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Astronomy glossary

Absolute Magnitude
A scale for measuring the actual brightness of a celestial object without accounting for the distance of the object. Absolute magnitude measures how bright an object would appear if it were exactly 10 parsecs (about 33 light-years) away from Earth. On this scale, the Sun has an absolute magnitude of +4.8 while it has an apparent magnitude of -26.7 because it is so close.

Absolute Zero
The temperature at which the motion of all atoms and molecules stops and no heat is given off. Absolute zero is reached at 0 degrees Kelvin or -273.16 degrees Celsius.

Ablation
A process by where the atmosphere melts away and removes the surface material of an incoming meteorite.

Accretion
The process by where dust and gas accumulated into larger bodies such as stars and planets.

Accretion Disk
A disk of gas that accumulates around a center of gravitational attraction, such as a white dwarf, neutron star, or black hole. As the gas spirals in, it becomes hot and emits light or even X-radiation.

Achondrite
A stone meteorite that contains no chondrules.

Albedo
The reflective property of a non-luminous object. A perfect mirror would have an albedo of 100% while a black hole would have an albedo of 0%.

Albedo Feature
A dark or light marking on the surface of an object that may or may not be a geological or topographical feature.

Altitude
The angular distance of an object above the horizon.

Am star
Am star is a chemically peculiar star belonging to the more general class of A-type stars. The spectrum of the Am stars shows abnormal enhancements and deficiencies of certain metals.

Antimatter
Matter consisting of particles with charges opposite that of ordinary matter. In antimatter, protons have a negative charge while electrons have a positive charge.

Antipodal Point
A point that is on the direct opposite side of a planet.

Apastron
The point of greatest separation of two stars, such as in a binary star system.

Aperture
The size of the opening through which light passes in an optical instrument such as a camera or telescope. A higher number represents a smaller opening while a lower number represents a larger opening.

Aphelion
The point in the orbit of a planet or other celestial body where it is farthest from the Sun.

Apoapsis
Apoapsis is the point of furthest excursion, or separation, between two orbiting objects.

Apogee
The point in the orbit of the Moon or other satellite where it is farthest from the Earth.

Apparent Magnitude
The apparent brightness of an object in the sky as it appears to an observer on Earth. Bright objects have a low apparent magnitude while dim objects will have a higher apparent magnitude.

Asterism
Asterism is a pattern of stars recognized on Earth's night sky. It may form part of an official constellation, or be composed of stars from more than one.

Asteroid
A small planetary body in orbit around the Sun, larger than a meteoroid but smaller than a planet. Most asteroids can be found in a belt between the orbits of Mars and Jupiter. The orbits of some asteroids take them close to the Sun, which also takes them across the paths of the planets.

Astrochemistry
The branch of science that explores the chemical interactions between dust and gas interspersed between the stars.

Astrometric binary
Astrometric binary is a type of binary system where evidence for an unseen orbiting companion is revealed by its periodic gravitational perturbation of the visible component. See also spectroscopic binary.

Astronomical Unit (AU)
A unit of measure equal to the average distance between the Earth and the Sun, approximately 93 million miles.

Atmosphere
A layer of gases surrounding a planet, moon, or star. The Earth's atmosphere is 120 miles thick and is composed mainly of nitrogen, oxygen, carbon dioxide, and a few other trace gases.

Aurora
A glow in a planet's ionosphere caused by the interaction between the planet's magnetic field and charged particles from the Sun. This phenomenon is known as the Aurora Borealis in the Earth's northern hemisphere and the Aurora Australis in the Earth's Southern Hemisphere.

Aurora Australis
Also known as the southern lights, this is an atmospheric phenomenon that displays a diffuse glow in the sky in the southern hemisphere. It is caused by charged particles from the Sun as they interact with the Earth's magnetic field. Known as the Aurora Borealis in the northern hemisphere.

Aurora Borealis
Also known as the northern lights, this is an atmospheric phenomenon that displays a diffuse glow in the sky in the northern hemisphere. It is caused by charged particles from the Sun as they interact with the Earth's magnetic field. Known as the Aurora Australis in the southern hemisphere.

Axis
Also known as the poles, this is an imaginary line through the center of rotation of an object.

Azimuth
The angular distance of an object around or parallel to the horizon from a predefined zero point.

Bar
A unit of measure of atmospheric pressure. One bar is equal to 0.987 atmospheres, 1.02 kg/cm2, 100 kilopascal, and 14.5 lbs/square inch.

Big Bang
The theory that suggests that the universe was formed from a single point in space during a cataclysmic explosion about 13.7 billion years ago. This is the current accepted theory for the origin of the universe and is supported by measurements of background radiation and the observed expansion of space.

Binary
A system of two stars that revolve around a common center of gravity.

Black Hole
The collapsed core of a massive star. Stars that are very massive will collapse under their own gravity when their fuel is exhausted. The collapse continues until all matter is crushed out of existence into what is known as a singularity. The gravitational pull is so strong that not even light can escape.

Blueshift
A shift in the lines of an object's spectrum toward the blue end. Blueshift indicates that an object is moving toward the observer. The larger the blueshift, the faster the object is moving.

Bolide
A term used to describe an exceptionally bright meteor. Bolides typically will produce a sonic boom.

Brown dwarf
Brown dwarf is a substellar object that is too low in mass to sustain the nuclear fusion of hydrogen-1 in its core, which is a characteristic of stars on the main sequence. Brown dwarfs can still generate energy from gravitational contraction and by the fusion of deuterium.

Caldera
A type of volcanic crater that is extremely large, usually formed by the collapse of a volcanic cone or by a violent volcanic explosion. Crater Lake is one example of a caldera on Earth.

