First Engineering School

Functions

Types of functions – Definitions - Inverse functions and Theorems - Domain, Range, Inverse of real valued functions.

Surds

A surd is an irrational number in root form.A number that cannot be expressed as a simple fraction i.e.a/b You can think of surds as being square roots of numbers that do not have a whole number as the root. Surds crop up in many situations in mathematics and we will learn some basic rules to deal with them. When we can't simplify a number to remove a square root (or cube root etc) then it is a surd. Example: √4 (square root of 4) can be simplified (to 2), so it is not a surd! The surds have a decimal which goes on forever without repeating: they are actually Irrational Numbers.

Logarithms

Mathematical Inductions

Principle of Mathematical Induction & Theorems - Applications of Mathematical Induction - Problems on divisibility.

Vectors Addition

ctor addition is the operation of adding two or more vectors together into a vector sum.The so-called parallelogram law gives the rule for vector addition of two or more vectors. For two vectors A and B, the vector sum A+B is obtained by placing them head to tail and drawing the vector from the free tail to the free head. In Cartesian coordinates, vector addition can be performed simply by adding the corresponding components of the vectors, so if A=(a_1,a_2,...,a_n) and B=(b_1,b_2,...,b_n), A+B=(a_1+b_1,a_2+b_2,...,a_n+b_n). Vector addition is indicated in the Wolfram Language using a plus sign, e.g., {a1, a2, ..., an}+{b1, b2, ..., bn}.

Scalar Product Of Two Vectors

In mathematics, the dot product, or scalar product (or sometimes inner product in the context of Euclidean space), is an algebraic operation that takes two equal-length sequences of numbers (usually coordinate vectors) and returns a single number. This operation can be defined either algebraically or geometrically. Algebraically, it is the sum of the products of the corresponding entries of the two sequences of numbers. Geometrically, it is the product of the Euclidean magnitudes of the two vectors and the cosine of the angle between them. The name "dot product" is derived from the centered dot " · " that is often used to designate this operation; the alternative name "scalar product" emphasizes the scalar (rather than vectorial) nature of the result.

Vector Product Of Two Vectors

In mathematics, the cross product or vector product is a binary operation on two vectors in three-dimensional space and is denoted by the symbol ×. The cross product a × b of two linearly independent vectors a and b is a vector that is perpendicular to both and therefore normal to the plane containing them. It has many applications in mathematics, physics, engineering, and computer programming. If two vectors have the same direction (or have the exact opposite direction from one another, i.e. are not linearly independent) or if either one has zero length, then their cross product is zero. More generally, the magnitude of the product equals the area of a parallelogram with the vectors for sides; in particular, the magnitude of the product of two perpendicular vectors is the product of their lengths. The cross product is anticommutative (i.e. a × b = −b × a) and is distributive over addition (i.e. a × (b + c) = a × b + a × c). The space R3 together with the cross product is an algebra over the real numbers, which is neither commutative nor associative, but is a Lie algebra with the cross product being the Lie bracket.

Triple Product

In vector calculus, a branch of mathematics, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. The name "triple product" is used for two different products, the scalar-valued scalar triple product and, less often, the vector-valued vector triple product.The scalar triple product (also called the mixed or box product) is defined as the dot product of one of the vectors with the cross product of the other two.

Trigonometric Ratios

In mathematics, the trigonometric functions (also called the circular functions) are functions of an angle. They relate the angles of a triangle to the lengths of its sides. Trigonometric functions are important in the study of triangles and modeling periodic phenomena, among many other applications.The most familiar trigonometric functions are the sine, cosine, and tangent. In the context of the standard unit circle (a circle with radius 1 unit), where a triangle is formed by a ray originating at the origin and making some angle with the x-axis, the sine of the angle gives the length of the y-component (the opposite to the angle or the rise) of the triangle, the cosine gives the length of the x-component (the adjacent of the angle or the run), and the tangent function gives the slope (y-component divided by the x-component). More precise definitions are detailed below. Trigonometric functions are commonly defined as ratios of two sides of a right triangle containing the angle, and can equivalently be defined as the lengths of various line segments from a unit circle. More modern definitions express them as infinite series or as solutions of certain differential equations, allowing their extension to arbitrary positive and negative values and even to complex numbers.

