Concise Handbook of Mathematics and Physics

by Alenitsyn; Alexander G.

• ISBN13: 9780849377457
• ISBN10: 0849377455
• Format: Hardcover
• Copyright: 1997-05-12
• Publisher: CRC Press

Summary

Concise Handbook of Mathematics and Physics presents a unified and coherent treatment of all the major aspects of modern elementary physics and mathematics. This complete text/reference includes definitions of fundamental notations and physical and mathematical quantities, formulas that express the laws of physics, axioms and theorems of mathematics, and more. The information is organized logically (instead of alphabetically) for better comprehension and quick, convenient access.The book contains extensive cross-referencing between the mathematical and physical sections. reflecting the considerable overlap between these two areas of study and increasing the usefulness of this handbook. Fundamental concepts, theorems, and laws are demonstrated through numerous practical examples and tasks to help build problem-solving skills.

Table of Contents

I MATHEMATICS	1	(206)
1 Basic Notations, Formulas, and Concepts	3	(12)
1.1 General Rules	3	(5)
1.1.1 Some notations	3	(1)
1.1.2 The rules to remove brackets	3	(1)
1.1.3 Short methods of multiplication	4	(1)
1.1.4 Fractions	5	(1)
1.1.5 The rules of handling with fractions	5	(2)
1.1.6 Fractional expressions	7	(1)
1.1.7 Proportions	7	(1)
1.1.8 Percentage	8	(1)
1.2 Decimal Fractions	8	(3)
1.2.1 Introduction	8	(1)
1.2.2 Handling with decimal fractions	8	(2)
1.2.3 Normalized form of numbers	10	(1)
1.2.4 Repeating decimals	10	(1)
1.3 Rounding off Numbers. Approximate Numbers	11	(2)
1.3.1 Rounding off	11	(1)
1.3.2 Approximate numbers	12	(1)
1.4 The Mathematical Induction Method	13	(2)
2 Sets. Real Numbers. Functions	15	(20)
2.1 Sets	15	(2)
2.1.1 Concept of a set	15	(1)
2.1.2 Subsets	16	(1)
2.1.3 Intervals	16	(1)
2.2 Real Numbers	17	(3)
2.2.1 Natural numbers	17	(2)
2.2.2 Rational numbers	19	(1)
2.2.3 Irrational numbers	19	(1)
2.2.4 Properties of arithmetic operations	19	(1)
2.3 Functions	20	(1)
2.3.1 Concept of a function	20	(1)
2.3.2 Variables	20	(1)
2.3.3 Graph	21	(1)
2.4 Basic Characteristics of Functions	21	(3)
2.4.1 Monotonicity	21	(2)
2.4.2 Periodicity	23	(1)
2.4.3 Evenness and oddness	23	(1)
2.4.4 Boundedness	24	(1)
2.5 Inverse Functions	24	(1)
2.5.1 Definition	24	(1)
2.5.2 Inverse function for a monotonic one	25	(1)
2.5.3 Graph of the inverse function	25	(1)
2.6 Linear and Quadratic Functions. Modulus	25	(4)
2.6.1 Linear function	25	(1)
2.6.2 Quadratic function	26	(2)
2.6.3 Modulus	28	(1)
2.7 Degree Function	29	(2)
2.8 Exponential and Logarithmic Functions	31	(4)
2.8.1 Exponential function	31	(1)
2.8.2 Hyperbolic functions	31	(1)
2.8.3 Logarithmic function	32	(3)
3 Equations and Systems of Equations. Inequalities	35	(24)
3.1 General Concepts	35	(2)
3.1.1 Concept of the equation	35	(1)
3.1.2 Multiplicity of a root	36	(1)
3.1.3 Equivalent equations	36	(1)
3.1.4 Extraneous roots	37	(1)
3.2 Linear and Quadratic Equations	37	(2)
3.2.1 Linear equation	37	(1)
3.2.2 Quadratic equation	37	(2)
3.2.3 Biquadratic equation	39	(1)