Catena
A series or chain of craters.

Cavus
A hollow, irregular depression.

Celestial Equator
An imaginary line that divides the celestial sphere into a northern and southern hemisphere.

Celestial Poles
The North and South poles of the celestial sphere.

Celestial Sphere
An imaginary sphere around the Earth on which the stars and planets appear to be positioned.

Cepheid Variable
This is a variable star whose light pulsates in a regular cycle. The period of fluctuation is linked to the brightness of the star. Brighter Cepheids will have a longer period.

Chaos
A distinctive area of broken terrain.

Chasma
Another name used to describe a canyon.

Chondrite
A meteorite that contains chondrules.

Chondrule
Small, glassy spheres commonly found in meteorites.

Chromosphere
The part of the Sun's atmosphere just above the surface.

Circumpolar Star
A star that never sets but always stays above the horizon. This depends on the location of the observer. The further South you go the fewer stars will be circumpolar. Polaris, the North Star, is circumpolar in most of the northern hemisphere.

Circumstellar Disk
A torus or ring-shaped accumulation of gas, dust, or other debris in orbit around a star in different phases of its life cycle.

Color index
A numeric value that is used to compare the brightness of a star measured from two different frequency bands of the electromagnetic spectrum. Because the energy output of a star varies by frequency as a function of temperature, the color index can be used to indicate the star's temperature.

Coma
An area of dust or gas surrounding the nucleus of a comet.

Comet
A gigantic ball of ice and rock that orbit the Sun in a highly eccentric orbit. Some comets have an orbit that brings them close to the Sun where they form a long tail of gas and dust as they are heated by the Sun's rays.

Commensurability
The property of two objects orbiting the same body whose periods are in a rational proportion. For example, the orbital period of Saturn around the Sun is very nearly 5/2 the orbital period of Jupiter.

Conjunction
An event that occurs when two or more celestial objects appear close together in the sky.

Constellation
A grouping of stars that make an imaginary picture in the sky.

Corona
The outer part of the Sun's atmosphere. The corona is visible from Earth during a total solar eclipse. It is the bright glow seen in most solar eclipse photos.

Cosmic Ray
Atomic nuclei (mostly protons) that are observed to strike the Earth's atmosphere with extremely high amounts of energy.

Cosmic String
A tube-like configuration of energy that is believed to have existed in the early universe. A cosmic string would have a thickness smaller than a trillionth of an inch but its length would extend from one end of the visible universe to the other.

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Cosmogony The study of celestial systems, including the Solar System, stars, galaxies, and galactic clusters. This is the definition of cosmology, not cosmogony.

Cosmology
A branch of science that deals with studying the origin, structure, and nature of the universe. This is the definition of the word 'cosmogony', not cosmology.

Crater
A bowl-shaped depression formed by the impact of an asteroid or meteoroid. Also the depression around the opening of a volcano.

Dark Matter
A term used to describe matter in the universe that cannot be seen, but can be detected by its gravitational effects on other bodies.

Debris Disk
A ring-shaped circumstellar disk of dust and debris in orbit around a star. Debris disks can be created as the next phase in planetary system development following the protoplanetary disk phase. They can also be formed by collisions between planetesimals.

Declination
The angular distance of an object in the sky from the celestial equator.

Density
The amount of matter contained within a given volume. Density is measured in grams per cubic centimeter (or kilograms per liter). The density of water is 1.0, iron is 7.9, and lead is 11.3.

Disk
The surface of the Sun or other celestial body projected against the sky.

Double Asteroid
Two asteroids that revolve around each other and are held together by the gravity between them. Also called a binary asteroid.

Doppler Effect
The apparent change in wavelength of sound or light emitted by an object in relation to an observer's position. An object approaching the observer will have a shorter wavelength (blue) while an object moving away will have a longer (red) wavelength. The Doppler effect can be used to estimate an object's speed and direction.

Double Star
A grouping of two stars. This grouping can be apparent, where the stars seem close together, or physical, such as a binary system.

Dwarf Planet
A celestial body orbiting the Sun that is massive enough to be rounded by its own gravity but has not cleared its neighboring region of planetesimals and is not a satellite. It has to have sufficient mass to overcome rigid body forces and achieve hydrostatic equilibrium. Pluto is considered to be a dwarf planet.

Eccentricity
The measure of how an object's orbit differs from a perfect circle. Eccentricity defines the shape of an object's orbit.

Eclipse
The total or partial blocking of one celestial body by another.

Eclipsing Binary
A binary system where one object passes in front of the other, cutting off some or all of its light.

Ecliptic
An imaginary line in the sky traced by the Sun as it moves in its yearly path through the sky.

Effective temperature
Effective temperature of a star or planet is the temperature of an ideal black body that would emit the same total amount of electromagnetic radiation.

Ejecta
Material from beneath the surface of a body such as a moon or planet that is ejected by an impact such as a meteor and distributed around the surface. Ejecta usually appear as a lighter color than the surrounding surface.

Electromagnetic Radiation
Another term for light. Light waves created by fluctuations of electric and magnetic fields in space.

Electromagnetic Spectrum
The full range of frequencies, from radio waves to gamma waves, that characterizes light.

Ellipse
An ellipse is an oval shape. Johannes Kepler discovered that the orbits of the planets were elliptical in shape rather than circular.

Elliptical Galaxy
A galaxy whose structure shaped like an ellipse and is smooth and lacks complex structures such as spiral arms.

Elongation
The angular distance of a planetary body from the Sun as seen from Earth. A planet at greatest eastern elongation is seen in the evening sky and a planet at greatest western elongation will be seen in the morning sky.

