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Fundamental Formulas of Physics (Volume-1) by Donald H. Menzel



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Fundamental Formulas of Physics (Volume-1) written by Donald H. Menzel , Harvard College Observatory, Cambridge, Mass. A survey of physical scientists, made several years ago, indicated the need for a comprehensive reference book on the fundamental formulas of mathematical physics. Such a book, the survey showed, should be broad, covering, in addition to basic physics, certain cross-field disciplines where physics touches upon chemistry, astronomy, meteorology, biology, and electronics. The present volume represents an attempt to fill the indicated need. I am deeply indebted to the individual authors, who have contributed time and effort to select and assemble formulas within their special fields. Each author has had full freedom to organize his material in a form most suitable for the subject matter covered. In consequence, the styles and modes of presentation exhibit wide variety. Some authors considered a mere listing of the basic formulas as giving ample coverage. Others felt the necessity of adding appreciable explanatory text.


Fundamental Formulas of Physics (Volume-1) written by Donald H. Menzel cover the following topics.


  • 1: BASIC MATHEMATICAL FORMULAS by Philip Franklin
    1. ALGEBRA
    1.1. Quadratic equations
    1.2. Logarithms
    1.3. Binomial theorem
    1.4. Multinomial theorem
    1.5. Proportion
    1.6. Progressions
    1.7. Algebraic equations
    1.8. Determinants
    1.9. Linear equations
    2. TRIGONOMETRY
    2.1. Angles
    2.2. Trigonometric functions
    2.3. Functions of sums and differences
    2.4. Addition theorems
    2.5. Multiple angles
    2.6. Direction cosmes
    2.7. Plane right triangle
    2.8. Amplitude and phase
    2.9. Plane oblique triangle
    2.10. Spherical right triangle
    2.11. Spherical oblique triangle
    2.12. Hyperbolic functions
    2.13. Functions of sums and differences
    2.14. Multiple arguments
    2.15. Sine,cosine,and complex exponential function
    2.16. Trigonometric and hyperbolic functions
    2.17. Sine and cosine of complex arguments
    2.18. Inverse functions and logarithms
    3. DIFFERENTIAL CALCULUS
    3.1. The derivative
    3.2. Higher derivatives
    3.3. Partial derivatives
    3.4. Derivatives of functions
    3.5. Products
    3.6. Powers and quotients
    3.7. Logarithmic differentiation
    3.8. Polynomials
    3.9. Exponentials and logarithms
    3.10. Trigonometric functions
    3.11. Inverse trigonometric functions
    3.12. Hyperbolic functions
    3.13. Inverse hyperbolic functions
    3.14. Differential
    3.15. Total differential
    3.16. Exact differential
    3.17. Maximum and minimum values
    3.18. Points of inflection
    3.19. Increasing absolute value
    3.20. Arc length
    3.21. Curvature
    3.22. Acceleration In plane motion
    3.23. Theorem of the mean
    3.24. Indeterminate forms
    3.25. Taylor
    s theorem
    3.26. Differentiation of integrals
    4. INTEGRAL CALCULUS
    4.1. Indefinite integral
    4.2. Indefinite integrals of functions
    4.3. Polynomials
    4.4. Simple rational fractions
    4.5. Rational functions
    4.6. Trigonometric functions
    4.7. Exponential and hyperbolic functions
    4.8. Radicals
    4.9. Products
    4~10. Trigonometric or exponential integrands
    4.11. Algebraic integrands
    4.12. Definite integral
    4.13. Approximation rules
    4.14. Linearity properties
    4.15. Mean values
    4.16. Inequalities
    4.17. Improper integrals
    4.18. Definite integrals of functions
    4.19. Plane area
    4.20. Length of arc
    4.21. Volumes
    4.22. Curves and surfaces in space.
    4.23. Change of variables In multiple integrals
    4.24. Mass and density
    4.25. Moment and center of gravity
    4.26. Moment of inertia and radius of gyration
    5. DIFFERENTIAL EQUATIONS
    5.1. Classification
    5.2. Solutions
    5.3. First order and first degree
    5.4. Variables separable
    5.5. Linear in y
    5.6. Reducible to linear
    5.7. Homogeneous
    5.8. Exact equations
    5.9. First order and higher degree
    5.10. Equations solvable for p
    5.11. Clairaut
    s form
    5.12. Second order
    5.13. Linear equations
    5.14. Constant coefficients
    5.15. Undetermined coefficients
    5.16. Variation of parameters
    5.17. The Cauchy - Euler "homogeneous linear equation "
    5.18. Simultaneous differential equations
    5.19. First order partial differential equations
    5.20. Second order partial differential equations
    5.21. Runge-Kutta method of finding numerical solutions
    6. VECTOR ANALYSIS
    6.1. Scalars
    6.2. Vectors
    6.3. Components
    6.4. Sums and products by scalars
    6.5. The scalar or dot product, Vi
    V2
    6.6. The vector or cross product,Vi X V
    6.7. The triple scalar product
    6.8. The derivative
    6.9. The Frenet formulas
    6.10. Curves with parameter t
    6.11. Relative motion
    6.12. The symbolic vector del
    6.13. The divergence theorem
    6.14. Green
    s theorem in a plane
