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"Everything should be made as simple as possible but not simpler"
"Mathematics is the queen of all sciences"

Theory of everything

Theory of everything is the ultimate theory of physics , that should describe all physical aspects and occurrences in a consistent manner. Such theory , if it is found, needs to unify all fundamental forces of nature. String theory is the best candidate for theory of everything. It is a theoretical framework that have merged quantum mechanics with theory of relativity.
General theory of relativity theory of quanta
A theory is like a boat. How well the boat floats gives the soundness of the theory. The better the boat floats, the better the theory is. As long as the theory is able to describe particular phenomena , it is accepted as valid. But it can never be taken as an irrevocable(irrefutable) and absolute. For a better theory can supersede(replace) the old one. Such is the case with Newton's universal law of gravitation.

Quantum Field Theory

Feynman's sum over histories   |   S-matrix

Theory of relativity

Relativity made simple   |   Special theory of relativity   |   General theory of relativity   |   Tensor calculus  |   Hamiltonian mechanics

Quantum mechanics

Schrodinger equation   |   Matrix mechanics

Electrical and electronics Engineering

Power Engineering   |   Telecommunication   |   Control System Engineering   |   Electronics  |   Fundamentals of EEE  |   Digital signal processing  |   Digital Filters |   Fields and Waves  |   Differential equation and calculus

Electrical Engineering

Science of electrical engineering focuses on various aspects of one fundamental force of nature , which is electromagnetic force. Electrical and electronics engineering has greatly influenced the development of modern technology. Technological achievements have stunned us. But it is not stopped. Electrical engineering is one of those disciplines that human knowledge has shaped over several hundred years. Nineteenth century was a high time for the physicist and mathematicians, when all the major developments of science took place. Quantum mechanics and photoelectric effect were discovered. Although major inventions were established in nineteenth century , electrical phenomena was known long before that. Theory of Magnetism and electromagnetism were also developed. Electricity and magnetism , together, form theoretical foundation of electrical engineering. Charles-Augustin de Coulomb first formulated the equation of force between two electrically charged particles, which is known as Coulomb's law. Every student of school or college more or less knows about the law. Coulomb's law is very similar to Newton's law of gravity which is still valid for any system of large or massive objects like sun, earth. A simple illustration of Newton's Law of Gravity can be given :

Universal  gravitation
A simple but powerful theory is the Newton's law of gravity which states that force between two object is proportional to their mass and inversely proportional to the distance r between them. Every student of science need to know about Newton's law. It is still used in astronomy and cosmological model. Newton's law can be used to derive Kepler's law of planetary motion. The orbit of the planets are not perfectly circular but rather elliptical.
Universal  gravitation
Coulomb's and Newton's law can both be classified as inverse square law. The inverse square law implies that the force reduces in quadratic manner as the distance increases. For example if the distance is doubled the force will be one-fourth, if tripled , one-sixteenth and so on. Gauss described the relationship between the charge density and electric field , which tacitly assumes the properties of inverse square law if the surface enclosing a charge distribution is spherical. Even Coulomb's law can be derived using Gauss flux theorem. And back in 16 century an inverse square law was proposed for the light source and its intensity. It seems nature is kind of predisposed to inverse square law and all these laws say something about spherical symmetry. Symmetry results from in-variance when we change our perspective. It can be applied to any shape, objects or many other abstract things. Nature is full of symmetrical shapes. A snowflake shows certain symmetry when we rotate them. Our body has certain symmetry and so have all spherical objects. Symmetry is simplification, which plays a vital roles in physics and mathematics. Whenever possible another chapter will be discussed on symmetry.