Ephemeris
A table of data arranged by date. Ephemeris tables are typically to list the positions of the Sun, Moon, planets and other solar system objects.

Equinox
The two points at which the Sun crosses the celestial equator in its yearly path in the sky. The equinoxes occur on or near March 21 and September 22. The equinoxes signal the start of the Spring and Autumn seasons.

Escape Velocity
The speed required for an object to escape the gravitational pull of a planet or other body.

Event Horizon
The invisible boundary around a black hole past which nothing can escape the gravitational pull - not even light.

Evolved Star
A star that is near the end of its life cycle where most of its fuel has been used up. At this point the star begins to loose mass in the form of stellar wind.

Extinction
The apparent dimming of star or planet when low on the horizon due to absorption by the Earth's atmosphere.

Extragalactic
A term that means outside of or beyond our own galaxy.

Extraterrestrial
A term used to describe anything that does not originate on Earth.

Eyepiece
The lens at the viewing end of a telescope. The eyepiece is responsible for enlarging the image captured by the instrument. Eyepieces are available in different powers, yielding differing amounts of magnification.

Faculae
Bright patches that are visible on the Sun's surface, or photosphere.

Filament
A strand of cool gas suspended over the photosphere by magnetic fields, which appears dark as seen against the disk of the Sun.

Finder
A small, wide-field telescope attached to a larger telescope. The finder is used to help point the larger telescope to the desired viewing location.

Fireball
An extremely bright meteor. Also known as bolides, fireballs can be several times brighter than the full Moon. Some can even be accompanied by a sonic boom.

Flare Star
A faint red star that appears to change in brightness due to explosions on its surface.

Galactic Halo
The name given to the spherical region surrounding the center, or nucleus of a galaxy.

Galactic Nucleus
A tight concentration of stars and gas found at the innermost regions of a galaxy. Astronomers now believe that massive black holes may exist in the center of many galaxies.

Galaxy
A large grouping of stars. Galaxies are found in a variety of sizes and shapes. Our own Milky Way galaxy is spiral in shape and contains several billion stars. Some galaxies are so distant the their light takes millions of years to reach the Earth.

Galilean Moons
The name given to Jupiter's four largest moons, Io, Europa, Callisto & Ganymede. They were discovered independently by Galileo Galilei and Simon Marius.

Gamma-ray
The highest energy, shortest wavelength form of electromagnetic radiation.

Geosynchronous Orbit
An orbit in which a satellite's orbital velocity is matched to the rotational velocity of the planet. A spacecraft in geosynchronous orbit appears to hang motionless above one position of a planet's surface.

Giant Molecular Cloud (GMC)
Massive clouds of gas in interstellar space composed primarily of hydrogen molecules. These clouds have enough mass to produce thousands of stars and are frequently the sites of new star formation.

Globular Cluster
A tight, spherical grouping of hundreds of thousands of stars. Globular clusters are composed of older stars, and are usually found around the central regions of a galaxy.

Granulation
A pattern of small cells that can be seen on the surface of the Sun. They are caused by the convective motions of the hot gases inside the Sun.

Gravitational Lens
A concentration of matter such as a galaxy or cluster of galaxies that bends light rays from a background object. Gravitational lensing results in duplicate images of distant objects.

Gravity
A mutual physical force of nature that causes two bodies to attract each other.

Greenhouse Effect
An increase in temperature caused when incoming solar radiation is passed but outgoing thermal radiation is blocked by the atmosphere. Carbon dioxide and water vapor are two of the major gases responsible for this effect.

Heliopause
The point in space at which the solar wind meets the interstellar medium or solar wind from other stars.

Heliosphere
The space within the boundary of the heliopause containing the Sun and the Solar System.

Hydrogen
An element consisting of one electron and one proton. Hydrogen is the lightest of the elements and is the building block of the universe. Stars form from massive clouds of hydrogen gas.

Hubble's Law
The law of physics that states that the farther a galaxy is from us, the faster it is moving away from us.

Hydrostatic equilibrium
A state that occurs when compression due to gravity is balanced by a pressure gradient which creates a pressure gradient force in the opposite direction. Hydrostatic equillibrium is responsible for keeping stars from imploding and for giving planets their spherical shape.

Hypergalaxy
A system consisting of a spiral galaxy surrounded by several dwarf white galaxies, often ellipticals. Our galaxy and the Andromeda galaxy are examples of hypergalaxies.

Ice
A term used to describe water or a number of gases such as methane or ammonia when in a solid state.

Inclination
A measure of the tilt of a planet's orbital plane in relation to that of the Earth.

Inferior Conjunction
A conjunction of an inferior planet that occurs when the planet is lined up directly between the Earth and the Sun.

Inferior Planet
A planet that orbits between the Earth and the Sun. Mercury and Venus are the only two inferior planets in our solar system.

International Astronomical Union (IAU)
An international organization that unites national astronomical societies from around the world and acts as the internationally recognized authority for assigning designations to celestial bodies and their surface features.

Interplanetary Magnetic Field
The magnetic field carried along with the solar wind.

Interstellar Medium
The gas and dust that exists in open space between the stars.

Ionosphere
A region of charged particles in a planet's upper atmosphere. In Earth's atmosphere, the ionosphere begins at an altitude of about 25 miles and extends outward about 250.

Iron Meteorite
A meteorite that is composed mainly of iron mixed with smaller amounts of nickel.

Irregular Galaxy
A galaxy with no spiral structure and no symmetric shape. Irregular galaxies are usually filamentary or very clumpy in shape.

