IMPROPER INTEGRAL

In calculus, an improper integral is the limit of a definite integral as an endpoint of the interval of integration approaches either a specified real number or ∞ or −∞ or, in some cases, as both endpoints approach limits.
Specifically, an improper integral is a limit of the form
or of the form
in which one takes a limit in one or the other (or sometimes both) endpoints (Apostol 1967, §10.23). Improper integrals may also occur at an interior point of the domain of integration, or at multiple such points.
It is often necessary to use improper integrals in order to compute a value for integrals which may not exist in the conventional sense (as a Riemann integral, for instance) because of a singularity in the function, or an infinite endpoint of the domain of integration.

FUNCTION

The mathematical concept of a function expresses dependence between two quantities, one of which is known and the other which is produced. A function associates a single output to each input element drawn from a fixed set, such as the real numbers (), although different inputs may have the same output.
There are many ways to give a function: by a formula, by a plot or graph, by an algorithm that computes it, or by a description of its properties. Sometimes, a function is described through its relationship to other functions (see, for example, inverse function). In applied disciplines, functions are frequently specified by their tables of values or by a formula. Not all types of description can be given for every possible function, and one must make a firm distinction between the function itself and multiple ways of presenting or visualizing it.
One idea of enormous importance in all of mathematics is composition of functions: if z is a function of y and y is a function of x, then z is a function of x. We may describe it informally by saying that the composite function is obtained by using the output of the first function as the input of the second one. This feature of functions distinguishes them from other mathematical constructs, such as numbers or figures, and provides the theory of functions with its most powerful structure.

INTEGRATION

Integration is an important concept in mathematics which, together with differentiation, forms one of the main operations in calculus. Given a function ƒ of a real variable x and an interval [a, b] of the real line, the definite integral
is defined informally to be the net signed area of the region in the xy-plane bounded by the graph of ƒ, the x-axis, and the vertical lines x = a and x = b.
The term "integral" may also refer to the notion of antiderivative, a function F whose derivative is the given function ƒ. In this case it is called an indefinite integral, while the integrals discussed in this article are termed definite integrals. Some authors maintain a distinction between antiderivatives and indefinite integrals.
The principles of integration were formulated independently by Isaac Newton and Gottfried Leibniz in the late seventeenth century. Through the fundamental theorem of calculus, which they independently developed, integration is connected with differentiation: if ƒ is a continuous real-valued function defined on a closed interval [a, b], then, once an antiderivative F of ƒ is known, the definite integral of ƒ over that interval is given by
Integrals and derivatives became the basic tools of calculus, with numerous applications in science and engineering. A rigorous mathematical definition of the integral was given by Bernhard Riemann. It is based on a limiting procedure which approximates the area of a curvilinear region by breaking the region into thin vertical slabs. Beginning in the nineteenth century, more sophisticated notions of integral began to appear, where the type of the function as well as the domain over which the integration is performed has been generalised. A line integral is defined for functions of two or three variables, and the interval of integration [a, b] is replaced by a certain curve connecting two points on the plane or in the space. In a surface integral, the curve is replaced by a piece of a surface in the three-dimensional space. Integrals of differential forms play a fundamental role in modern differential geometry. These generalizations of integral first arose from the needs of physics, and they play an important role in the formulation of many physical laws, notably those of electrodynamics. There are many modern concepts of integration. The most common notion of integration is based on the abstract mathematical theory known as Lebesgue integration, developed by Henri Lebesgue

Differentiaton

In calculus, a branch of mathematics, the derivative is a measure of how a function changes as its input changes. Loosely speaking, a derivative can be thought of as how much a quantity is changing at a given point. For example, the derivative of the position (or distance) of a vehicle with respect to time is the instantaneous velocity (respectively, instantaneous speed) at which the vehicle is travelling. Conversely, the integral of the velocity over time is the vehicle's position.
The derivative of a function at a chosen input value describes the best linear approximation of the function near that input value. For a real-valued function of a single real variable, the derivative at a point equals the slope of the tangent line to the graph of the function at that point. In higher dimensions, the derivative of a function at a point is a linear transformation called the linearization.[1] A closely related notion is the differential of a function.
The process of finding a derivative is called differentiation. The fundamental theorem of calculus states that differentiation is the reverse process to integration.