Compound Angles

sin(A + B) DOES NOT equal sinA + sinB. Instead, you must expand such expressions using the formulae below.The following are important trigonometric relationships: sin(A + B) = sinAcosB + cosAsinB cos(A + B) = cosAcosB - sinAsinB tan(A + B) = tanA + tanB / 1 - tanAtanB .To find sin(A - B), cos(A - B) and tan(A - B), just change the + signs in the above identities to - signs and vice-versa: sin(A - B) = sinAcosB - cosAsinB cos(A - B) = cosAcosB + sinAsinB tan(A - B) = tanA - tanB / 1 + tanAtanB

Multiple And Sub-Multiple Angels

Angle is the pivot around which the topic of Trigonometry revolves. Trigonometry studies angles and their relationship. When there is a single function or a single angle, the computation is comparatively easy. But there are various formulae for multiples and sub multiples of angles too. These multiple and sub multiple angles formula should rather be called as identities as they hold true for all angles. These formulae prove useful in solving intricate trigonometric equations. It is also possible to find the trigonometric ratios of negative angles, multiple and sub multiple of an angle or compound angles. The coming sections illustrate trigonometric ratios of multiple and sub multiple angles along with various examples.

Transformations

In mathematics, particularly in semigroup theory, a transformation is any function f mapping a set X to itself, i.e. f:X→X. In other areas of mathematics, a transformation may simply be any function, regardless of domain and codomain. This wider sense shall not be considered in this article; refer instead to the article on function for that sense. Examples include linear transformations and affine transformations, rotations, reflections and translations. These can be carried out in Euclidean space, particularly in dimensions 2 and 3. They are also operations that can be performed using linear algebra, and described explicitly using matrices.

Periodicity & Extreme Values

Trigonometric Equations

Inverse Trigonometric Functions

In mathematics, the inverse trigonometric functions (occasionally called cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions. They are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

Hyperbolic Functions

In mathematics, hyperbolic functions are analogs of the ordinary trigonometric, or circular functions. The basic hyperbolic functions are the hyperbolic sine "sinh" (/ˈsɪntʃ/ or /ˈʃaɪn/), and the hyperbolic cosine "cosh" (/ˈkɒʃ/),from which are derived the hyperbolic tangent "tanh" (/ˈtæntʃ/ or /ˈθæn/), hyperbolic cosecant "csch" or "cosech" (/ˈkoʊʃɛk/ or /ˈkoʊsɛtʃ/), hyperbolic secant "sech" (/ˈʃɛk/ or /ˈsɛtʃ/), and hyperbolic cotangent "coth" (/ˈkoʊθ/ or /ˈkɒθ/), corresponding to the derived trigonometric functions. The inverse hyperbolic functions are the area hyperbolic sine "arsinh" (also called "asinh" or sometimes "arcsinh") and so on. Just as the points (cos t, sin t) form a circle with a unit radius, the points (cosh t, sinh t) form the right half of the equilateral hyperbola. The hyperbolic functions take a real argument called a hyperbolic angle. The size of a hyperbolic angle is the area of its hyperbolic sector. The hyperbolic functions may be defined in terms of the legs of a right triangle covering this sector.

Properties Of Triangle

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. In Euclidean geometry any three points, when non-collinear, determine a unique triangle and a unique plane (i.e. a two-dimensional Euclidean space). This article is about triangles in Euclidean geometry except where otherwise noted.

Height & Distances

Trigonometry is the study of relationships between the sides and angles of a triangle. It is used in geography and in navigation. It is also used in constructing maps, determine the position of an Island in relation to the longitudes and latitudes. In this chapter trigonometry is used for finding the heights and distances of various objects without actually measuring it. The line joining the observer’s eye and the object observed is known as Line of Sight. The angle between the horizontal line and the line of sight which is above the observer’s eye is known as Angle of Elevation. The angle between the horizontal line and the line of sight which is below the observer’s eye is called Angle of Depression.

Complex Numbers

A complex number is a number that can be expressed in the form a + bi, where a and b are real numbers and i is the imaginary unit, that satisfies the equation i2 = −1. In this expression, a is the real part and b is the imaginary part of the complex number. Complex numbers extend the concept of the one-dimensional number line to the two-dimensional complex plane (also called Argand plane) by using the horizontal axis for the real part and the vertical axis for the imaginary part. The complex number a + bi can be identified with the point (a, b) in the complex plane. A complex number whose real part is zero is said to be purely imaginary, whereas a complex number whose imaginary part is zero is a real number. In this way, the complex numbers contain the ordinary real numbers while extending them in order to solve problems that cannot be solved with real numbers alone.