Irregular Satellite
A satellite that orbits a planet far away with an orbit that is eccentric and inclined. They also tend to have retrograde orbits. Irregular satellites are believed to have been captured by the planet's gravity rather than being formed along with the planet.

Jansky
A unit used in radio astronomy to indicate the flux density (the rate of flow of radio waves) of electromagnetic radiation received from outer space. A typical radio source has a spectral flux density of roughly 1 Jy. The jansky was named to honor Karl Gothe Jansky who developed radio astronomy in 1932.

Jet
A narrow stream of gas or particles ejected from an accretion disk surrounding a star or black hole.

Kelvin
A temperature scale used in sciences such as astronomy to measure extremely cold temperatures. The Kelvin temperature scale is just like the Celsius scale except that the freezing point of water, zero degrees Celsius, is equal to 273 degrees Kelvin. Absolute zero, the coldest known temperature, is reached at 0 degrees Kelvin or -273.16 degrees Celsius.

Kepler's First Law
A planet orbits the Sun in an ellipse with the Sun at one focus.

Kepler's Second Law
A ray directed from the Sun to a planet sweeps out equal areas in equal times.

Kepler's Third Law
The square of the period of a planet's orbit is proportional to the cube of that planet's semi major axis; the constant of proportionality is the same for all planets.

Kiloparsec
A distance equal to 1000 parsecs.

Kirkwood Gaps
Regions in the main belt of asteroids where few or no asteroids are found. They were named after the scientist who first noticed them.

Kuiper Belt
A large ring of icy, primitive objects beyond the orbit of Neptune. Kuiper Belt objects are believed to be remnants of the original material that formed the Solar System. Some astronomers believe Pluto and Charon are Kuiper Belt objects.

Lagrange Point
French mathematician and astronomer Joseph Louis Lagrange showed that three bodies could lie at the apexes of an equilateral triangle which rotates in its plane. If one of the bodies is sufficiently massive compared with the other two, then the triangular configuration is apparently stable. Such bodies are sometimes referred to as Trojans. The leading apex of the triangle is known as the leading Lagrange point or L4; the trailing apex is the trailing Lagrange point or L5.

Lenticular Galaxy
A disk-shaped galaxy that contains no conspicuous structure within the disk. Lenticular galaxies tend to look more like elliptical galaxies than spiral galaxies.

Libration
An effect caused by the apparent wobble of the Moon as it orbits the Earth. The Moon always keeps the same side toward the Earth, but due to libration, 59% of the Moon's surface can be seen over a period of time.

Light Year
An astronomical unit of measure equal to the distance light travels in a year, approximately 5.8 trillion miles.

Limb
The outer edge or border of a planet or other celestial body.

Local Group
A small group of about two dozen galaxies of which our own Milky Way galaxy is a member.

Luminosity
The amount of light emitted by a star.

Lunar Eclipse
A phenomenon that occurs when the Moon passes into the shadow of the Earth. A partial lunar eclipse occurs when the Moon passes into the penumbra, or partial shadow. In a total lunar eclipse, the Moon passes into the Earth's umbra, or total shadow.

Lunar Month
The average time between successive new or full moons. A lunar month is equal to 29 days 12 hours 44 minutes. Also called a synodic month.

Lunation
The interval of a complete lunar cycle, between one new Moon and the next. A lunation is equal to 29 days, 12 hours, and 44 minutes.

Magellanic Clouds
Two small, irregular galaxies found just outside our own Milky Way galaxy. The Magellanic Clouds are visible in the skies of the southern hemisphere.

Magnetic Field
A condition found in the region around a magnet or an electric current, characterized by the existence of a detectable magnetic force at every point in the region and by the existence of magnetic poles.

Magnetic Pole
Either of two limited regions in a magnet at which the magnet's field is most intense.

Magnetosphere
The area around a planet most affected by its magnetic field. The boundary of this field is set by the solar wind.

Magnitude
The degree of brightness of a star or other object in the sky according to a scale on which the brightest star has a magnitude -1.4 and the faintest visible star has magnitude 6. Sometimes referred to as apparent magnitude. In this scale, each number is 2.5 times the brightness of the previous number. Thus a star with a magnitude of 1 is 100 times brighter than on with a visual magnitude of 6.

Main Belt
The area between Mars and Jupiter where most of the asteroids in our solar system are found.

Major Planet
A name used to describe any planet that is considerably larger and more massive than the Earth, and contains large quantities of hydrogen and helium. Jupiter and Neptune are examples of major planets.

Mare
A term used to describe a large, circular plain. The word mare means "sea". On the Moon, the maria are the smooth, dark-colored areas.

Mass
A measure of the total amount of material in a body, defined either by the inertial properties of the body or by its gravitational influence on other bodies.

Matter
A word used to describe anything that contains mass.

Meridian
An imaginary circle drawn through the North and South poles of the celestial equator.

Metal
A term used by astronomers to describe all elements except hydrogen and helium, as in "the universe is composed of hydrogen, helium and traces of metals". This astronomical definition is quite different from the traditional chemistry definition of a metal.

Meteor
A small particle of rock or dust that burns away in the Earth's atmosphere. Meteors are also referred to as shooting stars.

Meteor Shower
An event where a large number of meteors enter the Earth's atmosphere from the same direction in space at nearly the same time. Most meteor showers take place when the Earth passes through the debris left behind by a comet.

Meteorite
An object, usually a chunk or metal or rock, that survives entry through the atmosphere to reach the Earth's surface. Meteors become meteorites if they reach the ground.

Meteoroid
A small, rocky object in orbit around the Sun, smaller than an asteroid.

