22-1 ;;Quote: solve algebraic equations by generalization of addition by iteration: get negative numbers and reciprocal powers from subtraction, fractions from division, irrationals from fractional powers, and complex numbers from the square root of -1

22-9 ;;Quote: complex imaginary powers are the same as sine and cosine; they oscillate; for small t, e^it = 1+it; for small t, cos t is nearly 1 and sin t is nearly 0

22-9+;;Quote: the most remarkable formula in mathematics: e^i \theta = cos \theta + i sin \theta

25-4 ;;Quote: linear systems are important because we can solve them and because the fundamental laws of physics are often linear, e.g., Maxwell's equations for electricity, the laws of quantum mechanics, and the approximations when displacements are small

26-2 ;;Quote: development of physical law: observe effect, measure it, make a table, find the rule

26-2+;;Quote: Ptolemy produce a table for the refraction of light in 140 A.D., Snell found the law of refraction in 1621

26-3 ;;Quote: the glory of science is to find a way of thinking that makes evident a law relating measurements

26-3+;;Quote: Fermat's principle of least time: light takes the path which requires the shortest time; it is an approximation for time differences of a period or longer

26-5 ;;Quote: use an ellipse to reflect all light from one point to another, i.e., all shortest paths have the same length

26-7 ;;Quote: the principle of least time: small changes to the path only make second-order changes to the time, i.e., there are many nearby paths which take almost exactly the same time

28-1 ;;Quote: electro-magnetic fields knit together the universe because they vary inversely to the first power of the distance instead of the inverse square

28-4 ;;Quote: Maxwell's equation for electrical force has three terms: an inverse square term for Coulomb's law, an inverse square correction for delay, and an inverse term for radiation

28-4+;;Quote: at a large enough distance, electrical force is proportional to the delayed transverse acceleration divided by the distance

29-1 ;;Quote: an electric field moves as a wave outward from the source; i.e., the electromagnetic field is delayed

29-2 ;;Quote: since ratio of the area of the surface of a cone to the kinetic energy due to an electric field is constant, the energy flux is never lost and the energy's amplitude varies as 1/r

31-1 ;;Quote: the electric field is the sum of the individual fields and the field of a single charge is given by its acceleration retarded by the speed c

31-1 ;;Quote: when light passes through glass it vibrates the electrons in the glass which in turn generate new fields; these fields effectively change the light's speed through the glass

31-2 ;;Quote: refraction, the bending of light, comes about because the speed of light is different in different materials; the only way for waves to fit at a boundary is to change the angle; yields Snell's law

31-4 ;;Quote: so far as problems involving light are concerned, electrons behave as though they were held by springs, i.e., oscillators with displacement proportional to force

31-6 ;;Quote: the natural frequency of electron oscillators in most ordinary gases and transparent substances corresponds to ultraviolet light

31-6+;;Quote: dispersion: as the driving frequency rises toward ultraviolet light, the index of refraction rises; so a prism spreads light

31-9 ;;Quote: dark spectral lines occur when the light frequency is nearly the natural frequency and the light is absorbed

31-9+;;Quote: from the sun's spectral lines we know that the chemical elements in the sun and stars are the same as those on earth

31-10 ;;Quote: a screen is opaque when the electric fields generated by the screen exactly cancel the light's electric field; this requires a sufficiently thick screen even for gold

32-1 ;;Quote: a radiating atom loses 1/e'th of its energy in 10^-8 seconds

32-5 ;;Quote: distinct light sources do not interfer only if measurements are averaged over more than 10^-8 seconds

32-6 ;;Quote: the scattering of sunlight by air is proportional to the fourth power of the frequency; why the sky is blue

32-8 ;;Quote: the wavelength of light is about 5000 times the diameter of an atom; small groups of atoms scatter light more strongly, but larger droplets scatter red more strongly

32-9 ;;Quote: at right angles to a light beam, scattered light is polarized

34-1 ;;Quote: associated with a vibrating electric field is a vibrating magnetic field at right angles and 1/c of the intensity of the electric field

33-1 ;;Quote: all electric fields are polarized; unpolarized light is the overlapping of many different polarizations

34-10 ;;Quote: light carries a momentum which is 1/c of its energy; from radiation pressure due to moving charges in a magnetic field

35-4 ;;Quote: brown light is a dark red and yellow mixture against a lighter background

35-5 ;;Quote: adding a light to two, indistinguishable spectral distributions is also indistinguishable

36-5 ;;Quote: it is impossible to turn both eyes out at the same time because the eye's muscles are controlled together

35-6 ;;Quote: any three differently colored lights whatsoever can always be mixed to produce any color whatsoever; may need to take one light from the other

36-6 ;;Quote: when light strikes strongly absorbing organic substances (e.g., rhodopsin), all electrons shift by one double bond; effectively moving an electron the width of the molecule

36-7 ;;Quote: the human eye is slightly sensitive to light polarization; can learn to tell the direction of the sun by rotating your head about the axis of vision

39-6 ;;Quote: the definition of equal temperature is the condition of two boxes of gas that sit next to each other long enough; i.e., the same mean kinetic energy of the center-of-mass motions

39-10 ;;Quote: from the ideal gas law equal volumes of different gases at the same pressure and temperature have the same number of molecules because of Newton's laws!

40-1 ;;Quote: kinetic theory is the description of matter from the point of view of collisions between the atoms

40-1+;;Quote: the gross properties of matter should be explainable in terms of the motion of its parts

40-8 ;;Quote: the first indication that classical physics was wrong was Maxwell's work on specific heats; molecules have discrete energy levels

41-3 ;;Quote: black-body radiation: real matter always emits light and radiates energy; in a closed box, the radiation and matter reach thermal equilibrium

41-3+;;Quote: by classical theory, black-body radiation (the color of a furnace) would predominate at high frequency with unbounded total energy

41-6 ;;Quote: Planck empirically determined the equation for black-body radiation and found a simple derivation under the assumption that harmonic oscillators have discrete energy levels

41-6+;;Quote: in the limit, Planck's equation for black-body radiation yields the classical equation, Rayleigh's law

41-8 ;;Quote: a single molecule of water receives 10^14 collisions per second; over a hundredth of a second the collisions are effectively random

49-7 ;;Quote: for linear systems independent of time, there are usually a series of special motions which vary exponentially in time; the most general motion is a superposition of these special motions; e.g., vibrating systems with imaginary exponentials

49-7 ;;Quote: quantum mechanics uses the amplitude of the probability of finding a system of electrons in a given configuration; since the function is linear it can be represented as the superposition of states of definite energy

50-1 ;;Quote: Pythagoras discovered that chords are pleasant when in ratios of small integers; first numerical relationship in nature outside of geometry

50-4 ;;Quote: notes sound dissonant if their upper harmonics have frequencies near enough to cause a rapid beat

50-4+;;Quote: consonant sounds have harmonics of the same frequency

52-1 ;;Quote: something is symmetrical if it is invariant under some transformation; e.g., Newtonian laws are symmetrical under translation

Table 52-1;;Quote: the laws of physics contain many symmetries: translation in space and time, rotation, uniform velocity, reversal in space and time, interchange of identical atoms, phase, matter-antimatter

52-3 ;;Quote: the scale of an individual atom is definite; Galileo discovered the effect of scale on the strength of materials

52-3 ;;Quote: each of the symmetries in physical law corresponds to a conservation law: e.g., symmetry under translation is space means that momentum is conserved; e.g., conservation of energy, angular momentum, and electrical charge