3.3 Polynomials	39	(4)
3.3.1 Definitions	39	(1)
3.3.2 Horner's method	39	(1)
3.3.3 Polynomial algebra	40	(2)
3.3.4 Factorization of a polynomial	42	(1)
3.4 Algebraic Equations	43	(2)
3.4.1 Roots of an algebraic equation	43	(1)
3.4.2 On general formulas for the roots	43	(1)
3.4.3 Reduction of the degree of a polynomial	44	(1)
3.4.4 Binomial algebraic equation	44	(1)
3.4.5 Rational equations	45	(1)
3.5 Irrational and Modulus Equations	45	(3)
3.5.1 Irrational equations	45	(2)
3.5.2 Modulus equations	47	(1)
3.6 Systems of Equations	48	(4)
3.6.1 Linear system, two equations	48	(1)
3.6.2 Linear system, three equations	49	(2)
3.6.3 Nonlinear system	51	(1)
3.7 Inequalities	52	(7)
3.7.1 Definitions	52	(1)
3.7.2 Basic properties of inequalities	53	(1)
3.7.3 Problems related with inequalities	54	(1)
3.7.4 Domain of definition	55	(1)
3.7.5 Algebraic inequalities	55	(1)
3.7.6 Irrational inequalities	56	(1)
3.7.7 Transcendental inequalities	57	(1)
3.7.8 Inequalities with modulus symbol	58	(1)
4 Trigonometry	59	(14)
4.1 Trigonometric Functions	59	(5)
4.1.1 Trigonometric functions of an acute angle	59	(1)
4.1.2 Trigonometric functions of arbitrary values of argument	60	(2)
4.1.3 Properties of the trigonometric functions	62	(2)
4.2 Formulas of Trigonometry	64	(2)
4.2.1 Reduction formulas	64	(1)
4.2.2 The basic formulas of trigonometry	65	(1)
4.3 Inverse Trigonometric Functions	66	(3)
4.3.1 Arcsine	66	(1)
4.3.2 Arccosine	67	(1)
4.3.3 Arctangent	67	(1)
4.3.4 Arccotangent	67	(1)
4.3.5 Formulas for inverse trigonometric functions	68	(1)
4.4 Trigonometric Equations and Inequalities	69	(4)
4.4.1 Simplest trigonometric equations	69	(1)
4.4.2 Equation reducible to the simplest one	69	(1)
4.4.3 Equation a sin x + b cos x = c	70	(1)
4.4.4 Trigonometric inequalities	71	(2)
5 Elements of Calculus	73	(38)
5.1 Sequences	73	(7)
5.1.1 Concept of a sequence	73	(1)
5.1.2 Limit of a sequence	73	(2)
5.1.3 Monotonic and bounded sequences. Infinitesimal sequences	75	(1)
5.1.4 Infinite limit	76	(1)
5.1.5 Arithmetic progression and series	76	(1)
5.1.6 Geometric progression and series	77	(1)
5.1.7 Infinitely decreasing geometric progression	78	(2)
5.1.8 The number "e"	80	(1)
5.2 Limit of Function	80	(8)
5.2.1 Definition and theorems	80	(2)
5.2.2 One-side limits	82	(1)
5.2.3 Infinite limit	82	(2)
5.2.4 Limit at infinity	84	(1)
5.2.5 Rules to calculate the limits of functions	85	(3)
5.3 Continuity of Function. Discontinuities	88	(3)
5.3.1 Continuity	88	(1)
5.3.2 Discontinuities	89	(2)
5.4 Derivative. Differentiation Rules	91	(4)
5.4.1 Derivative	91	(1)
5.4.2 Derivatives of higher order	92	(1)
5.4.3 Application of derivatives	92	(1)
5.4.4 Inflection	93	(1)
5.4.5 Differentiation rules	94	(1)
5.5 Some Differential Equations	95	(3)
5.5.1 Introduction	95	(1)
5.5.2 Some simple differential equations	96	(1)
5.5.3 Some problems related to differential equations	97	(1)
5.6 Antiderivative. Indefinite Integral	98	(3)
5.6.1 Antiderivative	98	(1)
5.6.2 Indefinite integral	99	(2)
5.7 Definite Integral and its Applications	101	(6)
5.7.1 Definition	101	(2)
5.7.2 Properties of the definite integral	103	(1)