DE MOIVRES Theorem

Trigonometric Expansions

CO-Ordinate System

In geometry, a coordinate system is a system which uses one or more numbers, or coordinates, to uniquely determine the position of a point or other geometric element on a manifold such as Euclidean space. The order of the coordinates is significant and they are sometimes identified by their position in an ordered tuple and sometimes by a letter, as in "the x-coordinate". The coordinates are taken to be real numbers in elementary mathematics, but may be complex numbers or elements of a more abstract system such as a commutative ring. The use of a coordinate system allows problems in geometry to be translated into problems about numbers and vice versa; this is the basis of analytic geometry.

Locus

In geometry, a locus (plural: loci) is a set of points whose location satisfies or is determined by one or more specified conditions.

Pair Of Straight Lines

Coordinate System - 3D

Direction Ratios And Direction Cosines

Limits

This is an overview of the idea of a limit in mathematics. For specific uses of a limit, see Limit of a sequence and Limit of a function.In mathematics, a limit is the value that a function or sequence "approaches" as the input or index approaches some value. Limits are essential to calculus (and mathematical analysis in general) and are used to define continuity, derivatives, and integrals.The concept of a limit of a sequence is further generalized to the concept of a limit of a topological net, and is closely related to limit and direct limit in category theory.

Continuity

in mathematics, rigorous formulation of the intuitive concept of a function that varies with no abrupt breaks or jumps. A function is a relationship in which every value of an independent variable—say x—is associated with a value of a dependent variable—say y. Continuity of a function is sometimes expressed by saying that if the x-values are close together, then the y-values of the function will also be close. But if the question “How close?” is asked, difficulties arise.

Differentiation

Errors And Approximations

An approximation is anything that is similar but not exactly equal to something else. The term can be applied to various properties (e.g. value, quantity, image, description) that are nearly, but not exactly correct; similar, but not exactly the same (e.g. the approximate time was 10 o'clock).Although approximation is most often applied to numbers, it is also frequently applied to such things as mathematical functions, shapes, and physical laws.In science, approximation can refer to using a simpler process or model when the correct model is difficult to use. An approximate model is used to make calculations easier. Approximations might also be used if incomplete information prevents use of exact representations.

Rate Of Measures

In mathematics, a rate is the ratio between two related quantities.[1][not in citation given] Often it is a rate of change. If the unit or quantity in respect of which something is changing is not specified, usually the rate is per unit time. However, a rate of change can be specified per unit time, or per unit of length or mass or another quantity. The most common type of rate is "per unit time", such as speed, heart rate and flux. Ratios that have a non-time denominator include exchange rates, literacy rates and electric flux. In describing the units of a rate, the word "per" is used to separate the units of the two measurements used to calculate the rate (for example a heart rate is expressed "beats per minute"). A rate defined using two numbers of the same units (such as tax rates) or counts (such as literacy rate) will result in a dimensionless quantity, which can be expressed as a percentage (for example, the global literacy rate in 1998 was 80%) or fraction or as a multiple.

Tangents & Normal’s

Maxima And Minima

In mathematical analysis, the maxima and minima (the plural of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema). Pierre de Fermat was one of the first mathematicians to propose a general technique, adequality, for finding the maxima and minima of functions.As defined in set theory, the maximum and minimum of a set are the greatest and least elements in the set, respectively. Unbounded infinite sets, such as the set of real numbers, have no minimum or maximum.

Unit And Dimensions

Vectors

Kinematics

Kinematics is the branch of classical mechanics which describes the motion of points, bodies (objects) and systems of bodies (groups of objects) without consideration of the causes of motion. Kinematics as a field of study is often referred to as the "geometry of motion". For further details, see Analytical dynamics.To describe motion, kinematics studies the trajectories of points, lines and other geometric objects and their differential properties such as velocity and acceleration. Kinematics is used in astrophysics to describe the motion of celestial bodies and systems, and in mechanical engineering, robotics and biomechanics to describe the motion of systems composed of joined parts (multi-link systems) such as an engine, a robotic arm or the skeleton of the human body.