    6.15. Stokes
    s theorem
    6.16. Curvilinear coordinates
    6.17. Cylindrical coordinates
    6.18. Spherical coordinates
    6.19. Parabolic coordinates
    7. TENSORS
    7.1. Tensors of the second rank
    7.2. Summation convention
    7.3. Transformation of components
    7.4. Matrix notation
    7.5. Matrix products
    7.6. Linear vector operation
    7.7. Combined operators
    7.8. Tensors from vectors
    7.9. Dyadics
    7.10. Conjugate tensor Symmetry
    7.11. Unit, orthogonal, unitary
    7.12. Principal axes of a symmetric tensor
    7.13. Tensors in n-dimensions
    7.14. Tensors of any rank
    7.15. The fundamental tensor
    7.16. Christoffel three-index symbols
    7.17. Curvature tensor
    8. SPHERICAL HARMONICS
    8.1. Zonal harmonics
    8.2. Legendre polynomials
    8.3. Rodrigues
    s formula
    8.4. Particular values
    8.5. Trigonometric polynomia1s .............. 52
    8.6. Generating functions
    8.7. Recursion formula and orthogonality
    8.8. Laplace
    s integral
    8.9. Asymptotic expression
    8.10. Tesseral harmonics
    8.11. Legendre
    s associated functions
    8.12. Particular values
    8.13. Recursion formulas
    8.14. Asymptotic expression
    8.15. Addition theorem
    8.16. Orthogonality
    9. BESSEL FUNCTIONS
    9.1. Cylindrical harmonics.
    9.2. Bessel functions of the first kind
    9.3. Bessel functions of the second kind
    9.4. Hankel functions
    9.5. Bessel
    s differential equation.
    9.6. Equation reducible to Bessel
    s
    9.7. Asymptotic expressions.
    9.8. Order half an odd integer
    9.9. Integral representation.
    9.10. Recursion formula.
    9.11. Derivatives
    9.12. Generating function
    9.13. Indefinite integrals
    9.14. Modified Bessel functions
    10. THE HYPERGEOMETRIC FUNCTION
    10.1. The hypergeometric equation
    10.2. The hypergeometric senes
    10.3. Contiguous functions
    10.4. Elementary functions
    10.5. Other functions
    10.6. Special relations
    10.7. Jacobi polynomials or hypergeometric polynomials
    10.8. Generalized hypergeometric functions
    10.9. The confluent hypergeometric function
    11. LAGUERRE FUNCTIONS
    11.1. Laguerre polynomials
    11.2. Generating function
    11.3. Recursion formula
    11.4. Laguerre functions
    11.5. Associated Laguerre polynomials
    11.6. Generating function
    11.7. Associated Laguerre functions
    12. HERMITE FUNCTIONS
    12.1. Hermite polynomials
    12.2. Generating function
    12.J. Recursion formula
    12.4. Hermite functions
    13. MISCELLANEOUS FUNCTIONS
    13.1. The gamma function.
    13.2. Functional equations
    13.3. Special values
    13.4. Logarithmic derivative
    13.5. Asymptotic expressions
    13.6. Stirling
    s formula
    13.7. The beta function
    13.8. Integrals
    13.9. The error integral
    13.10. The Riemann zeta function
    14. SERIES
    14.1. Bernoulli numbers
    14.2. Positive powers
    14.3. Negative powers
    14.4. Euler - Maclaurin sum formula
    14.5. Power series
    14.6. Elementary functions
    14.7. Integrals
    14.8. Expansions III rational fractions
    14.9. Infinite products for the sine and cosine
    14.10. Fourier
    s theorem for periodic functions
    14.11. Fourier series on an interval
    14.12. Half-range Fourier senes
    14.13. Particular Fourier senes
    14.14. ComplexFourierseries
    14.15. The Fourier integral theorem
    14.16. Fourier transforms
    14.17. Laplace transforms
    14.18. Poisson
    s formula.
    14.19. Orthogonal functions
    14.20. Weight functions.
    15. ASYMPTOTIC EXPANSIONS
    15.1. Asymptotic expansion
    15.2. Borel
    s expansion
    15.3. Steepest descent
    16. LEAST SQUARES
    16.1. Principle of least squares
    16.2. Weights
    16.3. Direct observations
    16.4. Linear equations
    16.5. Curve fitting
    16.6. Nonlinear equations
    17. STATISTICS
    17.1. Average
    17.2. Median
    17.3. Derived averages
    17.4. Deviations
    17.5. Normallaw
    17.6. Standard deviation
    17.7. Mean absolute error
    17.8. Probable error
    17.9. Measure of dispersion
    17.10. Poisson
    s distribution
    17.11. Correlation coefficient
    18. MATRICES
    18.1. Matrix
    18.2. Addition
    18.3. Multiplication
    18.4. Linear transformations
    18.5. Transposed matrix
    18.6. Inverse matrix
    19. GROUP THEORY
    18.7. Symmetry
    18.8. Linear equations
    18.9. Rank
    18.10. Diagonalization of matrices
    19.1. Group
    19.2. Quotients
    19.3. Order
    19.4. Abelian group
    19.5. Isomorphy
    19.6. Subgroup
    19.7. Normal divisor
    19.8. Representation
    19.9. Three-dimensional rotation group
    20. ANALYTIC FUNCTIONS
    20.1. Definitions
    20.2. Properties
    20.3. Integrals
    20.4. Laurent expansion
    20.5. Laurentexpansionabout infinity
    20.6. Residues
    21. INTEGRAL EQUATIONS
    21.1. Fredholm integral equations
    21.2. Symmetric kernel
    21.3. Volterra integral equations
    21.4. The Abel integral equation
    21.5. Green
    s function
    21.6. The Sturm - Liouville differential equations
    21.7. Examples of Green
    s function