5.7.3 Improper integrals: infinite interval	104	(1)
5.7.4 Improper integrals: discontinuous function	105	(1)
5.7.5 Some applications of the definite integral	106	(1)
5.8 Some Information about Series	107	(4)
5.8.1 Convergence of a series	107	(1)
5.8.2 Tests for convergence of series	108	(1)
5.8.3 Series whose members are of arbitrary sign	109	(1)
5.8.4 Power series	109	(2)
6 Combinatorics	111	(6)
6.1 Permutations. Arrangements. Combinations	111	(2)
6.1.1 Permutations	111	(1)
6.1.2 Factorial	111	(1)
6.1.3 Stirling formula	112	(1)
6.1.4 Semi-factorial	112	(1)
6.1.5 Arrangements	112	(1)
6.1.6 Combinations	113	(1)
6.2 Binomial Formula and Applications	113	(4)
6.2.1 Binomial formula	113	(1)
6.2.2 Properties of the binomial coefficients	114	(1)
6.2.3 Pascal triangle	114	(1)
6.2.4 Sum of natural numbers in a certain power	115	(2)
7 Complex Numbers	117	(10)
7.1 Basic Concepts	117	(1)
7.1.1 Notations	117	(1)
7.1.2 Rules to operate with complex numbers	117	(1)
7.1.3 Conjugate numbers	118	(1)
7.2 Algebraic Form of Complex Number	118	(1)
7.3 Trigonometric and Exponential Forms	119	(6)
7.3.1 Vector interpretation	119	(1)
7.3.2 Modulus and argument of a complex number	120	(1)
7.3.3 Trigonometric form	120	(2)
7.3.4 Exponential form	122	(1)
7.3.5 Euler formulas	122	(1)
7.3.6 De Moivre formula	123	(1)
7.3.7 Roots of complex numbers	124	(1)
7.4 Logarithms of Complex Numbers	125	(1)
7.5 Complex Roots of Equations	125	(2)
8 Vectors. Coordinates. Symmetries	127	(18)
8.1 Vectors. Projections	127	(5)
8.1.1 Vectors	127	(3)
8.1.2 Projections	130	(1)
8.1.3 Expansion in unit vectors	131	(1)
8.2 Scalar and Vector Products	132	(3)
8.2.1 Scalar product	132	(1)
8.2.2 Vector product	133	(2)
8.3 Coordinate Systems	135	(4)
8.3.1 Coordinate axis	135	(1)
8.3.2 Coordinate system in a plane	135	(1)
8.3.3 Coordinate systems in space	136	(2)
8.3.4 Polar coordinates	138	(1)
8.4 Displacement. Symmetry. Similarity	139	(6)
8.4.1 Displacement	139	(1)
8.4.2 Symmetry	140	(2)
8.4.3 Spatial symmetry	142	(1)
8.4.4 Similarity	143	(2)
9 Geometry. Stereometry	145	(36)
9.1 Points, Straight Lines and Angles in a Plane	145	(4)
9.1.1 Points and straight lines	145	(1)
9.1.2 Segment	146	(1)
9.1.3 Angle	146	(1)
9.1.4 Degree	147	(1)
9.1.5 Radian	147	(1)
9.1.6 Intersection of straight lines	148	(1)
9.2 Triangles. Polygons	149	(10)
9.2.1 Triangle	149	(1)
9.2.2 Elements of a triangle	150	(1)
9.2.3 Equal triangles	151	(2)
9.2.4 Similar triangles	153	(1)
9.2.5 Formulas for a triangle	154	(1)
9.2.6 Polygons	155	(2)
9.2.7 Parallelogram	157	(1)
9.2.8 Rhombus	158	(1)
9.2.9 Rectangle	158	(1)
9.2.10 Square	158	(1)
9.2.11 Trapezoid	159	(1)
9.3 Circle, Ellipse, Hyperbola, Parabola	159	(6)
9.3.1 Circle	159	(2)
9.3.2 Ellipse	161	(2)
9.3.3 Hyperbola	163	(1)
9.3.4 Parabola	164	(1)
9.3.5 Curvature of a curve	164	(1)
9.4 Planes and Straight Lines in Space	165	(4)
9.4.1 Parallelism of planes and lines	165	(1)
9.4.2 Skew-lines	165	(1)
9.4.3 Perpendicular	166	(1)
9.4.4 Angle between two planes	167	(1)
9.4.5 Dihedral angle	168	(1)
9.4.6 Projection of a figure on a plane	168	(1)
9.5 Polyhedrons	169	(4)
9.5.1 Polyhedral surface	169	(1)