Millibar
A measure of atmospheric pressure equal to 1/1000 of a bar. Standard sea-level pressure on Earth is about 1013 millibars.

Minor Planet
A term used since the 19th century to describe objects, such as asteroids, that are in orbit around the Sun but are not planets or comets. In 2006, the International Astronomical Union reclassified minor planets as either dwarf planets or small solar system bodies.

Molecular Cloud
An interstellar cloud of molecular hydrogen containing trace amounts of other molecules such as carbon monoxide and ammonia.

Nadir
A term used to describe a point directly underneath an object or body.

Nebula
A cloud of dust and gas in space, usually illuminated by one or more stars. Nebulae represent the raw material the stars are made of.

Neutrino
A fundamental particle produced by the nuclear reactions in stars. Neutrinos are very hard to detect because the vast majority of them pass completely through the Earth without interacting.

Neutron Star
A compressed core of an exploded star made up almost entirely of neutrons. Neutron stars have a strong gravitational field and some emit pulses of energy along their axis. These are known as pulsars.

Newton's First Law of Motion
A body continues in its state of constant velocity (which may be zero) unless it is acted upon by an external force.

Newton's Second Law of Motion
For an unbalanced force acting on a body, the acceleration produced is proportional to the force impressed; the constant of proportionality is the inertial mass of the body.

Newton's Third Law of Motion
In a system where no external forces are present, every action force is always opposed by an equal and opposite reaction.

Nova
A star that flares up to several times its original brightness for some time before returning to its original state.

Nuclear Fusion
The nuclear process whereby several small nuclei are combined to make a larger one whose mass is slightly smaller than the sum of the small ones. Nuclear fusion is the reaction that fuels the Sun, where hydrogen nuclei are fused to form helium.

Obliquity
The angle between a body's equatorial plane and orbital plane.

Oblateness
A measure of flattening at the poles of a planet or other celestial body.

Occultation
An event that occurs when one celestial body conceals or obscures another. For example, a solar eclipse is an occultation of the Sun by the Moon.

Oort Cloud
A theoretical shell of comets that is believed to exist at the outermost regions of our solar system. The Oort cloud was named after the Dutch astronomer who first proposed it.

Open Cluster
A collection of young stars that formed together. They may or may not be still bound by gravity. Some of the youngest open clusters are still embedded in the gas and dust from which they formed.

Opposition
The position of a planet when it is exactly opposite the Sun in the sky as seen from Earth. A planet at opposition is at its closest approach to the Earth and is best suitable for observing.

Orbit
The path of a celestial body as it moves through space.

Parallax
The apparent change in position of two objects viewed from different locations.

Parsec
A large distance often used in astronomy. A parsec is equal to 3.26 light-years.

Patera
A shallow crater with a complex, scalloped edge.

Penumbra
The area of partial illumination surrounding the darkest part of a shadow caused by an eclipse.

Perigee
The point in the orbit of the Moon or other satellite at which it is closest to the Earth.

Perihelion
The point in the orbit of a planet or other body where it is closest to the Sun.

Perturb
To cause a planet or satellite to deviate from a theoretically regular orbital motion.

Phase
The apparent change in shape of the Moon and inferior planets as seen from Earth as they move in their orbits.

Photon
A particle of light composed of a minute quantity of electromagnetic energy.

Photosphere
The bright visible surface of the Sun.

Planemo
A large planet or planetary body that does not orbit a star. Planemos instead wander cold and alone through the cosmos. It is believed that most planemos once orbited their mother star but were ejected from the star system by gravitational interaction with another massive object.

Planet
A celestial body orbiting a star or stellar remnant that is massive enough to be rounded by its own gravity, is not massive enough to cause thermonuclear fusion, and has cleared its neighboring region of planetesimals.

Planetary Nebula
A shell of gas surrounding a small, white star. The gas is usually illuminated by the star, producing a variety of colors and shapes.

Planetesimal
A solid object that is believed to exist in protoplanetary disks and in debris disks. Planetesimals are formed from small dust grains that collide and stick together and are the building blocks that eventually form planets in new planetary systems.

Planitia
A low plain.

Planum
A high plain or plateau.

Plasma
A form of ionized gas in which the temperature is too high for atoms to exist in their natural state. Plasma is composed of free electrons and free atomic nuclei.

Precession
The apparent shift of the celestial poles caused by a gradual wobble of the Earth's axis.

Prominence
An explosion of hot gas that erupts from the Sun's surface. Solar prominences are usually associated with sunspot activity and can cause interference with communications on Earth due to their electromagnetic effects on the atmosphere.

Prograde Orbit
In reference to a satellite, a prograde orbit means that the satellite orbits the planet in the same direction as the planet's rotation. A planet is said to have a prograde orbit if the direction of its orbit is the same as that of the majority of other planets in the system.

Proper Motion
The apparent angular motion across the sky of an object relative to the Solar System.

Protoplanetary Disk
A rotating circumstellar disk of dense gas surrounding a young newly formed star. It is thought that planets are eventually formed from the gas and dust within the protoplanetary disk.

Protostar
Dense regions of molecular clouds where stars are forming.

Pulsar
A spinning neutron star that emits energy along its gravitational axis. This energy is received as pulses as the star rotates.

Quadrature
A point in the orbit of a superior planet where it appears at right angles to the Sun as seem from Earth.

Quasar
An unusually bright object found in the remote areas of the universe. Quasars release incredible amounts of energy and are among the oldest and farthest objects in the known universe. They may be the nuclei of ancient, active galaxies.

Quasi-Stellar Object
Sometimes also called quasi-stellar source, this is a star-like object with a large redshift that gives off a strong source of radio waves. They are highly luminous and presumed to be extragalactic.