Applied vs pure mathematics

Computer Science is another revolutionary branch of engineering science , which is directly related to applied mathematics. Semiconductor devices led the rapid development of computer technology. Computer science and electrical engineering are contingent and complementary. Practical computer would not be feasible without applications of electrical and electronics engineering . Any electrical or computer engineer would not hesitate to admit the fact. But at present there is a race between the two and in many cases computer science has outpaced electronics and electrical engineering. Information technology is now a dominating field. Nothing has connected the world more than the internet has in recent years. The information age actually began when Claude Shannon formulated his famous equation relating channel capacity to channel bandwidth and signal-to-noise ratio. The formula is simple enough to specify :
information theory
Where B is the specific bandwidth of the channel. But the equation describes a communication related phenomena, which is thus a topic that falls under the scope of electrical and electronics engineering. Claude Shannon was a mathematician too. Mathematics is at the heart of telecommunication like all other fields of science. Mathematics provides a model for the real world phenomena and simplify many problems related to them. Electrical engineering is dependable on applied mathematics rather than higher level abstraction used in pure physics or mathematics. So mathematics is concerned with problem solving in engineering practices and its applications. In order to solve the problems , we use the mathematical formula that best explains the phenomena. Various mathematical formulas of algebra, calculus, geometry and trigonometry are applied in solving the problems. The variables and parameters studied must correspond to real world application. In particular these must quantify the properties of the engineering system. So applied mathematics is always concerned with system modeling, problem and puzzle solving related to real world applications. The variables and parameters used in the electrical circuit analysis can be given definite value by applying measurement.
On the other hand pure mathematics is the mathematics for its own sake. Pure mathematician develops theorems and focus on proving it. It is totally abstract reasoning. Pure mathematics deals with patterns , logic , propositions, theorems and argument. In pure mathematics there are statements or propositions which may contain variables. When these variables are given specific value the statements becomes specific and part of applied mathematics. Let us think about a statement of pure mathematics : for any a, b and c , if they are the base , vertical and hypotenuse of a right triangle respectively then a(squared) + b(squared) = c(squared). a, b and c can be anything and this statement is always true as long as they are the sides of any right triangle. But when we substitute a for real power and b for imaginary power and c for apparent power we get a specific right angle triangle whose base , hypotenuse and vertical sides real, apparent and imaginary power. We thus step into the realm of applied mathematics. All that we need are the numbers to be used as length of the sides of that triangle. If we know real and imaginary power we can find the apparent power and vice versa. The stated proposition containing " if (proposition) then (proposition)" is an example of material implication. Material implication ( if-then) is a rule of propositional calculus , by which we validly infer something. "P implies Q materially" means that either P is false or Q is true. In this regard false proposition implies every propositions and a true proposition is implied by every proposition. On the other hand formal implication is more general. Formal implication is the relation of inclusion to obtain from the logic of predicates of the form (x) { if 'x is F ' then 'x is G'} . For example, if the two predicate functions stated are ' x is a man' and 'x is mortal' , we can infer that all men are mortal. We now have a new relation of inclusion. Thus formal implication is a single proposition. It is not a relation of two propositions. Material implication is a limiting case of formal implication when the variables in the formal statements are replaced with specific value. It is concerned with the existing state of affairs. These two kinds of