9.5.2 Polyhedron	169	(1)
9.5.3 Prism	169	(1)
9.5.4 Parallelepiped	170	(1)
9.5.5 Pyramid	171	(1)
9.5.6 Frustum of a pyramid	171	(1)
9.5.7 Regular polyhedrons	172	(1)
9.6 Bodies of Revolution	173	(5)
9.6.1 Surface of revolution	173	(1)
9.6.2 Cylinder	173	(1)
9.6.3 Cone	173	(2)
9.6.4 Sphere	175	(1)
9.6.5 Spherical segment	176	(1)
9.6.6 Spherical sector	176	(1)
9.6.7 Spherical layer	177	(1)
9.6.8 Torus	177	(1)
9.7 Curvature of a Surface	178	(3)
10 Numerical Analysis	181	(18)
10.1 Rounding off and Errors	181	(2)
10.2 Approximation of Functions	183	(6)
10.2.1 Approximation formulas	183	(2)
10.2.2 Function given by a table	185	(3)
10.2.3 Method of least squares	188	(1)
10.3 Numerical Integration	189	(5)
10.3.1 Trapezoid rule	190	(1)
10.3.2 Formula of rectangles	191	(1)
10.3.3 Simpson's formula	191	(2)
10.3.4 Taylor approximation	193	(1)
10.3.5 Improper integrals	193	(1)
10.4 Approximate Solution of Equations	194	(3)
10.4.1 Bisection method	194	(1)
10.4.2 Iteration method	194	(1)
10.4.3 Newton's method	195	(2)
10.5 Approximate Solution of Differential Equations	197	(2)
10.5.1 Euler's method	197	(1)
10.5.2 Runge-Kutta method	198	(1)
11 Probability Theory	199	(8)
11.1 Random Events and Probabilities	199	(5)
11.1.1 Random event	199	(1)
11.1.2 Probability	200	(2)
11.1.3 Bernoulli formula	202	(1)
11.1.4 Large numbers' law	203	(1)
11.2 Random Variables and Distributions	204	(3)
11.2.1 Random variable	204	(1)
11.2.2 Mean value and dispersion	205	(2)
II PHYSICS	207	(272)
12 Physical Quantities and Systems of Units	209	(18)
12.1 Basic Concepts. Laws of Physics	209	(2)
12.1.1 Physical quantities and measurements	209	(1)
12.1.2 Equations in physics	210	(1)
12.1.3 Physical models	210	(1)
12.2 Systems of Units	211	(8)
12.2.1 Base and derived units	211	(1)
12.2.2 Dimensions of physical quantities	211	(2)
12.2.3 Standards of base units	213	(1)
12.2.4 Units of magnetic quantities in Gaussian system of units	214	(1)
12.2.5 Units of magnetic quantities in SI	215	(2)
12.2.6 Relationship between SI and Gaussian units	217	(2)
12.3 The Method of Dimensional Analysis	219	(8)
12.3.1 Dimensionless and dimensional units	219	(1)
12.3.2 Example: velocity in free fall	219	(1)
12.3.3 Example: flight range	220	(1)
12.3.4 Example: viscous flow	221	(1)
12.3.5 Example: speed of sound	222	(1)
12.3.6 Example: velocity of waves	223	(1)
12.3.7 Example: microscopic model of a real gas	224	(1)
12.3.8 Example: time of relaxation in a gas	224	(1)
12.3.9 Example: time of relaxation in plasma	225	(1)
12.3.10 Example: temperature dependence of black-body radiation	226	(1)
13 Mechanics	227	(54)
13.1 Kinematics	228	(8)
13.1.1 Kinematics of a particle	228	(1)
13.1.2 Example: motion along an ellipse	229	(1)
13.1.3 Velocity and acceleration	229	(2)
13.1.4 Tangential and radial acceleration	231	(1)
13.1.5 Rectilinear motion	231	(2)
13.1.6 Circular uniform motion	233	(1)
13.1.7 Kinematics of a rigid body	233	(1)
13.1.8 Rotation about a fixed axis	234	(1)
13.1.9 Plane motion of a solid	234	(2)
13.1.10 Rotation about a fixed point	236	(1)
13.2 Dynamics	236	(7)
13.2.1 Basic concepts of classical dynamics	236	(3)