Radial Velocity
The movement of an object either towards or away from a stationary observer.

Radiant
A point in the sky from which meteors in a meteor shower seem to originate.

Radiation
Energy radiated from an object in the form of waves or particles.

Radiation Belt
Regions of charged particles in a magnetosphere.

Radio Galaxy
A galaxy that gives off large amounts of energy in the form of radio waves.

Red Giant
A stage in the evolution of a star when the fuel begins to exhaust and the star expands to about fifty times its normal size. The temperature cools, which gives the star a reddish appearance.

Redshift
A shift in the lines of an object's spectrum toward the red end. Redshift indicates that an object is moving away from the observer. The larger the redshift, the faster the object is moving.

Regular Satellite
A satellite that orbits close to a planet in a nearly circular, equatorial orbit. Regular satellites are believed to have been formed at the same time as the planet, unlike irregular satellites which are believed to have been captured by the planet's gravity.

Resonance
A state in which an orbiting object is subject to periodic gravitational perturbations by another.

Retrograde Motion
The phenomenon where a celestial body appears to slow down, stop, them move in the opposite direction. This motion is caused when the Earth overtakes the body in its orbit.

Retrograde Orbit
The orbit of a satellite where the satellite travels in a direction opposite to that direction of the planet's rotation.

Right Ascension
The amount of time that passes between the rising of Aries and another celestial object. Right ascension is one unit of measure for locating an object in the sky.

Ring Galaxy
A galaxy that has a ring-like appearance. The ring usually contains luminous blue stars. Ring galaxies are believed to have been formed by collisions with other galaxies.

Roche Limit
The smallest distance from a planet or other body at which purely gravitational forces can hold together a satellite or secondary body of the same mean density as the primary. At a lesser distance the tidal forces of the primary would break up the secondary.

Rotation
The spin of a body about its axis.

Satellite
A natural or artificial body in orbit around a planet.

Scarp
A line of cliffs produced erosion or by the action of faults.

Seyfert Galaxy
A main-sequence star that rotates rapidly, causing a loss of matter to an ever-expanding shell.

Shell Star
A type of star which is believed to be surrounded by a thin envelope of gas, which is often indicated by bright emission lines in its spectrum.

Shepherd Satellite
A satellite that constrains the extent of a planetary ring through gravitational forces. Also known as a shepherd moon.

Sidereal
Of, relating to, or concerned with the stars. Sidereal rotation is that measured with respect to the stars rather than with respect to the Sun or the primary of a satellite.

Sidereal Month
The average period of revolution of the Moon around the Earth in reference to a fixed star, equal to 27 days, 7 hours, 43 minutes in units of mean solar time.

Sidereal Period
The period of revolution of a planet around the Sun or a satellite around its primary.

Singularity
The center of a black hole, where the curvature of space time is maximal. At the singularity, the gravitational tides diverge. Theoretically, no solid object can survive hitting the singularity.

Small Solar System Body
A term defined in 2006 by the International Astronomical Union to describe objects in the Solar System that are neither planets or dwarf planets. These include most of the asteroids, comets, and other small bodies in the Solar System.

Solar Cycle
The approximately 11-year quasi-periodic variation in frequency or number of solar active events.

Solar Eclipse
A phenomenon that occurs when the Earth passes into the shadow of the Moon. A total solar eclipse occurs when the Moon is close enough to completely block the Sun's light. An annular solar eclipse occurs when the Moon is farther away and is not able to completely block the light. This results in a ring of light around the Moon.

Solar Flare
A bright eruption of hot gas in the Sun's photosphere. Solar prominences are usually only detectable by specialized instruments but can be visible during a total solar eclipse.

Solar Nebula
The cloud of dust and gas out of which the Solar System was believed to have formed about 5 billion years ago.

Solar Wind
A flow of charged particles that travels from the Sun out into the Solar System.

Solstice
The time of the year when the Sun appears furthest north or south of the celestial equator. The solstices mark the beginning of the Summer and Winter seasons.

Spectrometer
The instrument connected to a telescope that separates the light signals into different frequencies, producing a spectrum.

Spectroscopy
The technique of observing the spectra of visible light from an object to determine its composition, temperature, density, and speed.

Spectrum
The range of colors that make up visible white light. A spectrum is produced when visible light passes through a prism.

Spicules
Grass-like patterns of gas seen in the atmosphere of the Sun.

Spiral Galaxy
A galaxy that contains a prominent central bulge and luminous arms of gas, dust, and young stars that wind out from the central nucleus in a spiral formation. Our galaxy, the Milky Way, is a spiral galaxy.

Star
A giant ball of hot gas that creates and emits its own radiation through nuclear fusion.

Star Cluster
A large grouping of stars, from a few dozen to a few hundred thousand, that are bound together by their mutual gravitational attraction.

Steady State Theory
The theory that suggests the universe is expanding but exists in a constant, unchanging state in the large scale. The theory states that new matter is being continually being created to fill the gaps left by expansion. This theory has been abandoned by most astronomers in favor of the big bang theory.

Stellar Wind
The ejection of gas from the surface of a star. Many different types of stars, including our Sun, have stellar winds. The stellar wind of our Sun is also known as the Solar wind. A star's stellar wind is strongest near the end of its life when it has consumed most of its fuel.

Stone Meteorite
A meteorite that resembles a terrestrial rock and is composed of similar materials.

Stony Iron
A meteorite that contains regions resembling both a stone meteorite and an iron meteorite.

