12. Make up dialogues on the following topics.

1. The atomic structure of matter. 2. The phenomenon of electric current. 3. The laws of electricity.

13. Match the words.

1) sets, variety, mapping, bound, limit, real numbers, probability,

integration, sequence, function, continuity, equation, differencial, maxima and minima, fraction.

2) множинність, послідовність чисел, неперервність, функція, вірогідність, границя (2), диференціал, дійсні числа, інтегрування, рівняння, максимут та мінімум, відображення, дріб, різноманіття.

14. Consider, comment on and examplify the notion.

Ordinary Differential Equations

1. An ordinary differential equation is an equation in­volving one or more derivatives of the dependent variable y with respect to a single independent variable x.

The order of the equation is that of the highest deriva­tive contained in it, so that the general differential equation of order n can be written in the form

F {y , y … y , y, x} = 0

the symbols y . denoting d‘ y / dx . The degree of the equation is defined mathematically to be that of its highest order derivative, when the equation has been made rational as far as the derivatives are concerned. The equation

y’’ = + ,

for example, is of order 2 and degree 2, since the equation must be

squared to rationalize the contributions from the derivatives.

Text 3

1. Find in the text the descriptions of motors. Translate the text. Electric Motors

Electric motor is a machine that converts electrical energy to mechanical energy. When a motor is connected to a source of electrical energy it develops a twisting effort called torque which tends to rotate the shaft of the motor. When the motor shaft is directly connected or geared, belted to a machine, that machine is driven by the motor to produce useful work.

Motors are used to drive the domestic electric appliances, in the modern industry for driving lathed milling machines, printing presses, conveyors, and grinders. Also rail and vehicular transportation systems, water-supply systems, and pump plants are dependent on electric motors.

Direct-current motors still play a significant role. They are used in many applications where a wide range of motor speeds is required ─ for instance, to

drive elevators, machine tools, cranes, and conveyors. A direct-current motor consists of the same essen­tial parts as a direct-current generator, namely, field mag­net, armature with its com­mutator, and brush gear. The armature and commu­tator are constructed on exactly the same principles as the armature and commutator of a dynamo, and any difference in exter­nal appearances of dynamos and motors is due to a mod­ification in the arrange­ment of the field magnets and frame, designed to give the motor the maxi­mum amount of protec­tion.

Alternating-Current Motors are much more commonly used than dc motors because practically all electric supply systems now in use are ac

systems. There are three general classes of alternating-current motors —

polyphase induction, polyphase synchronous, and single-phase motors.

Three-phase motors are by far the most com­mon kind of polyphase motors simply because 3-phase power systems are much more com­mon than other polyphase systems. Three-phase motors are widely used for industrial service because 3-phase power can be generated and distributed more economically in large quantities thai, single-phase power. Also, a 3-phase power supply provides the simplest means for producing a rotating magnetic field which is needed in an induction or a synchronous motor for starting or running.

Because most homes and rural areas are pro­vided only with single-phase power, such equip­ment as household appliances necessarily is driven by single-phase motor. Various designs are used Other kinds of polyphase motors, such as 2-phase motors, are not considered here.

Three-Phase Motor Principles—Rotating Magnetic Field. The operation of 3-phase induction motors depends on a rotating magnetic fieid in the air gap between the stator (stationary part) and the rotor. The comutator of the 3-phase motor has three in­dividual and identical windings arranged sym­metrically around its periphery.