13.2.2 Momentum	239	(1)
13.2.3 Determination of force on the basis of given motion	240	(1)
13.2.4 Motion caused by given forces	240	(2)
13.2.5 Restricted motion	242	(1)
13.3 Forces of Gravitation, Friction, and Elasticity	243	(5)
13.3.1 The law of gravitation	244	(1)
13.3.2 Friction and elasticity	245	(3)
13.4 Conservation Laws	248	(9)
13.4.1 Conservation of momentum	248	(1)
13.4.2 The Center of mass	249	(1)
13.4.3 The law of motion of the center of mass	250	(1)
13.4.4 Jet propulsion	251	(1)
13.4.5 Work and kinetic energy	251	(1)
13.4.6 Potential energy	252	(2)
13.4.7 Conservation of mechanical energy	254	(1)
13.4.8 Collisions	255	(2)
13.5 Motion in a Central Gravitational Field	257	(3)
13.5.1 Kepler's laws of planetary motion	257	(1)
13.5.2 Cosmic velocities	258	(1)
13.5.3 Example: elliptic orbit of a satellite	259	(1)
13.6 Mechanical Equilibrium	260	(4)
13.6.1 Conditions of equilibrium	260	(1)
13.6.2 Plane system of forces	261	(1)
13.6.3 Example: determination of forces of reaction	261	(2)
13.6.4 Statics and energy conservation	263	(1)
13.6.5 The stability of equilibrium	263	(1)
13.7 Dynamics of a Solid	264	(5)
13.7.1 The principal laws	264	(1)
13.7.2 Moment of inertia	265	(2)
13.7.3 Energy of rotation	267	(1)
13.7.4 A gyroscope	267	(2)
13.8 Hydrostatics	269	(4)
13.8.1 Pressure in a liquid	269	(1)
13.8.2 Hydrostatic pressure	270	(1)
13.8.3 Archimedes' principle and buoyant force	271	(1)
13.8.4 Measurement of density	271	(1)
13.8.5 Floating on the surface	272	(1)
13.9 Hydrodynamics	273	(8)
13.9.1 Equation of continuity	273	(1)
13.9.2 Bernoulli's principle	274	(2)
13.9.3 Motion of a viscous fluid	276	(3)
13.9.4 Turbulent flow of viscous fluid	279	(2)
14 Molecular Physics	281	(40)
14.1 Principles of Thermodynamics	282	(13)
14.1.1 Thermal equilibrium	282	(1)
14.1.2 Parameters of the equilibrium state	283	(1)
14.1.3 Equation of state for the ideal gas	284	(2)
14.1.4 Gas thermometer	286	(1)
14.1.5 Components and phases	286	(1)
14.1.6 Reversible and irreversible processes	287	(1)
14.1.7 Internal energy	287	(1)
14.1.8 Heat capacity	288	(1)
14.1.9 Isoprocesses in the ideal Gas	289	(1)
14.1.10 Efficiency of a heat engine	290	(1)
14.1.11 The second law of thermodynamics	291	(2)
14.1.12 A refrigerator machine	293	(1)
14.1.13 Thermodynamic temperature	293	(1)
14.1.14 Enthropy	294	(1)
14.2 The Principles of Statistical Mechanics	295	(4)
14.2.1 Thermal motion	295	(1)
14.2.2 Molecular interaction	296	(1)
14.2.3 Amount of substance	297	(1)
14.2.4 Kinetic theory of an ideal gas	297	(2)
14.3 Statistical Distributions	299	(6)
14.3.1 Distributions of different quantities	299	(1)
14.3.2 Maxwell distribution	300	(1)
14.3.3 Probabilities	301	(1)
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	(38)
15.1 Electrostatics	321	(9)
15.1.1 Interaction of electric charges	321	(1)
15.1.2 Electrostatic field	322	(4)
15.1.3 Electrostatic field in dielectrics	326	(1)
15.1.4 Electric field near conductors	326	(1)
15.1.5 Capacitors	327	(1)
15.1.6 Connection of capacitors	328	(1)
15.1.7 Energy of electric field	329	(1)
15.2 Electric Current	330	(11)
15.2.1 Ohm's law	330	(1)