  • 2: statistics by Joseph M. Cameron
    1. INTRODUCTION
    1.1. Characteristics of a measurement process
    1.2. Statistical estimation
    1.3. Notation
    2. STANDARD DISTRIBUTIONS
    2.1. The normal distribution
    2.2. Additive property
    2.3. The logarithmic-normal distribution
    2.4. Rectangular distribution
    2.5. The X" distribution
    2.6. Student
    s t distribution.
    2.7. The F distribution
    2.8. Binomial distribution
    2.9. Poisson distribution
    3. ESTIMATORS OF THE LIMITING MEAN
    3.1. The average or arithmetic mean
    3.2. The weighted average
    3.3. The median
    4. MEASURES OF DISPERSION
    4.1. The standard deviation
    4.2. The variance s" = nL (Xi - x)"/(n - 1)
    4.3. Average deviation, 1 n - L IXi -x I
    4.4. Range: difference between largest and smallest value in a set of observations, (n) = X(I)
    5. THE FITTING OF STRAIGHT LINES
    5.1. Introduction 116
    5.2. The case of the underlying physical law
    6. LINEAR REGRESSION
    6.1. Linear regression
    7. THE FITTING OF POLYNOMIALS
    7.1. Unequal intervals between The X
    s
    7.2. The case of equal intervals between the x
    sthe method of orthogonal polynomials
    7.3. Fitting the coefficients of a function of several variables
    7.4. Multiple regression
    8. ENUMERATIVE STATISTICS
    8.1. Estimator of parameter of binomial distribution
    8.2. Estimator of parameter of Poisson distribution
    8.3. Rank correlation coefficient
    9. INTERVAL ESTIMATION
    9.1. Confidence interval for parameters
    9.2. Confidence interval for the mean of a normal distribution
    9.3. Confidence interval for the standard deviation
    9.4. Confidence interval for slope of straight line
    9.5. Confidence interval for intercept of a straight line
    9.6. Tolerance limits
    10. STATISTICAL TESTS OF HYPOTHESIS
    10.1. Introduction
    10.2. Test of whether the means of two normal mean of a normal distribution IS greater a specified value
    10.3. Test of whether the mean of a normal distribution IS different from some specified value
    10.4. Test of whether the mean of one normal distribution is greater than the mean of normal distribution
    10.5. Test of whether the means of two normal distributions differ
    10.6. Tests concerning the parameters ofa linear law
    10.7. Test of the homogeneity of a set of variances
    10.8. Test of homogeneity of a set of averages
    10.9. Test of whether a correlation coefficient is different from zero.
    10.10. Test of whether the correlation coeffianother is equal to a specified value
    11. ANALYSIS OF VARIANCE
    11.1. Analysis of variance
    12. DESIGN OF EXPERIMENTS
    12.1. Design of experiments
    13. PRECISION AND ACCURACY
    13.1. Introduction
    13.2. Measure of precision
    14. LAW OF PROPAGATION OF ERROR
    14.1. Introduction
    14.2. Standard deviation of a ratio of normally distributed variables
    13.3, Measurement of accuracy
    14.3. Standard deviation of a product of normally distributed variables