Sunspot
Areas of the Sun's surface that are cooler than surrounding areas. The usually appear black on visible light photographs of the Sun. Sunspots are usually associated disturbances in the Sun's electromagnetic field.

Supergiant
The stage in a star's evolution where the core contracts and the star swells to about five hundreds times its original size. The star's temperature drops, giving it a red color.

Superior Conjunction
A conjunction that occurs when a superior planet passes behind the Sun and is on the opposite side of the Sun from the Earth.

Superior Planet
A planet that exists outside the orbit of the Earth. All of the planets in our solar system are superior except for Mercury and Venus. These two planets are inferior planets.

Supernova
A supernova is a cataclysmic explosion caused when a star exhausts its fuel and ends its life. Supernovae are the most powerful forces in the universe. All of the heavy elements were created in supernova explosions.

Supernova Remnant
An expanding shell of gas ejected at high speeds by a supernova explosion. Supernova remnants are often visible as diffuse gaseous nebulae usually with a shell-like structure. Many resemble "bubbles" in space.

Synchronous Rotation
A period of rotation of a satellite about its axis that is the same as the period of its orbit around its primary. This causes the satellite to always keep the same face to the primary. Our Moon is in synchronous rotation around the Earth.

Synodic Period
The interval between points of opposition of a superior planet.

Tektite
A small, glassy material formed by the impact of a large body, usually a meteor or asteroid. Tektites are commonly found at the sites of meteor craters.

Telescope
An instrument that uses lenses and sometimes mirrors to collect large amounts of light from distant objects and enable direct observation and photography. A Telescope can also include any instrument designed to observe distant objects by their emissions of invisible radiation such as x-rays or radio waves.

Terminator
The boundary between the light side and the dark side of a planet or other body.

Terrestrial
A term used to describe anything originating on the planet Earth.

Terrestrial Planet
A name given to a planet composed mainly of rock and iron, similar to that of Earth.

Tidal Force
The differential gravitational pull exerted on any extended body within the gravitational field of another body.

Tidal Heating
Frictional heating of a satellite's interior due to flexure caused by the gravitational pull of its parent planet and/or other neighboring satellites.

Transit
The passage of a celestial body across an observer's meridian; also the passage of a celestial body across the disk of a larger one.

Trans-Neptunian Object (TNO)
Any one of a number of celestial objects that orbit the Sun at a distance beyond the orbit of the planet Neptune.

Trojan
An object orbiting in the Lagrange points of another (larger) object. This name derives from a generalization of the names of some of the largest asteroids in Jupiter's Lagrange points. Saturn's moons Helene, Calypso and Telesto are also sometimes called Trojans.

Ultraviolet
Electromagnetic radiation at wavelengths shorter than the violet end of visible light. The atmosphere of the Earth effectively blocks the transmission of most ultraviolet light, which can be deadly to many forms of life.

Umbra
The area of total darkness in the shadow caused by an eclipse.

Universal Time (UT)
Also known as Greenwich Mean Time, this is local time on the Greenwich meridian. Universal time is used by astronomers as a standard measure of time.

Van Allen Belts
Radiation zones of charged particles that surround the Earth. The shape of the Van Allen belts is determined by the Earth's magnetic field.

Variable Star
A star that fluctuates in brightness. These include eclipsing binaries.

Visible Light
Wavelengths of electromagnetic radiation that are visible to the human eye.

Virgo Cluster
A gigantic cluster of over 2000 galaxies that is located mainly within the constellation of Virgo. This cluster is located about 60 million light-years from Earth.

Visual Magnitude
A scale used by astronomers to measure the brightness of a star or other celestial object. Visual magnitude measures only the visible light from the object. On this scale, bright objects have a lower number than dim objects.

Wavelength
The distance between consecutive crests of a wave. This serves as a unit of measure of electromagnetic radiation.

White Dwarf
A very small, white star formed when an average sized star uses up its fuel supply and collapses. This process often produces a planetary nebula, with the white dwarf star at its center.

X-ray
Electromagnetic radiation of a very short wavelength and very high-energy. X-rays have shorter wavelengths than ultraviolet light but longer wavelengths than cosmic rays.

X-ray Astronomy
The field of astronomy that studies celestial objects by the x-rays they emit.

X-ray Star
A bright celestial object that gives off x-rays as a major portion of its radiation.

Yellow Dwarf
An ordinary star such as the Sun at a stable point in its evolution.

Zenith
A point directly overhead from an observer.

Zodiac
An imaginary belt across the sky in which the Sun, moon, and all of the planets can always be found.

Zodiacal Light
A faint cone of light that can sometimes be seen above the horizon after sunset or before sunrise. Zodiacal light is caused by sunlight reflecting off small particles of material in the plane of the Solar System.

title: Astronomy glossary


text:
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license: Creative Commons - Attribution Share-Alike - https://creativecommons.org/licenses/by-sa/4.0/

title: Template:Compact ToC/doc


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text:
TESOL/Gratitude

Homework
{Put these words in the correct order. -+ Word 1 --+--- Word 2 +- Word 3 +- Word 4 -+ Word 5 ---+-- Word 6
 * type=""}
 * for | I | am | opportunity | grateful | this

{Put these words in the correct order. -+ Word 1 ---+-- Word 2 +- Word 3 --+--- Word 4 -+ Word 5 +- Word 6
 * type=""}
 * them | I | graduated | couldn't | have | without

{Put these words in the correct order. +--- Word 1 ---+ Word 2 +--- Word 3 -+-- Word 4 --+- Word 5 ---+ Word 6 --+- Word 7
 * type=""}
 * it | all | parents | owe | I | all | to | my

title: TESOL/Gratitude


text:
TESOL/Describing a journey

Review
{Put these words in the correct order. +--- Word 1 ---+ Word 2 +--- Word 3 ---+ Word 4 -+-- Word 5 --+- Word 6 --+- Word 7 -+-- Word 8
 * type=""}
 * while, | got | our | we | After | hotel | to | a