15.2.2 Series and parallel connection of resistors	332	(1)
15.2.3 Measurements in direct current circuits	333	(2)
15.2.4 Circuit with a source	335	(1)
15.2.5 Kirchhoff's rules	336	(2)
15.2.6 The work of electric current	338	(1)
15.2.7 A power source in a circuit	339	(2)
15.2.8 Faraday's laws of electrolysis	341	(1)
15.3 Magnetic Field	341	(4)
15.3.1 Induction of magnetic field	341	(2)
15.3.2 Ampere's force and Lorentz' force	343	(1)
15.3.3 Magnetic field energy	344	(1)
15.3.4 Magnetic field in substances	345	(1)
15.4 Electromagnetic Induction	345	(2)
15.4.1 Faraday's law	345	(1)
15.4.2 Inductance	346	(1)
15.5 Alternating Electric Current (AC)	347	(8)
15.5.1 AC in circuits with one element	347	(2)
15.5.2 Series RLC-circuit	349	(1)
15.5.3 Parallel RLC-circuit	350	(1)
15.5.4 Impedance of a circuit	351	(2)
15.5.5 Resonance of voltages and resonance of currents	353	(1)
15.5.6 Power of alternating current	353	(1)
15.5.7 Transformer	354	(1)
15.6 Electromagnetic Field	355	(4)
15.6.1 Relative character of electric and magnetic fields	355	(1)
15.6.2 Invariants of electromagnetic field	356	(1)
15.6.3 Maxwell's equations	356	(3)
16 Oscillations and Waves	359	(50)
16.1 Classification of Oscillations	359	(2)
16.2 Harmonic Oscillations	361	(2)
16.2.1 Kinematics of simple harmonic motion	361	(1)
16.2.2 Vector diagrams for harmonic oscillations	362	(1)
16.3 Natural Oscillations of Simple Systems	363	(7)
16.3.1 Differential equation of harmonic oscillator	363	(1)
16.3.2 Initial conditions	364	(1)
16.3.3 Transformations of energy in oscillations	365	(1)
16.3.4 Nonlinear free oscillations	366	(1)
16.3.5 Damped natural oscillations	367	(3)
16.3.6 Damping by dry friction	370	(1)
16.4 Forced oscillations. Resonance	370	(6)
16.4.1 Steady-state forced oscillations	370	(2)
16.4.2 Resonance curves of linear oscillator	372	(2)
16.4.3 Resonance of velocity	374	(1)
16.4.4 Energy in forced oscillations	374	(1)
16.4.5 Transient processes	375	(1)
16.4.6 Non-sinusoidal external force	375	(1)
16.5 Parametric Resonance. Self-Excited Oscillations	376	(4)
16.5.1 Parametric excitation of oscillations	376	(2)
16.5.2 Self-excited oscillations	378	(2)
16.6 Oscillations of Complex Systems. Composition of Oscillations	380	(8)
16.6.1 Degenerate oscillatory systems	380	(1)
16.6.2 Normal oscillations (modes)	381	(1)
16.6.3 Coupled pendulums	382	(2)
16.6.4 Forced oscillations of coupled pendulums	384	(2)
16.6.5 Coupled electromagnetic circuits	386	(1)
16.6.6 Standing waves as normal oscillations	386
16.7 Waves	388	(21)
16.7.1 Waves of different physical nature	388	(1)
16.7.2 Polarization of waves	388	(1)
16.7.3 Kinematics of wave motion	389	(2)
16.7.4 The speed of waves	391	(2)
16.7.5 Energy transferred by waves	393	(1)
16.7.6 Plane, spherical, and cylindrical waves	394	(1)
16.7.7 Reflection and refraction of waves	395	(1)
16.7.8 Interference of waves	395	(2)
16.7.9 Standing waves	397	(1)
16.7.10 Diffraction of waves	398	(1)
16.7.11 Doppler effect	398	(3)
16.7.12 Electromagnetic waves	401	(3)
16.7.13 Waves on the water	404	(2)
16.7.14 Speed of wave packets	406	(3)
17 Optics	409
