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| spelling | Alenitsyn, Alexander G. Verfasser aut Concise handbook of mathematics and physics Alexander G. Alenitsyn ; Eugene I. Butikov ; Alexander S. Kondratyev Boca Raton [u.a.] CRC Press [u.a.] 1997 499 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathématiques - Guides, manuels, etc Physique - Guides, manuels, etc Mathematik Mathematics Handbooks, manuals, etc Physics Handbooks, manuals, etc Mathematik (DE-588)4037944-9 gnd rswk-swf Physik (DE-588)4045956-1 gnd rswk-swf Mathematische Physik (DE-588)4037952-8 gnd rswk-swf (DE-588)4151278-9 Einführung gnd-content Mathematische Physik (DE-588)4037952-8 s DE-604 Physik (DE-588)4045956-1 s Mathematik (DE-588)4037944-9 s Butikov, Eugene I. Verfasser aut Kondratyev, Alexander S. Verfasser aut GBV Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007696206&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Alenitsyn, Alexander G. Butikov, Eugene I. Kondratyev, Alexander S. Concise handbook of mathematics and physics Mathématiques - Guides, manuels, etc Physique - Guides, manuels, etc Mathematik Mathematics Handbooks, manuals, etc Physics Handbooks, manuals, etc Mathematik (DE-588)4037944-9 gnd Physik (DE-588)4045956-1 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4045956-1 (DE-588)4037952-8 (DE-588)4151278-9 |
| title | Concise handbook of mathematics and physics |
| title_auth | Concise handbook of mathematics and physics |
| title_exact_search | Concise handbook of mathematics and physics |
| title_full | Concise handbook of mathematics and physics Alexander G. Alenitsyn ; Eugene I. Butikov ; Alexander S. Kondratyev |
| title_fullStr | Concise handbook of mathematics and physics Alexander G. Alenitsyn ; Eugene I. Butikov ; Alexander S. Kondratyev |
| title_full_unstemmed | Concise handbook of mathematics and physics Alexander G. Alenitsyn ; Eugene I. Butikov ; Alexander S. Kondratyev |
| title_short | Concise handbook of mathematics and physics |
| title_sort | concise handbook of mathematics and physics |
| topic | Mathématiques - Guides, manuels, etc Physique - Guides, manuels, etc Mathematik Mathematics Handbooks, manuals, etc Physics Handbooks, manuals, etc Mathematik (DE-588)4037944-9 gnd Physik (DE-588)4045956-1 gnd Mathematische Physik (DE-588)4037952-8 gnd |
| topic_facet | Mathématiques - Guides, manuels, etc Physique - Guides, manuels, etc Mathematik Mathematics Handbooks, manuals, etc Physics Handbooks, manuals, etc Physik Mathematische Physik Einführung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=007696206&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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