implication namely material and formal implication, are vital to mathematics for all kinds of deduction. Pure mathematics is the class of all propositions of the form "P implies Q". P and Q are propositions but not propositional functions which are entirely different concept. Propositional functions are also statements which does not have the truth value of true or false except when the variables in it are given specific value. Premise is a proposition which can be either true or false as opposed to axioms which is assumed to be true. In pure mathematics , premise is used to draw a conclusion which dictates the premise has to be true. There is other rules of logic like conjunction, dis-junction, negation, contra -positive, principle of importation and few others. The implication ( material and formal) is what describes the essence of mathematics. Mathematics, in this way, can be interpreted as "if such and such thing is true of something then such and such other things is also true of that thing". It is irrelevant to mathematics what such thing really means or what such things are. Pure mathematics has logical constant which is different than usual constant in mathematics. All logical constants can be defined in terms of implication or relations. Logical constants are the forms that does not change when we vary other terms in the proposition. Terms can be anything which occuro in mathematical statements. So terms and relations constitute the general form of propositions. We can get different instance of the same proposition by varying the terms in that proposition. The relation remains the same , which can be termed logical constant. All the theorems and truths of mathematics can easily be established by using few premises and some rules of deductions. This is how logic has imparted(given) a solid foundation to mathematics although the conversion can be difficult and too abstract. But reduction of mathematics to logic is one of the greatest achievements human mind have ever made. Bertrand Russel and Alfred North Whitehead had established a rigorous foundation of mathematics through logic in their famous Principia Mathematica. They came up with a definition of cardinal number with pure logic :
"Cardinal number of a class is the class of all classes that are similar to it."
Number is a concept which have surprised many philoshopers and mathematician for centuries. Numbers are of many kinds. They can be rational numbers, irrational numbers, prime numbers, transcendental numbers and many others. Prime numbers are still a mystery. Euclid first proved that there are infinite number of prime numbers. He proved it by using proof by contradiction.
Suppose there is a list of primes denoted by p(1), p(2), p(3),...p(n) where n is finite integer. We now form a new number q = p(1)p(2)p(3)..p(n) + 1; This number must be divided by a prime. Let it be m. If m is one of the prime listed above then q- p(1)p(2)p(3)..p(n) must be some number other than 1. This is a contradiction. So we must conclude that the list is incomplete. No matter how long the list is there is another prime not in the list. This proves our hypothesis.
Measurement can be done when superposition of two magnitudes is possible. By "superposition" we simply mean the coincidence of two things. But it has other definition in mathematics and physics. Measurement is an integral part of modern physics and engineering. By performing measurement we attribute (assign) units to certain physical quantities like scalars and vectors. In engineering there are standard units for every quantities measured. Measurement and standard of units are all maintained by convention. Conventional system is like keeping a name of a child when it is first born. The name serves as a standard by which we all know the child. There is no reason to suppose that all the systems of measurement and units are absolute or one measurement is more valid than the other. Measurement precedes magnitude. Magnitude can be defined when we have general conceptions which are capable of determination. Any set of such different magnitudes is called manifold. Manifold can be continuous or discrete based on whether the passage through it is continuous or discrete. Magnitude is the relative size of things by which we can compare those things. A scalar quantity has only magnitude whereas vector quantities have both magnitude and direction. These are very useful entities in the field of both engineering and science.