17.1 Geometrical Optics	409	(11)
17.1.1 The principal laws	409	(4)
17.1.2 Plane mirrors	413	(1)
17.1.3 Paraxial approximation and optical images	414	(1)
17.1.4 Spherical mirrors	415	(2)
17.1.5 Lenses	417	(3)
17.2 Optical Instruments	420	(6)
17.2.1 Camera	420	(1)
17.2.2 Diascope	421	(1)
17.2.3 Magnifying glass	422	(1)
17.2.4 Microscope	423	(2)
17.2.5 Telescope	425	(1)
17.3 Interference of Light	426	(8)
17.3.1 Interference and coherent light	426	(1)
17.3.2 Interference fringes	427	(1)
17.3.3 Young's double-slit experiment	428	(2)
17.3.4 Localized interference patterns	430	(3)
17.3.5 Multiple-ray interference	433	(1)
17.3.6 The enlightenment of optical systems	434	(1)
17.4 Diffraction of Light	434	(13)
17.4.1 The Huygens-Fresnel principle	434	(1)
17.4.2 Diffraction spreading of a parallel light beam	434	(3)
17.4.3 Fresnel diffraction	437	(1)
17.4.4 Fraunhofer diffraction	438	(1)
17.4.5 Diffraction grating	439	(2)
17.4.6 Dispersion spectrometer	441	(1)
17.4.7 Holography	442	(2)
17.4.8 Photometry	444	(3)
18 Relativistic and Quantum Physics	447	(32)
18.1 The Theory of Relativity	447	(1)
18.2 Relativistic Kinematics	448	(6)
18.2.1 Galilean transformation	448	(1)
18.2.2 Insufficiency of classical concepts	449	(1)
18.2.3 Main principles of the theory of relativity	450	(1)
18.2.4 The relativity of simultaneity. Time dilation and Lorentz contraction	451	(1)
18.2.5 Lorentz transformations	452	(1)
18.2.6 Relativistic interval	453	(1)
18.3 Relativistic Dynamics	454	(6)
18.3.1 Relativistic momentum and energy	454	(1)
18.3.2 Mass and energy	455	(1)
18.3.3 Relativistic kinetic energy	456	(1)
18.3.4 Relativistic transformation of energy and momentum	457	(1)
18.3.5 Example: acceleration by a constant force	457	(1)
18.3.6 Example: relativistic particle in magnetic field	458	(1)
18.3.7 Transmutations of elementary particles	459	(1)
18.4 The Principles of Quantum Physics	460	(6)
18.4.1 Uncertainty relations	460	(2)
18.4.2 Wave-particle dualty	462	(1)
18.4.3 Range of validity of classical theory	463	(1)
18.4.4 Quanta of light--photons	463	(1)
18.4.5 Photoelectric effect	464	(1)
18.4.6 Light pressure	465	(1)
18.4.7 Doppler effect	465	(1)
18.4.8 Compton effect	465	(1)
18.5 The Structure of an Atom	466	(5)
18.5.1 Bohr's model of the hydrogen atom	466	(2)
18.5.2 Electron shells	468	(2)
18.5.3 Light radiation of an atom	470	(1)
18.5.4 Black-body radiation	470	(1)
18.6 Atomic Nucleus	471	(5)
18.6.1 Composition of atomic nuclei	471	(3)
18.6.2 Radioactive decay	474	(1)
18.6.3 Nuclear reactions	474	(2)
18.7 Elementary Particles	476	(3)
APPENDIX	479	(12)
I Fundamental Physical Constants	479	(1)
II Physical Quantities and their SI Units	480	(3)
III Conversion of Gaussian Units into SI Units	483	(1)
IV Conversion of Non-system Units into SI Units	484	(1)
V Main Formulas of Electrodymamics in Gaussian Units and in SI Units	485	(2)
VI Atomic Elements and their Masses	487	(1)
VII Table of Elementary Particles	488	(1)
VIII Decimal Multiples to be Used with SI Units	489	(1)
IX Relations between Fundamental Constants (in Gaussian system of units)	489	(1)
X Table of Mathematical Symbols	490	(1)
Index	491