ELECTRICITY

Electricity (from the New Latin ēlectricus, "amber-like"[a]) is a general term that encompasses a variety of phenomena resulting from the presence and flow of electric charge. These include many easily recognizable phenomena such as lightning and static electricity, but in addition, less familiar concepts such as the electromagnetic field and electromagnetic induction.
In general usage, the word 'electricity' is adequate to refer to a number of physical effects. However, in scientific usage, the term is vague, and these related, but distinct, concepts are better identified by more precise terms:
Electric charge – a property of some subatomic particles, which determines their electromagnetic interactions. Electrically charged matter is influenced by, and produces, electromagnetic fields. Electric current – a movement or flow of electrically charged particles, typically measured in amperes. Electric field – an influence produced by an electric charge on other charges in its vicinity. Electric potential – the capacity of an electric field to do work on a electric charge, typically measured in volts. Electromagnetism – a fundamental interaction between the magnetic field and the presence and motion of an electric charge. Electrical phenomena have been studied since antiquity, though advances in the science were not made until the seventeenth and eighteenth centuries. Practical applications for electricity however remained few, and it would not be until the late nineteenth century that engineers were able to put it to industrial and residential use. The rapid expansion in electrical technology at this time transformed industry and society. Electricity's extraordinary versatility as a source of energy means it can be put to an almost limitless set of applications which include transport, heating, lighting, communications, and computation. The backbone of modern industrial society is, and for the foreseeable future can be expected to remain, the use of electrical power.

MAGNETISM

In physics, magnetism is one of the forces in which materials and moving charged particles exert attractive, repulsive force or moments on other materials or charged particles. Some well-known materials that exhibit easily detectable magnetic properties (called magnets) are nickel, iron, cobalt, gadolinium and their alloys; however, all materials are influenced to greater or lesser degree by the presence of a magnetic field. Substances which are negligibly affected by magnetic fields are known as non-magnetic substances. They include copper, aluminum, water, and gases.
Magnetism also has other definitions and descriptions in physics, particularly as one of the two components of electromagnetic waves such as light.

LIGHT

Light is electromagnetic radiation, particularly radiation of a wavelength that is visible to the human eye (about 400–700 nm), or perhaps 380–750 nm.In physics, the term light sometimes refers to electromagnetic radiation of any wavelength, whether visible or not.
Three primary properties of light are:
Intensity Frequency or wavelength Polarization Light, which exists in tiny "packets" called photons, exhibits properties of both waves and particles. This property is referred to as the wave–particle duality. The study of light, known as optics, is an important research area in modern physics.

HEAT ENERGY

The term was first used explicitly by James Prescott Joule, who studied the relationship between heat, work, and temperature. He observed that if he did mechanical work on a fluid such as water, by agitating the fluid, its temperature increased. He proposed that the mechanical work he was doing on the system was converted to "thermal energy." Specifically, he found that 4200 joules of energy were needed to raise the temperature of a kilogram of water by one degree Celsius.

Thermal energy is most easily defined in the context of an ideal gas. In a monatomic ideal gas, the thermal energy is exactly given by the kinetic energy of the constituent particles.

THEROMODYNAMICS

In physics, thermodynamics (from the Greek θερμ-<θερμότης, therme, meaning "heat" and δυναμις, dynamis, meaning "power") is the study of the conversion of energy into work and heat and its relation to macroscopic variables such as temperature and pressure. Its underpinnings, based upon statistical predictions of the collective motion of particles from their microscopic behavior, is the field of statistical thermodynamics, a branch of statistical mechanics.Historically, thermodynamics developed out of need to increase the efficiency of early steam engines.