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Academic courses

Science of telecommunication and electronic engineering is very impressive branch of education now a days. Power electronics and semiconductor devices are some of the sub fields of electrical and electronics engineering. The courses and subjects of it are huge in numbers and vary from universities to universities. Some of the courses of computer science are Boolean algebra, data structures, microprocessor design, automata theory, complexity theory and many types of computer programming languages. The courses of electrical and electronics engineering are divided into two main fields : one is telecommunication and other is power engineering. Each field has number of courses to be studied by students of electrical and electronics engineering. Some of the courses have prerequisite courses to be passed in order to take the former courses. All courses are distributed among a number of semesters during certain interval of time. This gives student sufficient time to study and understand the concepts of the subjects. It is imperative that students of EEE understand the basics of dc and ac circuit. Transient analysis plays an important role in circuit analysis. Transient state is the interval during which system changes its behavior from one state to another state. During transient state system output may be very oscillatory and thus it can be unstable. It is the time a system takes to reach steady state. The time taken is called transient time. The relationship between voltage and current that system gives during transient state are called the transient response. More details will be studied when we analyze dc and ac R-L-C circuit and control system engineering. Elementary circuit theory utilize Thevenin's theorem and Norton theorem. These two theorems or laws play an important role in simplifying linear circuits.

Electrical machines and equipment

Transformer testing and Electrical machinery are some of things that electrical and electronics engineering is concerned with. Synchronous or asynchronous motors and generators fall in the scope of electrical machines engineering. As the name suggests, the synchronous machines run at a constant speed called synchronous speed. They are useful in many cases when constant speed is expected. They maintain a constant speed irrespective of the mechanical load connected to the rotor. Synchronous motor is not self starting inherently. When it is connected to the supply voltage it does not get necessary torque to rotate. So some kind of starting mechanism is needed to start synchronous motor. On the other hand induction motor does not rotate at synchronous speed. The synchronous speed is the speed of the rotating magnetic field inside motor. Rotating magnetic field is the resultant of all the separate out-of-phase magnetic fields that the stator poles create.
rotating magnetic field
The rotating magnetic field is a vector or phasor whose frequency is proportional to the frequency. There is a precise mathematical relationship between the synchronous speed and line voltage frequency. It is 120f/P where f= frequency, P= number of poles. Induction motor is started and rotated by the principles of induction. Induction motor can not run at synchronous speed. The deviation from the synchronous speed provides necessary torque to rotate the rotor . So there should be a non zero relative speed between the rotor and rotating magnetic field. The induced emf in the rotor produces current in the rotor coil. The current in turn produces the necessary torque. If there were no relative speed there would be no emf generated, hence no torque. The rotor always try to catch up with the rotating magnetic field but could not reach synchronous speed for the reason mentioned above. The numerical difference between the synchronous speed and rotor speed is called slip. Speed of induction motor vary according to the load attached to them. The induction motor when seen as an application of electromagnetic induction is nothing but a transformer. We can derive an equivalent circuit for the induction motor too.
induction motor

Generators are the reversed operation of synchronous motors. In the field winding of generators dc voltage is supplied. Thus a strong magnetic flux is created to excite the rotor winding. A prime mover is used to rotate the rotor at constant speed. The flux created by the rotor field cuts the stator winding and generates desired power. So a kind of energy conversion takes place. Prime mover provides mechanical energy which is converted to electrical energy. Generators are the most important component of a power plant where electricity is generated. There can be many type of power plant like hydro-electric, gas or oil driven plant. In almost every power plant there may be one or several generators operating at the same time. This is to meet the growing demand of electricity.
In heat engine energy conversion takes place between heat and mechanical work. Laws of thermodynamics governs such system. The zeroth law states that if two systems A and B are in equilibrium with a third system C then they are in equilibrium with themselves. First law implies that perpetual machine is not practically implementable. The internal energy of a system always changes when some work is done on the system. The most important of those laws is the second law which says entropy of closed or isolated system can never decrease over time. The universe is heading toward a state of maximum entropy. Let us try to explain what entropy really is. Heat is the by product of any process no matter how efficiently the process runs. So heat is considered the worst form of energy. it degrades all forms of energy. That's why entropy has been defined in terms of heat energy. It is actually the amount of lost heat that can not be recovered. It is impossible to construct a heat engine whose sole purpose is to convert heat to work, which is an alternative statement of the second law. So we are losing heat energy every moment and it is happening spontaneously. When all the heat energy is lost , the entropy will be maximum. Entropy can be formulated as below :

 entropy equation

Small incremental change of heat per unit temperature in irreversible cycle is less than small entropy change S which is zero. The total change of this quantity turns out to be negative. As a result the the entropy of environment increases . On the other hand the change (dQ/T) of reversible cycle is the same as the system entropy ds. If we integrate these two values over a complete cycle both terms of the equation will be zero. As a result the entropy of system and environment does not change. This is so called Clausius formulation of entropy , which says for a cyclic process the integral of the quantity (dQ/T) always equals zero or less than that.

∮dQ/T <= 0
Greatest scientist Stephen Hawking proved that Black hole has entropy. That means black hole has temperature and it radiates energy. He theorized a mathematical relationship between black hole temperature and its surface area (A).
black hole entropy

Radiation means energy and energy means mass which Einstein's showed by his famous equation (E=mc.c). So Every black hole will be extinct with a pop. The time required for such a process is very long though. Entropy can be defined in terms of disorder that always increases over time.