Newton's Law Of Motion

Newton's laws of motion are three physical laws that, together, laid the foundation for classical mechanics. They describe the relationship between a body and the forces acting upon it, and its motion in response to those forces. They have been expressed in several different ways, over nearly three centuries.

Work Power Energy

Collisions

A collision is an event in which two or more bodies exert forces on each other for a relatively short time. Although the most common colloquial use of the word "collision" refers to incidents in which two or more objects collide, the scientific use of the word "collision" implies nothing about the magnitude of the forces.

Centre Of Mass

In physics, the center of mass of a distribution of mass in space is the unique point where the weighted relative position of the distributed mass sums to zero or the point where if a force is applied causes it to move in direction of force without rotation. The distribution of mass is balanced around the center of mass and the average of the weighted position coordinates of the distributed mass defines its coordinates. Calculations in mechanics are often simplified when formulated with respect to the center of mass. In the case of a single rigid body, the center of mass is fixed in relation to the body, and if the body has uniform density, it will be located at the centroid. The center of mass may be located outside the physical body, as is sometimes the case for hollow or open-shaped objects, such as a horseshoe. In the case of a distribution of separate bodies, such as the planets of the Solar System, the center of mass may not correspond to the position of any individual member of the system.

Friction

Friction is the force resisting the relative motion of solid surfaces, fluid layers, and material elements sliding against each other.When surfaces in contact move relative to each other, the friction between the two surfaces converts kinetic energy into thermal energy. This property can have dramatic consequences, as illustrated by the use of friction created by rubbing pieces of wood together to start a fire. Kinetic energy is converted to thermal energy whenever motion with friction occurs, for example when a viscous fluid is stirred. Another important consequence of many types of friction can be wear, which may lead to performance degradation and/or damage to components. Friction is a component of the science of tribology.

Rotatory Motion

Gravitation

Gravity or gravitation is a natural phenomenon by which all things attract one another including stars, planets, galaxies and even light and sub-atomic particles. Gravity is responsible for the formation of the universe (e.g. creating spheres of hydrogen, igniting them under pressure to form stars and grouping them in to galaxies). Gravity is a cause of time dilation (time lapses more slowly in strong gravitation). Without gravity, the universe would be without thermal energy and composed only of equally spaced particles.

Oscillations

Elasticity

In physics, elasticity (from Greek ἐλαστός "ductible") is the ability of a body to resist a distorting influence or stress and to return to its original size and shape when the stress is removed. Solid objects will deform when forces are applied on them. If the material is elastic, the object will return to its initial shape and size when these forces are removed.The physical reasons for elastic behavior can be quite different for different materials. In metals, the atomic lattice changes size and shape when forces are applied (energy is added to the system). When forces are removed, the lattice goes back to the original lower energy state. For rubbers and other polymers, elasticity is caused by the stretching of polymer chains when forces are applied.

Surface Tension

Surface tension is the elastic tendency of liquids which makes them acquire the least surface area possible. Surface tension is an important property that markedly influences many ecosystems. Surface tension is responsible, for example, when an object or insect (e.g. water striders) that is denser than water is able to float or run along the water surface. At liquid-air interfaces, surface tension results from the greater attraction of water molecules to each other (due to cohesion) than to the molecules in the air (due to adhesion). The net effect is an inward force at its surface that causes water to behave as if its surface were covered with a stretched elastic membrane. Because of the relatively high attraction of water molecules for each other, water has a high surface tension (72.8 millinewtons per meter at 20 °C) compared to that of most other liquids. Surface tension is an important factor in the phenomenon of capillarity.

Thermal expansion

Thermal expansion is the tendency of matter to change in volume in response to a change in temperature, through heat transfer.Temperature is a monotonic function of the average molecular kinetic energy of a substance. When a substance is heated, the kinetic energy of its molecules increases. Thus, the molecules begin moving more and usually maintain a greater average separation. Materials which contract with increasing temperature are unusual; this effect is limited in size, and only occurs within limited temperature ranges (see examples below). The degree of expansion divided by the change in temperature is called the material's coefficient of thermal expansion and generally varies with temperature.