  • 3: NOMOGRAMS by Donald H. Menzel
    1. NOMOGRAPHIC SOLUTIONS
    1.1. A nomogram (or nomograph)

  • 4: PHYSICAL CONSTANTS by Jesse W. M. DuMond and E. Richard Cohen
    1. CONSTANTS AND CONVERSION FACTORS ,OF ATOMIC AND NUCLEAR PHYSICS
    2. TABLE OF LEAST-SQUARES-ADJUSTED OUTPUT VALUES

  • 5: CLASSICAL MECHANICS by Henry Zatzkis
    1. MECHANICS OF A SINGLE MASS POINT AND A SYSTEM OF MASS POINTS
    1.1. Newton
    s laws of motion and fundamental motions
    1.2. Special cases
    1.3. Conservation laws
    1.4. Lagrange equations of the second kind for arbitrary curvilinear coordinates
    1.5. The canonical equations of motion
    1.6. Poisson brackets
    1.7. Variational principles
    1.8. Canonical transformations
    1.9. Infinitesimal contact transformations
    1.10. Cyclic variables
    1.11. Transition to wave mechanics. The opticalmechanical analogy
    1.12. The Lagrangian and Hamiltonian formalism for continuous systems and fields

  • 6: SPECIAL THEORY OF RELATIVITy by Henry Zatzkis
    1. THE KINEMATICS OF THE SPACE-TIME CONTINUUM
    1.1. The Minkowski "world"
    1.2. The Lorentz transformation
    1.3. Kinematic consequences of the Lorentz transformation.
    2. DYNAMICS
    2.1. Conservation laws
    2.2. Dynamics of a free mass point
    2.3. Relativistic force
    2.4. Relativistic dynamics
    2.5. Gauge invariance
    2.6. Transformation laws for the field strengths
    2.7. Electrodynamics in moving, isotropic ponderable media (Minkowski's equation)
    2.8. Field of a uniformly moving point charge in empty space. Force between point charges moving with the same constant velocity ....
    2.9. The stress energy tensor and its relation to the conservation laws
    3. MISCELLANEOUS ApPLICATIONS
    3.1. Theponderomotiveequation
    3.2. Application to electron optics
    3.3. Sommerfeld
    s theory of the hydrogen fine structure
    4. SPINOR CALCULUS
    4.1. Algebraic properties
    4.2. Connection between spinors and world tensors
    4.3. Transformation laws for mixed spinors of second rank.Relation between spinor and Lorentz transformations
    4.4. Dual tensors
    4.5. Electrodynamics of empty space in spinor form
    5. FUNDAMENTAL RELATIVISTIC INVARIANTS

  • 7: THE GENERAL THEORY OF RELATIVITY by Henry Zatzkis
    1. MATHEMATICAL BASIS OF GENERAL RELATIVITY "
    1.1. Mathematical introduction
    1.2. The field equations
    1.3. The variational principle
    1.4. The ponderomotive law
    1.5. The Schwarzschild solution
    1.6. The three "Einstein effects"