Introdution to Vector

Euclidean vector, a geometric entity endowed with both length and direction; an element of a Euclidean vector space. In physics, euclidean vectors are used to represent physical quantities which have both magnitude and direction, such as force, in contrast to scalar quantities, which have no direction. Vector product, or cross product, an operation on two vectors in a three-dimensional Euclidean space, producing a third three-dimensional Euclidean vector The vector part of a quaternion, a term used in 19th century mathematical literature on quaternions Burgers vector, a vector that represents the magnitude and direction of the lattice distortion of dislocation in a crystal lattice Displacement vector, a vector that specifies the change in position of a point relative to a previous position Laplace–Runge–Lenz vector, a vector used chiefly to describe the shape and orientation of the orbit of one astronomical body around another Vector bundle, a topological construction which makes precise the idea of a family of vector spaces parameterized by another space Vector calculus, a branch of mathematics concerned with differentiation and integration of vector fields Vector Analysis, a free, online book on vector calculus first published in 1901 by Edwin Bidwell Wilson Vector decomposition, refers to decomposing a vector of Rn to several vectors, each linearly independent Vector differential, or del, is a vector differential operator represented by the nabla symbol: Vector boson, a boson with the spin quantum number equal to 1 Vector measure, a function defined on a family of sets and taking vector values satisfying certain properties Vector meson, a meson with total spin 1 and odd parity Vector quantization, a quantization technique used in signal processing

Metric Spaces

In mathematics, a metric space is a set where a notion of distance (called a metric) between elements of the set is defined.
The metric space which most closely corresponds to our intuitive understanding of space is the 3-dimensional Euclidean space. In fact, the notion of "metric" is a generalization of the Euclidean metric arising from the four long known properties of the Euclidean distance. The Euclidean metric defines the distance between two points as the length of the straight line connecting them.
The geometric properties of the space depends on the metric chosen, and by using a different metric we can construct interesting non-Euclidean geometries such as those used in the theory of general relativity.
A metric space also induces topological properties like open and closed sets which leads to the study of even more abstract topological spaces.

ocsillation

Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. Familiar examples include a swinging pendulum and AC power. The term vibration is sometimes used more narrowly to mean a mechanical oscillation but sometimes is used to be synonymous with "oscillation." Oscillations occur not only in physical systems but also in biological systems and in human society.

Waves in the eye of Physics

A wave is a disturbance that propagates through space and time, usually with transference of energy. A mechanical wave is a wave that propagates or travels through a medium due to the restoring forces it produces upon deformation. There also exist waves capable of traveling through a vacuum, including electromagnetic radiation and probably gravitational radiation. Waves travel and transfer energy from one point to another, often with no permanent displacement of the particles of the medium (that is, with little or no associated mass transport); they consist instead of oscillations or vibrations around almost fixed locations.

Math helping physics in solving problems

Mathematical physics is the scientific discipline concerned with the interface of mathematics and physics. There is no real consensus about what does or does not constitute mathematical physics. A very typical definition is the one given by the Journal of Mathematical Physics: "the application of mathematics to problems in physics and the development of mathematical methods suitable for such applications and for the formulation of physical theories."[1] However, this definition does not cover the situation where results from physics are used to help prove facts in abstract mathematics which themselves have nothing particular to do with physics. This phenomenon has become increasingly important, with developments from string theory research breaking new ground in mathematics. Eric Zaslow coined the phrase physmatics to describe these developments[2], although other people would consider them as part of mathematical physics proper.
Important fields of research in mathematical physics include: functional analysis/quantum physics, geometry/general relativity and combinatorics/probability theory/statistical physics. More recently, string theory has managed to make contact with many major branches of mathematics including algebraic geometry, topology, and complex geometry.

Trigonometry

Trigonometry (from Greek trigōnon "triangle" + metron "measure")[1] is a branch of mathematics that deals with triangles, particularly those plane triangles in which one angle has 90 degrees (right triangles). Trigonometry deals with relationships between the sides and the angles of triangles and with the trigonometric functions, which describe those relationships.
Trigonometry has applications in both pure mathematics and in applied mathematics, where it is essential in many branches of science and technology. It is usually taught in secondary schools either as a separate course or as part of a precalculus course. Trigonometry is informally called "trig".
A branch of trigonometry, called spherical trigonometry, studies triangles on spheres, and is important in astronomy and navigation