Inverse Trigonometric Functions

In mathematics, the inverse trigonometric functions (occasionally called cyclometric functions) are the inverse functions of the trigonometric functions (with suitably restricted domains). Specifically, they are the inverses of the sine, cosine, tangent, cotangent, secant, and cosecant functions. They are used to obtain an angle from any of the angle's trigonometric ratios. Inverse trigonometric functions are widely used in engineering, navigation, physics, and geometry.

Thermodynamics

Thermodynamics is a branch of physics concerned with heat and temperature and their relation to energy and work. It defines macroscopic variables, such as internal energy, entropy, and pressure, that partly describe a body of matter or radiation. It states that the behavior of those variables is subject to general constraints, that are common to all materials, not the peculiar properties of particular materials. These general constraints are expressed in the four laws of thermodynamics. Thermodynamics describes the bulk behavior of the body, not the microscopic behaviors of the very large numbers of its microscopic constituents, such as molecules. Its laws are explained by statistical mechanics, in terms of the microscopic constituents.

Transmission Of Heat

Heat transfer is the exchange of thermal energy between physical systems, depending on the temperature and pressure, by dissipating heat. The fundamental modes of heat transfer are conduction or diffusion, convection and radiation.Heat transfer always occurs from a region of high temperature to another region of lower temperature. Heat transfer changes the internal energy of both systems involved according to the First Law of Thermodynamics.The Second Law of Thermodynamics defines the concept of thermodynamic entropy, by measurable heat transfer.

Current electricity

Thermo Electricity

Electro magnetism

Electromagnetism is the study of the electromagnetic force which is a type of physical interaction that occurs between electrically charged particles. The electromagnetic force usually shows electromagnetic fields, such as electric fields, magnetic fields, and light. The electromagnetic force is one of the four fundamental interactions in nature. The other three fundamental interactions are the strong interaction, the weak interaction, and gravitation.

Electro Magnetic Induction & a.c Circuits

Atomic Physics

Nuclear Physics

Semi Conductors Devices

Semiconductor devices are electronic components that exploit the electronic properties of semiconductor materials, principally silicon, germanium, and gallium arsenide, as well as organic semiconductors. Semiconductor devices have replaced thermionic devices (vacuum tubes) in most applications. They use electronic conduction in the solid state as opposed to the gaseous state or thermionic emission in a high vacuum.

Communication Systems

Electro Magnetic Waves

sound

In physics, sound is a vibration that propagates as a typically audible mechanical wave of pressure and displacement, through a medium such as air or water. In physiology and psychology, sound is the reception of such waves and their perception by the brain.

Ray Optics And Optical Instruments

Physical Optics

Electro Statics

Electrostatics is a branch of physics that deals with the phenomena and properties of stationary or slow-moving electric charges with no acceleration.Since classical physics, it has been known that some materials such as amber attract lightweight particles after rubbing. The Greek word for amber, ήλεκτρον electron, was the source of the word 'electricity'. Electrostatic phenomena arise from the forces that electric charges exert on each other. Such forces are described by Coulomb's law. Even though electrostatically induced forces seem to be rather weak, the electrostatic force between e.g. an electron and a proton, that together make up a hydrogen atom, is about 36 orders of magnitude stronger than the gravitational force acting between them.

Atomic Structure

An atom is a complex arrangement of negatively charged electrons arranged in defined shells about a positively charged nucleus. This nucleus contains most of the atom's mass and is composed of protons and neutrons (except for common hydrogen which has only one proton). All atoms are roughly the same size. A convenient unit of length for measuring atomic sizes is the angstrom (Å), which is defined as 1 x 10-10 meters. The diameter of an atom is approximately 2-3 Å.

Periodic Classifications

The periodic table is a tabular arrangement of the chemical elements, ordered by their atomic number (number of protons in the nucleus), electron configurations, and recurring chemical properties. The table also shows four rectangular blocks: s-, p- d- and f-block. In general, within one row (period) the elements are metals on the lefthand side, and non-metals on the righthand side.

Chemical Bonding

A chemical bond is an attraction between atoms that allows the formation of chemical substances that contain two or more atoms. The bond is caused by the electrostatic force of attraction between opposite charges, either between electrons and nuclei, or as the result of a dipole attraction. The strength of chemical bonds varies considerably; there are "strong bonds" such as covalent or ionic bonds and "weak bonds" such as dipole–dipole interactions, the London dispersion force and hydrogen bonding.