  • 8: HYDRODYNAMICS AND AERODYNAMICS by Max M. Munk
    1. ASSUMPTIONS AND DEFINITIONS
    2. KINEMATICS
    3. HYDROSTATICS
    4. FORCES AND STRESSES
    5. THERMODYNAMICS
    6. DYNAMIC EQUATIONS
    7. EQUATIONS OF CONTINUITY FOR STEADY POTENTIAL FLOW OF NONVISCOUS FLUIDS
    8. PARTICULAR SOLUTIONS OF LAPLACE
    S EQUATION
    9. ApPARENT ADDITIONAL MASS
    10. AIRSHIP THEORY
    11. WING PROFILE CONTOURS; Two-DIMENSIONAL FLOW WITH CIRCULATION
    12. AIRFOILS IN THREE DIMENSIONS
    13. THEORY OF A UNIFORMLY LOADED PROPELLER DISK
    14. FREE SURFACES
    15. VORTEX MOTION
    16. WAVES
    17. MODEL RULES
    18. VISCOSITy
    19. GAS FLOW, ONE- AND Two-DIMENSIONAL
    20. GAS FLOWS, THREE DIMENSIONAL
    21. HYPOTHETICAL GASES
    22. SHOCKWAVES
    23. COOLING
    24. BOUNDARY LAYERS

  • 9: BOUNDARY VALUE PROBLEMS IN MATHEMATICAL PHySICS by Henry Zatzkis
    1. THE SIGNIFICANCE OF THE BOUNDARY
    1.1. Introductory remarks
    1.2. The Laplace equation
    1.3. Method of separation of variables
    1.4. Method of integral equations
    1.5. Method of Green
    s function
    1.6. Additional remarks about The two - dimensional Area " 251"
    1.7. The one - dimensional wave equation
    1.8. The general eigenvalue problem and the higher dimensional wave equation
    1.9. Heat conduction equation
    1.10. Inhomogeneous differential equations

  • 10: HEAT AND THERMODYNAMICS by Percy W. Bridgman
    1. FORMULAS OF THERMODYNAMICS
    1.1. Introduction
    1.2. The laws of thermodynamics
    1.3. The variables
    1.4. One-component systems
    1.5. One-component, usually two-phase systems
    1.6. Transitions of higher orders
    1.7. Equations of state
    1.8. One - component, twovariable systems, with dW = Xdy
    1.9. One - component, twovariable systems, with dW = Xdy
    1.10. One-component, multivariable systems, with dW = ~ X,dy,
    1.11. Multicomponent, multivariable systems, dW = pdv
    1.12. Homogeneous systems
    1.13. Heterogeneous systems

  • 11: STATISTICAL MECHANICS by Donald H. Menzel
    1. STATISTICS OF MOLECULAR ASSEMBLIES
    1.1. Partition functions
    1.2. Equations of state
    1.3. Energies and specific heats of a one-component assembly
    1.4. Adiabatic processes
    1.5. Maxwell
    s and Boltzmann
    s laws
    1.6. Compound and dissociating assemblies
    1.7. Vapor pressure
    1.8. Convergence of partition functions
    1.9. Fermi-Dirac and BoseEinstein statistics
    1.10. Relativistic degeneracy
    1.11. Dissociation law for new statistics
    1.12. Pressure of a degener ate gas
    1.13. Statistics oflight quanta

  • 12: KINETIC THEORY OF GASES: VISCOSITY, THERMAL CONDUCTION, AND DIFFUSION by Sydney Chapman
    1. PRELIMINARY DEFINITIONS AND EQUATIONS FOR A MIXED GAS, NOT IN EQUILIBRIUM
    1.1. Definition of r, x, y, Z, t, dr
    1.2. Definition of m, n, P, nlO, nu, mo
    1.3. The external forces F, X, Y, Z,.p
    1.4. Definition of c, u, v, w, de
    1.5. The velocity distribution functionj
    1.6. Mean values of velocity functions
    1.7. The mean mass velocity co; u o, v o, Woo
    1.8. The random velocity C; U, V, W; dC
    1.9. The "heat" energy of a molecule E: its mean value E
    1.10. The molecular weight Wand the constants mu , NC
    1.11. The constants J, k, R
    1.12. The kinetic theory temperature T
    1.13. The symbols cv , C v
    1.14. The stress distribution, P.XJ P.o
    1.15. The hydrostatic pressure P; the partial pressures PI
    P2
    1.16. Boltzmann
    s equation for f
    1.17. Summational invariants
    1.18. Boltzmann
    s H theorem
    2. RESULTS FOR A GAS IN EQUILIBRIUM
    2.1. Maxwell
    s steady-state solutions
    2.2. Mean values when f is Maxwellian
    2.3. The equation of state for a perfect gas
    2.4. Specific heats
    2.5. Equation of state for an imperfect gas
    2.6. The free path, collision frequency, collision interval, and collision energy (perfect gas)
    3. NONUNIFORM GAS
    3.1. The second approximation to f
    3.2. The stress distribution
    3.3. Diffusion
    3.4. Thermal conduction
    4. THE GAS COEFFICIENTS FOR PARTICULAR MOLECULAR MODELS
    4.1. Models a to d
    4.2. Viscosity /1- and thermal conductivity ,\ for a simple gas
    4.3. The first approximation to D ,2
    4.4. Thermal diffusion
    5. ELECTRICAL CONDUCTIVITY IN A NEUTRAL IONIZED GAS WITH OR WITHOUT A MAGNETIC FIELD
    5.1. Definitions and symbols
    5.2. The diameters as
    5.3. Slightly ionized gas
    5.4. Strongly ionized gas

