The formal theory of waves is developed by solving the wave equation. The condition for a solution to exist leads to a dispersion equation, and each specific solution of this equation is called the dispersion relation for a particular wave mode. An arbitrary wave mode is referred to as “the mode M”. The polarization vector for the mode M is defined as a unimodular vector along the direction of the electric vector found by solving the wave equation for waves in the mode M. Specific examples of wave modes are discussed for isotropic media, anisotropic crystals and cold magnetized plasmas. Transverse waves in a isotropic medium correspond to two degenerate wave modes, and the description of their polarization is discussed separately.

The first sustained nuclear chain reaction was achieved by Enrico Fermi and his collaborators at the University of Chicago on December 2, 1942. Since then, nuclear energy has been one of the dominant factors in our society. Fission reactors are widely used to supplement the generation of electric power and, when it is realized, controlled thermonuclear fusion promises to be an inexhaustible source of energy for mankind. Yet the most decisive and terrifying aspect of nuclear energy so far has been in the production of weapons of unprecedented destructive power. These weapons if used in the large quantities presently available can alter the ecology of the planet and completely destroy, or at the least, radically change human and animal life from what we know it to be today.

In Chapter 5 we begin by discussing the units of energy, the various levels of energy consumption and supply, and the global balance of energy on the earth. The earth receives its energy from the sun, which generates energy by nuclear fusion. Next we review the facts associated with nuclear forces in order to discuss the release of energy in fission and fusion processes. We also discuss radioactivity, its detection and its effect on living organisms. One section is devoted to nuclear reactors and another section to the principles of controlled nuclear fusion. For completeness we also consider solar energy, which even though still economically impractical is an inexhaustible source of clean energy.

Transportation, of people and materials, is among the major factors that have made our civilization possible. The harnessing of animals and the use of ships were exploited early in the history of man. The sailing boat was an extraordinary invention because the sea offered reduced friction to the point where the wind would suffice to propel the ship. Railroads provided the freight capacity that made possible the industrial revolution, to be followed by the introduction of the automobile in the 20th century. The first airplane flight by the Wright brothers took place in 1903, and today transportation has brought within easy access all parts of the globe. This speed and ease in transportation has had and continues to have a profound effect in shaping the social and economic structure of the world community. In 1969 man landed on the moon, and unmanned spacecraft have reached to the edge of our planetary system. More ambitious missions into space can be foreseen as technology advances and the desire to carry them out persists.

Chapter 7 is devoted to a discussion of airplane and rocket flight and propulsion. In contrast to ships which are buoyant, airplanes are heavier than air and are supported by the dynamically produced lift. The reduced friction in air allows airplanes to reach high velocities, even in excess of the speed of sound. While airplanes must fly in the atmosphere, rockets are not subject to such a restriction.

Modern electronic devices operate in general, on digital principles. That is, signals are transmitted in numerical form such that the numbers are coded by binary digits. A binary digit has only two states: ‘one’ and ‘zero’, or ‘high’ and ‘low’ etc. The reason for relying almost exclusively on digital information is that binary data can be easily manipulated and can be reliably stored and retrieved. That this approach is practical and economically advantageous is due to the great advances in large scale integration and chip manufacture as already discussed. In this chapter we will consider digital systems and the representation and storage of binary data. We will conclude by discussing the architecture of a small 3-bit computer, which nevertheless, contains all the important features of large machines.

Elements of Boolean algebra

In digital logic circuits a variable can take only one of the two possible values: 1 or 0. The rules for operating with such variables were first discussed by the British mathematician George Boole (1815–64) and are now referred to by his name. Since in pure logic a statement is either true or false, Boolean algebra can be applied when manipulating logic statements as well. This material is conceptually simple yet it is most relevant to the understanding of complex logic circuits.

Boolean algebra contains three basic operations: AND, OR and Complement. The result of these operations can be best represented by a truth table as introduced in Section 1.9, where also the symbols for the corresponding circuits were given.

Fluid flow and dynamic lift

The motion of a fluid is extremely complex because the individual molecules are subject to random thermal motion as well as to the collective motion of the fluid as a whole. Thus we consider a small element dτ of the fluid and follow its motion as a function of time. We will assume that the fluid is incompressible, so that the mass dm = ρ dτ contained in the volume dτ remains fixed and the density ρ is constant throughout the fluid; we will also assume that the fluid is non-viscous, that is there are no internal frictional forces. These two assumptions are applicable to motion through air when the velocity v is small as compared to the velocity of sound vs, i.e. v « vs. The velocity of sound is a measure of the random thermal velocity of the molecules; its value for air at s.t.p. is vs ≃ 330 m/s. When necessary we will relax these assumptions.

The simplest form of flow occurs when the velocity at each point of the liquid remains constant in time. This is illustrated in Fig. 7.1(a) where the element dτ follows the path from the point P to Q to R and has the velocity vP, vQ, vR; at a later time another element of the fluid will be at P but it will again follow the path to Q to R and have the same velocity.

Communication implies the transmission of messages and is the basis of human civilization. Speech, smoke signals, or written notes are all forms of communication. We will be concerned principally with communication over large distances, often refered to as telecommunications. Telecommunications are based on the transmission of electromagnetic (em) waves from a sending to a receiving station. The em wave can propagate either in a guided structure such as a pair of conductors, a waveguide or an optical fiber or it can propagate in free space. As technology progressed, higher frequency em waves became available and they offer important advantages as information carriers.

In Chapter 3 we introduce some general principles of information transmission. We examine the analysis of an arbitrary signal into a Fourier series, methods for modulating the carrier, and the sampling theorem for digital encoding of analog signals. The topic of noise in communication channels and of the expected level of random noise is treated next. Finally a brief overview of information theory is given. Information theory assigns a quantitative measure to the information contained in a message and is used to define the capacity of a communication channel.

Chapter 4 is devoted to the problems of the generation, propagation and detection of electromagnetic radiation at different frequencies. The physical laws governing these phenomena are Maxwell's equations and are universally valid. Different frequencies however present different problems in their transmission through the atmosphere and in their propagation along guided structures.

Intrinsic semiconductors

It is well known that certain materials conduct electricity with little resistance whereas others are good insulators. There also exist materials whose resistivity is between that of good conductors and insulators, and is strongly dependent on temperature; these materials are called semiconductors. Silicon (Si), germanium (Ge) and compounds such as gallium arsenide (GaAs) are semiconductors, silicon being by far the most widely used material. Solids, in general, are crystalline and their electrical properties are determined by the atomic structure of the overall crystal. This can be understood by analogy to the energy levels of a free atom.

A free atom, for instance the hydrogen atom, exhibits discrete energy levels which can be exactly calculated. A schematic representation of such an energy diagram is shown in Fig. 1.1(a). If two hydrogen atoms are coupled, as in the hydrogen molecule, the number of energy levels doubles as shown in part (b) of the figure. If the number of atoms that are coupled to each other is very large – as is the case for a crystal – the energy levels coalesce into energy bands as in Fig. 1.1(c). The electrons in the crystal can only have energies lying in these bands.

When an atom is not excited the electrons occupy the lowest possible energy levels. In accordance with the Pauli principle only two electrons (one with spin projection up and the other down) can be found at any one particular energy level.