Gaseous State

Stoichiometry

Stoichiometry is founded on the law of conservation of mass where the total mass of the reactants equals the total mass of the products leading to the insight that the relations among quantities of reactants and products typically form a ratio of positive integers. This means that if the amounts of the separate reactants are known, then the amount of the product can be calculated. Conversely, if one reactant has a known quantity and the quantity of product can be empirically determined, then the amount of the other reactants can also be calculated.

Hydrogen And Its Compounds

Hydrogen is a chemical element with chemical symbol H and atomic number 1. With an atomic weight of 1.00794 u, hydrogen is the lightest element on the periodic table. Its monatomic form (H) is the most abundant chemical substance in the universe, constituting roughly 75% of all baryonic mass.[9][note 1] Non-remnant stars are mainly composed of hydrogen in its plasma state. The most common isotope of hydrogen, termed protium (name rarely used, symbol 1H), has one proton and no neutrons.

Alkaline Earth Metals

The alkaline earth metals are six chemical elements in column (group) 2 of the Periodic table. They are beryllium (Be), magnesium (Mg), calcium (Ca), strontium (Sr), barium (Ba), and radium (Ra). They have very similar properties: they are all shiny, silvery-white, somewhat reactive metals at standard temperature and pressure.Structurally, they have in common an outer s- electron shell which is full;. that is, this orbital contains its full complement of two electrons, which these elements readily lose to form cations with charge 2+, and an oxidation state (oxidation number) of +2.All the discovered alkaline earth metals occur in nature. Experiments have been conducted to attempt the synthesis of element 120, next potential member of the group, but they have all met with failure.

IV A Group Elements

Group 4 is a group of elements in the periodic table. It contains the elements titanium (Ti), zirconium (Zr), hafnium (Hf) and rutherfordium (Rf). This group lies in the d-block of the periodic table. The group itself has not acquired a trivial name; it belongs to the broader grouping of the transition metals. The three Group 4 elements that occur naturally are titanium (Ti), zirconium (Zr) and hafnium (Hf). The first three members of the group share similar properties; all three are hard refractory metals under standard conditions. However, the fourth element rutherfordium (Rf), has been synthesized in the laboratory; none of its isotopes have been found occurring in nature. All isotopes of rutherfordium are radioactive. So far, no experiments in a supercollider have been conducted to synthesize the next member of the group, unpenthexium (Uph), and it is unlikely that they will be synthesized in the near future.

Chemistry Of Carbon Compounds

Compounds of carbon are defined as chemical substances containing carbon. More compounds of carbon exist than any other chemical element except for hydrogen. Organic carbon compounds are far more numerous than inorganic carbon compounds. In general bonds of carbon with other elements are covalent bonds. Carbon is tetravalent but carbon free radicals and carbenes occur as short-lived intermediates. Ions of carbon are carbocations and carbanions and are also short-lived. An important carbon property is catenation as the ability to form long carbon chains and rings.

Noble Gases

The noble gases make a group of chemical elements with similar properties. Under standard conditions, they are all odorless, colorless, monatomic gases with very low chemical reactivity. The six noble gases that occur naturally are helium (He), neon (Ne), argon (Ar), krypton (Kr), xenon (Xe), and the radioactive radon (Rn). For the first six periods of the periodic table, the noble gases are exactly the members of group 18 of the periodic table. It is possible that due to relativistic effects, the group 14 element flerovium exhibits some noble-gas-like properties, instead of the group 18 element ununoctium.Noble gases are typically highly unreactive except when under particular extreme conditions. The inertness of noble gases makes them very suitable in applications where reactions are not wanted. For example: argon is used in lightbulbs to prevent the hot tungsten filament from oxidizing; also, helium is breathed by deep-sea divers to prevent oxygen and nitrogen toxicity.

Environmental Chemistry

Environmental chemistry is the scientific study of the chemical and biochemical phenomena that occur in natural places. It should not be confused with green chemistry, which seeks to reduce potential pollution at its source. It can be defined as the study of the sources, reactions, transport, effects, and fates of chemical species in the air, soil, and water environments; and the effect of human activity and biological activity on these. Environmental chemistry is an interdisciplinary science that includes atmospheric, aquatic and soil chemistry, as well as heavily relying on analytical chemistry and being related to environmental and other areas of science. Environmental chemistry is the study of chemical processes occurring in the environment which are impacted by humankind's activities. These impacts may be felt on a local scale, through the presence of urban air pollutants or toxic substances arising from a chemical waste site, or on a global scale, through depletion of stratospheric ozone or global warming. The focus in our courses and research activities is upon developing a fundamental understanding of the nature of these chemical processes, so that humankind's activities can be accurately evaluated.