Calculas by mathematics

Calculus (Latin, calculus, a small stone used for counting) is a discipline in mathematics focused on limits, functions, derivatives, integrals, and infinite series, and which constitutes a major part of modern university education. It has two major branches, differential calculus and integral calculus, which are related by the fundamental theorem of calculus. Calculus is the study of change, in the same way that geometry is the study of shape and algebra is the study of equations. A course in calculus is a gateway to other, more advanced courses in mathematics devoted to the study of functions and limits, broadly called mathematical analysis. Calculus has widespread applications in science, economics, and engineering and can solve many problems for which algebra alone is insufficient.
Historically, calculus was called "the calculus of infinitesimals", or "infinitesimal calculus". More generally, calculus (plural calculi) may refer to any method or system of calculation guided by the symbolic manipulation of expressions. Some examples of other well-known calculi are propositional calculus, variational calculus, lambda calculus, pi calculus and join calculus

Urdu and hindi

Hindustani,also known as "Hindi-Urdu," is a term covering several closely related dialects in Pakistan and northern India, especially the vernacular form of the two national languages, Standard Hindi and Urdu, also known as Khariboli, but also several nonstandard dialects of the Hindi languages.
In other words, Standard Hindi and Urdu are standardized registers of Hindustani/Khariboli. They are nearly identical in grammar and share a basic common vocabulary.
Before the Partition of British India, the terms Hindustani and Urdu were synonymous; both covered what would be called Urdu and Hindi today.

English(Language)

English is a West Germanic language that originated in Anglo-Saxon England. As a result of the military, economic, scientific, political and cultural influence of the British Empire during the 18th, 19th and 20th centuries and of the United States since the late 19th century[citation needed], it has become the lingua franca in many parts of the world.[7] It is used extensively as a second language and as an official language in Commonwealth countries and many international organizations.
Historically, English originated from several dialects, now called Old English, which were brought to Great Britain by Anglo-Saxon settlers beginning in the 5th century. The language was heavily influenced by the Old Norse language of Viking invaders. After the Norman conquest, Old English developed into Middle English, borrowing heavily from the Norman (Anglo-French) vocabulary and spelling conventions. Modern English developed from there and continues to adopt foreign words from a variety of languages, as well as coining new words. A significant number of English words, especially technical words, have been constructed based on roots from Latin and ancient Greek.
Contents [hide]1 Significance 2 History 3 Classification and related languages 4 Geographical distribution 4.1 Countries in order of total speakers 4.2 English as a global language 4.3 Dialects and regional varieties 4.4 Constructed varieties of English 5 Phonology 5.1 Vowels 5.1.1 Notes 5.2 Consonants 5.2.1 Notes 5.2.2 Voicing and aspiration 5.3 Supra-segmental features 5.3.1 Tone groups 5.3.2 Characteristics of intonation 6 Grammar 7 Vocabulary 7.1 Number of words in English 7.2 Word origins 7.2.1 Dutch origins 7.2.2 French origins 8 Writing system 8.1 Basic sound-letter correspondence 8.2 Written accents 9 Formal written English 10 Basic and simplified versions 11 See also 12 References 12.1 Bibliography 12.2 Notes 13 External links

what is IT

Information technology, a broad subject concerned with aspects of managing, editing and processing information it, the ISO 639 alpha-2 short code for the Italian language IT, the ISO 3166-1 alpha-2 and FIPS 10-4 country code for Italy IT, Iran Time, the time zone used in Iran, UTC+3:30 (also IRST) .it, the Internet country code top-level domain ccTLD for Italy The Irish Times Income tax The IATA code for Kingfisher Airlines and Irtysh Avia Institutes of Technology in Ireland, in the educational system of Ireland Impulse Tracker, music sequencer software for the MS-DOS operating system IEEE Transactions on Information Theory, a scientific journal published by the Institute of Electrical and Electronic Engineers Internet television, television distributed via the Internet Internal Translator, an early compiler for the IBM 650 Inclusive Tour, a package holiday that includes accommodation in addition to transportation International Times, an underground newspaper in London A type of electrical earthing system A metalinguistic marker in the Sanskrit grammar of Panini (grammarian) A series of enduro motorcycles from Yamaha Motor Company (e.g. IT175, IT250, IT490) Intercity Transit, a public transportation service in the State of Washington
Inferotemporal cortex, the highest-order cortical visual processing area of the brain (it), an abbreviation for intrathecal injection IT (file format), an audio file format