  • 13: ELECTROMAGNETIC THEORY by Nathaniel H. Frank and William Tobocman
    1. DEFINITIONS AND FUNDAMENTAL LAWS
    1.1. Primary definitions
    1.2. Conductors
    1.3. Ferromagnetic materials
    1.4. Fundamental laws
    1.5. Boundary conditions
    1.6. Vector and scalar potentials
    1.7. Bound charge
    1.8. Amperian currents
    2. ELECTROSTATICS
    2.1. Fundamental laws
    2.2. Fields of some simple charge distributions
    2.3. Electric multipoles; the double layer
    2.4. Electrostatic boundary value problems
    2.5. Solutions of simple e1ectrostatic boundary value problems
    2.6. The method of images
    2.7. Capacitors
    2.8. Normal stress on a conductor
    2.9. Energy density of the electrostatic field
    3. MAGNETOSTATICS
    3.1. Fundamental laws
    3.2. Fields of some simple distributions
    3.3. Scalar potential for magnetostatics ; the magnetic dipole
    3.4. Magnetic multiples
    3.5. Magnetostatic boundarycurrent value problems
    3.6. Inductance
    3.7; Magnetostatic energy density
    4. ELECTRIC CIRCUITS
    4.1. The quasi - stationary approximation.
    4.2. Voltage and impedance
    4.3. Resistors and capacitdrs in series and parallel connection
    4.4. Kirchhoff
    s rules
    4.5. Alternating current circuits
    5. ELECTROMAGNETIC RADIATION
    5.1. Poynting
    s theorem
    5.2. Electromagnetic stress and momentum
    5.3. The Hertz vector; magnetic waves
    5.4. Plane waves
    5.5. Cylindrical waves
    5.6. Spherical waves
    5.7. Radiation of e1ectromagnetic waves; the oscilg dipole
    5.8. Huygen
    s principle
    5.9. Electromagnetic waves at boundaries in dielecelectro- tricmedia
    5.10. Propagation of electromagnetic radiation in wave guides
    5.11. The retarded potentials; the Lienard-Wiechert potentials; the selflatinforce of electric charge

  • 14: ELECTRONICS by Emory L. Chaffee
    1. ELECTRON BALLISTICS
    1.1. Current
    1.2. Forces on electrons
    1.3. Energy of electron
    1.4. Electron orbit
    2. SPACE CHARGE
    2.1. Infinite parallel planes
    2.2. Cylindrical electrodes
    3. EMISSION OF ELECTRODES
    3.1. Thermionic emission
    3.2. Photoelectric emission
    4. FLUCTUATION EFFECTS
    4.1. Thermal noise
    4.2. Shot noise

  • 15: SOUND AND ACOUSTICS by Philip M. Morse
    1. SOUND AND ACOUSTICS
    1.1. Wave equation, definition
    1.2. Energy, intensity
    1.3. Plane wave of sound.
    1.4. Acoustical constants for various media
    1.5. Vibrations of sound producers; simple oscillator
    1.6. Flexible string under tensIOn
    1.7. Circular membrane under tension
    1.8. Reflection of plane sound waves, acoustical impedance
    1.9. Sound transmission through ducts
    1.10. Transmission through long hom
    1.ll. Acoustical circuits
    1.12. Radiation of sound from a vibrating cylinder
    1.13. Radiation from a simple Source
    1.14. Radiation from a dipole Source
    1.15. Radiation from a piston in a wall
    1.16. Scattering of sound from a cylinder
    1.17. Scattering of sound from a sphere
    1.18. Room acoustics

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