Group IIIA (Boron Family)

The boron group are the chemical elements in group 13 of the periodic table, comprising boron (B), aluminium (Al), gallium (Ga), indium (In), thallium (Tl), and ununtrium (Uut). The elements in the boron group are characterized by having three electrons in their outer energy levels (valence layers).These elements have also been referred to as icosagens and triels.Boron is classified as a metalloid while the rest, with the possible exception of ununtrium, are considered post-transition metals. Ununtrium has not yet been confirmed to be post-transition, due to relativistic effects, might not turn out to be one. Boron occurs sparsely, probably because bombardment by the subatomic particles produced from natural radioactivity disrupts its nuclei. Aluminium occurs widely on earth, and indeed is the third most abundant element in the Earth's crust (8.3%). Gallium is found in the earth with an abundance of 13 ppm. Indium is the 61st most abundant element in the earth's crust, and thallium is found in moderate amounts throughout the planet. Ununtrium is never found in nature and therefore is termed a synthetic element.

Solutions

In chemistry, a solution is a homogeneous mixture composed of only one phase. In such a mixture, a solute is a substance dissolved in another substance, known as a solvent. The solution more or less takes on the characteristics of the solvent including its phase, and the solvent is commonly the major fraction of the mixture. The concentration of a solute in a solution is a measure of how much of that solute is dissolved in the solvent, with regard to how much solvent is present.

Transition Elements

Chemistry in Biology and Medicine

Innovations in chemistry have been essential for major breakthroughs in biology and medicine. At the heart of bioorthogonal chemical reactions is the development of uniquely reactive functional groups that allows specific covalent ligation of molecules in biological systems. Despite the challenges of performing specific chemical reactions in biological settings, a variety of bioorthogonal ligation methods such as native chemical ligation, Staudinger ligation and many cycloaddition reactions have been developed.

Chemistry in Carbon Compounds

Compounds of carbon are defined as chemical substances containing carbon. More compounds of carbon exist than any other chemical element except for hydrogen. Organic carbon compounds are far more numerous than inorganic carbon compounds. In general bonds of carbon with other elements are covalent bonds. Carbon is tetravalent but carbon free radicals and carbenes occur as short-lived intermediates. Ions of carbon are carbocations and carbanions and are also short-lived. An important carbon property is catenation as the ability to form long carbon chains and rings.

Nuclear Chemistry

Nuclear chemistry is the subfield of chemistry dealing with radioactivity, nuclear processes, such as nuclear transmutation, and nuclear properties.It is the chemistry of radioactive elements such as the actinides, radium and radon together with the chemistry associated with equipment (such as nuclear reactors) which are designed to perform nuclear processes. This includes the corrosion of surfaces and the behavior under conditions of both normal and abnormal operation (such as during an accident). An important area is the behavior of objects and materials after being placed into a nuclear waste storage or disposal site.

Acids and Bases

There are three major classifications of substances known as acids or bases. The Arrhenius definition states that an acid produces H+ in solution and a base produces OH-. This theory was developed by Svante Arrhenius in 1883. Later, two more sophisticated and general theories were proposed. These are the Brønsted-Lowry and the Lewis definitions of acids and bases. The Lewis theory is discussed elsewhere.

Chemical Kinetics

Chemical kinetics, also known as reaction kinetics, is the study of rates of chemical processes. Chemical kinetics includes investigations of how different experimental conditions can influence the speed of a chemical reaction and yield information about the reaction's mechanism and transition states, as well as the construction of mathematical models that can describe the characteristics of a chemical reaction. In 1864, Peter Waage and Cato Guldberg pioneered the development of chemical kinetics by formulating the law of mass action, which states that the speed of a chemical reaction is proportional to the quantity of the reacting substances.

V A Group Elements

The group 5A elements aren't as recognizable as other elements on the periodic table, but they are important nonetheless. This lesson will examine properties they share and will give some examples of why this group is so important.

VI A Group Elements

VII A Group Elements