introduction to computer

A computer is a machine that manipulates data according to a set of instructions.
mechanical examples of computers have existed through much of recorded human history, the first resembling a modern computer were developed in the mid-20th century (1940–1945). The first electronic computers were the size of a large room, consuming as much power as several hundred modern personal computers (PC). Modern computers based on tiny integrated circuits are millions to billions of times more capable than the early machines, and occupy a fraction of the space. Simple computers are small enough to fit into a wristwatch, and can be powered by a watch battery. Personal computers in their various forms are icons of the Information Age, what most people think of as a "computer", but the embedded computers found in devices ranging from fighter aircraft to industrial robots, digital cameras, and toys are the most numerous.
The ability to store and execute lists of instructions called programs makes computers extremely versatile, distinguishing them from calculators. The Church–Turing thesis is a mathematical statement of this versatility: any computer with a certain minimum capability is, in principle, capable of performing the same tasks that any other computer can perform.

Accounting

Accountancy or accounting is the art of communicating financial information about a business entity to users such as shareholders and managers. The communication is generally in the form of financial statements that show in money terms the economic resources under the control of manager.
Such financial information is primarily used by lenders, managers, investors, tax authorities, and other decision makers to make resource allocation decisions between and within companies, organizations, and public agencies. It involves the process of recording, verifying, and reporting of the value of assets, liabilities, income, and expenses in the books of account (ledger) to which debit and credit entries (recognizing transactions) are chronologically posted to record changes in value (see bookkeeping). Accounting has also been defined by the AICPA as "The art of recording, classifying, and summarizing in a significant manner and in terms of money, transactions and events which are, in part at least, of financial character, and interpreting the results thereof."

Ecomics

An economy (or "the economy") is the realized economic system of a country or other area. It includes the production, exchange, distribution, and consumption of goods and services of that area. The study of different types and examples of economies is the subject of economic systems. A given economy is the end result of a process that involves its technological evolution, history and social organization, as well as its geography, natural resource endowment, and ecology, among other factors. These factors give context, content, and set the conditions and parameters in which an economy functions.
Today the range of fields of study exploring, registering and describing the economy or a part of it, include social sciences such as economics, as well as branches of history (economic history) or geography (economic geography). Practical fields directly related to the human activities involving production, distribution, exchange, and consumption of goods and services as a whole, range from engineering to management and business administration to applied science to finance. All kind of professions, occupations, economic agents or economic activities, contribute to the economy. Consumption, saving and investment are core variable components in the economy and determine market equilibrium. There are three main sectors of economic activity: primary, secondary and tertiary.
The word "economy" can be traced back to the Greek word "one who manages a household", derived from "house", and , "distribute (especially, manage)". From "of a household or family" but also senses such as "thrift", "direction", "administration", "arrangement", and "public revenue of a state". The first recorded sense of the word "economy", found in a work possibly composed in 1440, is "the management of economic affairs", in this case, of a monastery. Economy is later recorded in other senses shared by οἰκονομία in Greek, including "thrift" and "administration". rent sense, "the economic system of a country or an area", seems not to have developed until the 19th or 20th century.

Introduction to Urdu (Language)