This is an indication that heat always flows from hot body to cold body. If it is to be reversed, work has to be done on the system. Boltzmann formulated the entropy equation based on any system's microscopic configurations. The basic idea is that nature evolve toward the state that is more probable than others. We see a egg falling from a table and getting scattered on the floor. We do not see the opposite : scrambled egg getting back on the table and reassembled into its original form. This is highly unlikely and if we could wait for sufficient amount of time(probably the age of the universe) we were able to see that happen. Universe will ultimately face heat death and no process will continue any more. We do not need to worry at the moment. That will not happen any time soon. Our sun will still be active for the next few billions of years from now. And there are countless number of other stars in the universe to die out. The concepts of entropy and second law are extremely crucial in physics and scientific development. Physicists are aware of the fact that if their scientific law violates the second law then there is no hope for it.

Use of electrical machinery is pervasive all around the world. They are useful because they can do physical work or can convert energy into another form. They save a lot of human work and time. Modern day machines are now more sophisticated than those of early age. This have been possible because of advanced technology. Machines are becoming more automatic day by day. Electrical machines are driven electrically. Most of electrical machines deliver mechanical power. But there is some difference between electrical and mechanical system. This distinction is necessary to understand although there is an analogy between them. We can come up with the same differential equation by replacing the analogous variables for each other. An analogy can be found between mass -spring system and R-L-C circuit. And we have a number of parameters like force(f), spring constant(K), mass for mechanical system, which can be replaced with voltage(v), inductance(L) and capacitor(1/C) respectively. Exact understanding would require knowledge of control system designing.

Science and Engineering

Science and Engineering is what we heavily dependable on now a days. Knowledge of science and mathematics can help us to understand the concepts of engineering much better. Theoretical physics is a much honorable branch of physics and science. Although theoretical physics is now an advanced branch of physics , it does not always have practical application of its theory and predictions. It relies heavily on the abstract mathematics and assumption. Modern engineering and other science have lots of similarity and they are dependent on each other. Mathematics is considered to be the foundation of all science. Logic is very vital to foundation of mathematics. Logic is any valid reasoning which is part of an argument itself. Logic is the rules of deduction and soundness of mathematical statements. The relation between mathematics and logic is like that between child and man. Logic is the childhood of man and man is the fatherhood of logic. They are very much alike. Much can be discussed about mathematical logic, which at the moment can be avoided as it does not give much relevance to applied science and engineering. Science is the blending of logic and application. Scientific study can not progress without mathematics. Science can be defined as the study of natural laws. So in this way of defining, physics comes before engineering. Applied physics can be regarded as engineering and its application. Philosophy encompasses both science and arts. So philosophy is one step ahead of science although science is more exact than philosophy. Philosophy is the most primitive knowledge. It is basically the knowledge about world and life at large. Some regard it as the intermediate knowledge between science and religion. To be specific, theology is the study of religion and science is a modern systematic study which includes technical ideas. So engineering is also a technical discipline. Scientist and engineer differ in terms of their work and responsibility. Scientists study the laws of nature and their role in the working of the universe. They do not focus on the practical aspects of these laws. On the other hand, engineers apply these laws to develop and design real world application. As an example, aeronautics engineers are concerned with making airplanes and flying them into sky using Newton's and other law of physics. So they have to rely heavily on mathematical formulas. Once they come up with appropriate formula that describes a system , they solve it to design that particular system.

Engineering as we can see, is dependent on science. The former can not progress without the later. Life may be troublesome without engineering applications but we could still know how the universe works as a whole since science is the study of natural laws that govern our lives and the physical world.

Overcoming Premature ejaculation

What is the relation of science with sexuality ? you will find the answer after you have read this. We all need a good sexual health. It is our prime need. This section is for those who are afraid of having sex with their partner. There is good news for them. A girl wants his partner to be strong and lasting. Marriage life could not be happy without a good sexual relationship. So if you are worried and anxious this section might help you.
How to overcome premature ejaculation

Web Applications

php and mysql are now a popular web programming languages . They usually work together. HTML is hypertext markup language. So the web development involves both programming and scripting languages which includes a large class of computer languages and style sheets.

Computer science and Engineering

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