Urdu ( pronunciation Urdū, historically spelled Ordu) is a Central Indo-Aryan language of the Indo-Iranian branch, belonging to the Indo-European family of languages. It is the national language and one of the two official languages (the other being English) of Pakistan. Being spoken in five Indian states, it is also one of the 22 official languages of India. Its vocabulary developed under Persian, Arabic, Turkic and Sanskrit. In modern times Urdu vocabulary has been significantly influenced by Punjabi and even English. Urdu was mainly developed in western Uttar Pradesh, India, but began taking shape during the Delhi Sultanate as well as Mughal Empire (1526–1858) in the Indian Subcontinent.
Language scholars independently categorize Urdu as a standardised register of Hindustani termed the standard dialect Khariboli. The grammatical description in this article concerns this standard Urdu. In general, the term "Urdu" can encompass dialects of Hindustani other than the standardised versions. The original language of the Mughals had been Turkic, but after their arrival in South Asia, they came to adopt Persian and later Urdu.
The word Urdu is believed to be derived from the Turkic or Mongolian word 'Ordu', which means army encampment. It was initially called Zabān-e-Ordu-e-Mu'alla "language of the Exalted Camp" (in Persian) and later just Urdu. It obtained its name from Urdu Bazar, i.e. encampment (Urdu in Turkic) market, the market near the Red Fort in the walled city of Delhi.
Standard Urdu has approximately the twentieth largest population of native speakers, among all languages.
Urdu is often contrasted with Hindi, another standardised form of Hindustani. The main differences between the two are that Standard Urdu is conventionally written in Nastaliq calligraphy style of the Perso-Arabic script and draws vocabulary more heavily from Persian and Arabic, while Standard Hindi is conventionally written in Devanāgarī and draws vocabulary from Sanskrit comparatively more heavily. Most linguists nonetheless consider Urdu and Hindi to be two standardized forms of the same language however, others classify them separately due to sociolinguistic differences.

Statatics

Statics is the branch of mechanics concerned with the analysis of loads (force, torque/moment) on physical systems in static equilibrium, that is, in a state where the relative positions of subsystems do not vary over time, or where components and structures are at a constant velocity. When in static equilibrium, the system is either at rest, or its center of mass moves at constant velocity. The study of moving bodies is known as dynamics.
By Newton's first law, this situation implies that the net force and net torque (also known as moment of force) on every body in the system is zero. From this constraint, such quantities as stress or pressure can be derived. The net forces equalling zero is known as the first condition for equilibrium, and the net torque equalling zero is known as the second condition for equilibrium. See statically determinate.

Introdution to Biology

Biology (from Greek βιολογία - βίος, bios, "life"; -λογία, -logia, study of) is the science that studies living organisms. Prior to the nineteenth century, biology came under the general study of all natural objects called natural history. The term biology was first coined by Gottfried Reinhold Treviranus.[citation needed] It is now a standard subject of instruction at schools and universities around the world, and over a million papers are published annually in a wide array of biology and medicine journals.[1]
Biology examines the structure, function, growth, origin, evolution, distribution and classification of all living things. Five unifying principles form the foundation of modern biology: cell theory, evolution, gene theory, energy, and homeostasis.[2]
Traditionally, the specialized disciplines of biology are grouped by the type of organism being studied: botany, the study of plants; zoology, the study of animals; and microbiology, the study of microorganisms. These fields are further divided based on the scale at which organisms are studied and the methods used to study them: biochemistry examines the fundamental chemistry of life, molecular biology studies the complex interactions of systems of biological molecules, cellular biology examines the basic building block of all life, the cell; physiology examines the physical and chemical functions of the tissues and organ systems of an organism; and ecology examines how various organisms interrelate with their environment.

Introdution to Chemistry

Chemistry (from Egyptian kēme (chem), meaning "earth" is the science concerned with the composition, structure, and properties of matter, as well as the changes it undergoes during chemical reactions. It is a physical science for studies of various atoms, molecules, crystals and other aggregates of matter whether in isolation or combination, which incorporates the concepts of energy and entropy in relation to the spontaneity of chemical processes. Modern chemistry evolved out of alchemy following the chemical revolution (1773).
Disciplines within chemistry are traditionally grouped by the type of matter being studied or the kind of study. These include inorganic chemistry, the study of inorganic matter; organic chemistry, the study of organic matter; biochemistry, the study of substances found in biological organisms; physical chemistry, the energy related studies of chemical systems at macro, molecular and submolecular scales; analytical chemistry, the analysis of material samples to gain an understanding of their chemical composition and structure. Many more specialized disciplines have emerged in recent years, e.g. neurochemistry the chemical study of the nervous system.

Introduction to Physics

Physics (Greek: physis – φύσις meaning "nature") a natural science, is the study of matter and energy and the relationship between them.its motion through spacetime and all that derives from these, such as energy and force.More broadly, it is the general analysis of nature, conducted in order to understand how the world and universe behave.it also deals with motion of the bodt,the every body in the universe.Physics is one of the oldest academic disciplines, perhaps the oldest through its inclusion of astronomy.[5] Over the last two millennia, physics had been considered synonymous with philosophy, chemistry, and certain branches of mathematics and biology, but during the Scientific Revolution in the 16th century, it emerged to become a unique modern science in its own right.[6] However, in some subject areas such as in mathematical physics and quantum chemistry, the boundaries of physics remain difficult to distinguish.
Physics is both significant and influential, in part because advances in its understanding have often translated into new technologies, but also because new ideas in physics often resonate with the other sciences, mathematics and philosophy. For example, advances in the understanding of electromagnetism led directly to the development of new products which have dramatically transformed modern-day society (e.g., television, computers, and domestic appliances); advances in thermodynamics led to the development of motorized transport; and advances in mechanics inspired the development of calculus.

Mathematics, The mother of all science

why it is so talk about maths?why it is so important?it is. beacuse it holds all science in it.whether we talk about physics, chemistry etc.......The math teacher can teach students about exponential notation. Once students become proficient in reading and writing numbers in exponential form, and in converting numbers between exponential form, factor form, and standard form, they can apply this knowledge to topics in science. For example, they can write the distance between the sun and each planet using scientific notation. For advanced students, you can teach them about negative exponents and then look at the half-life of certain radioactive elementsThere are many to connect math and other subject areas. It is just a matter of finding ideas that work for you and your students. My students are very motivated to learn when math is connected to other disciplines. Below are some lesson ideas that I used in my classroom with much success., or aAfter teaching a unit on how to read, interpret, and draw graphs, you can have your students apply these skills to topics in Social Studies. For example, they can draw bar graphs to compare the Population, Per Capita Income, and Population Density of various countries. For other connections between math and social studies,

Introduction to Mathematics

Mathematics is universally regarded as the science of all sciences. The crowning glory of Indian Mathematics was the invention of Zero and the introduction of Decimal notation without which mathematics as a scientific discipline could not make much progress. Indian Mathematics (Vedic Mathematics) is a living discipline with a huge potential for diversified modern world applications.
According to Sir J F Herbert Everything that the greatest minds of all times have accomplished towards the comprehension of forms by means of concepts is gathered into one great science, popularly known as Mathematics.
It's uncertain as to when the Vedic Literature actually began but according to modern historians, the Vedas(Rig veda, Sama veda, Yajur veda, and Atharva veda) began to be developed in about 1600BC. In the course of time, much of the vedic tradition fell into stagnancy. Then in the 19th centuary scholars took again took interest in the vedas. Then Sri Bharti Krishna Tirathji after lengthy and careful investigations produced a reconstruction of ancient Indian Mathematics based on 16 sutras, together with a subsutra.
Vedic Mathematics is not only a sophisticated tool but also an introduction to ancient civilization. It takes us back to millennia of India's cultural and scientific heritage. It is rooted in the ancient vedic sources which heralded the dawn of human history and illuminated by their erudite exegesis. Vedic Mathematics deals mainly with various mathematical formulae and their applications for carrying out tedious and cumbersome algebra equations and to a large extent try to execute these formulae mentally. Vedic Maths is a unique system of calculations based on simple rules & principles, with which any mathematical problem - be it arithmetic, algebra, geometry or trigonometry - can be solved orally. Further it offers us the choices of doing the calculations with different methods and ways also. Calculation can be done both ways, from left to right and also right to left and in the end same result can be obtained. In this way an overall development of the child easily and permanently takes place and their creativity levels are boosted above the roof.
Calculating with the help of this ancient system is like entering Playway School where every step is taken according to the minds of tiny tots and not by any rule. In this system multiplication becomes a game of additions and also subtraction is done with addition. Division can be a process of multiplication and addition. The simplicity of approach exposes the top-heavy processes of our logic-driven world