{Put these words in the correct order. --+ Word 1 --+ Word 2 +-- Word 3 +-- Word 4 ---+--- Word 5 -+- Word 6 -+- Word 7
 * type=""}
 * back, | lost | On | I | way | got | the

{Put these words in the correct order. ---+- Word 1 -+--- Word 2 -+--- Word 3 + Word 4 + Word 5 --+-- Word 6 + Word 7 ---+- Word 8 --+-- Word 9
 * type=""}
 * I | as | relieved. | As | got | soon | there, | felt | we

title: TESOL/Describing a journey


text:
User:Egm4313.s12.team17/Report 7

=Problem R7.1 - Verification of the Orthogonality of Given Basis Function=

Given

 * {| style="width:100%" border="0"

$$  \displaystyle \left \langle \phi_i,\phi_j \right \rangle=0 $$ for $$  \displaystyle i\not\equiv j $$ (Eq.1.1)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \left \langle \phi_j,\phi_j \right \rangle=\frac{L}{2} $$ for $$  \displaystyle i=j $$     (Eq.1.2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \phi_i=sin_i(n x) $$
 * style="width:95%" |
 * style="width:95%" |

$$  \displaystyle \phi_j=sin_j(m x) $$ (Eq.1.3)
 *
 * }

Problem Statement
Verify that the equations 1.1 and 1.2 are true.

Solution
Using the Orthogonality relations:
 * {| style="width:100%" border="0"

$$  \displaystyle \int_{-\pi}^{\pi}cos(nx)cos(mx)dx=0 $$     (Eq.1.4)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \int_{-\pi}^{\pi}sin(nx)sin(mx)dx=0 $$     (Eq.1.5)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \int_{-\pi}^{\pi}sin(nx)cos(mx)dx=0 $$     (Eq.1.6)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

To verify that $$\left \langle \phi_i,\phi_j \right \rangle=0$$ for $$i\not\equiv j$$ is true, we change the form to:
 * {| style="width:100%" border="0"

$$  \displaystyle \int_{0}^{L}sin_i(nx)sin_j(mx)dx=0 $$     (Eq.1.7)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

Simplifying Eq.1.7:
 * {| style="width:100%" border="0"

$$  \displaystyle \frac{-cos_i(nL)sin_j(mL)}{2n}+\frac{sin_i(nL)cos_j(mL)}{2m}-\frac{-cos_i(0)sin_j(0)}{2n}-\frac{sin_i(0)cos_j(0)}{2m}=0 $$     (Eq.1.8)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle 0+0-0-0=0 $$     (Eq.1.9)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

To verify that $$\left \langle \phi_j,\phi_j \right \rangle=\frac{L}{2}$$ for $$i=j$$ is true the following is done:
 * {| style="width:100%" border="0"

$$  \displaystyle \int_{0}^{L}sin_j^2(mx)dx=\frac{L}{2} $$     (Eq.1.10)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \int_{0}^{L}\frac{1-cos(2mx)}{2}dx=\frac{L}{2} $$     (Eq.1.11)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \frac{L}{2}-\frac{sin(2mL)}{4}-\frac{0}{2}+\frac{sin(2m0)}{4}=\frac{L}{2} $$     (Eq.1.12)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \frac{L}{2}=\frac{L}{2} $$     (Eq.1.13)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

Author & Proofreaders
Author: Egm4313.s12.team17.axelrod.a 17:39, 24 April 2012 (UTC)

Proofreader: Egm4313.s12.team17.hintz 18:20, 24 April 2012 (UTC)

Editor: Egm4313.s12.team17.deaver.md 09:01, 25 April 2012 (UTC)

=Problem R7.2 - Plotting the Motion of the Wave=

Given

 * {| style="width:100%" border="0"

$$  \displaystyle u(x,t)=\sum_{j=1}^{n}a_j\cos c\omega_j t \sin \omega_j x $$ (Eq.2.1)
 * style="width:80%" |
 * style="width:80%" |
 *
 * }

Problem Statement
Plot the truncated series with n=5 and for
 * {| style="width:100%" border="0"

$$  \displaystyle t=\alpha P_1=\alpha \frac{2\pi}{c\omega_1}=\alpha \frac{2L}{c} $$     (Eq.2.2)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \alpha=0.5, 1, 1.5, 2 $$     (Eq.2.3)
 * style="width:95%" |
 * style="width:95%" |
 *
 * }

Solution
Using the following information to solve the problem:
 * {| style="width:100%" border="0"

$$  \displaystyle f(x)=x(x-2) $$     (Eq.2.4)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle g(x)=0 $$     (Eq.2.5)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle c=3 $$     (Eq.2.5)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle L=2 $$     (Eq.2.6)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

We have:
 * {| style="width:100%" border="0"

$$  \displaystyle a_j=\frac{2}{L}\int_{0}^{L}f(x)\sin \omega_j x dx=2\left [ \frac{(-1)^j-1}{\pi^3j^3} \right ] $$     (Eq.2.7)
 * style="width:80%" |
 * style="width:80%" |
 *

 * }

Therefore:
 * {| style="width:100%" border="0"

$$  \displaystyle a_j=\begin{cases} 0, & \mbox{for }j=2m\mbox{ (even)} \\ -4/(\pi^3 j^3), & \mbox{for }j=2m+1\mbox{ (odd)} \end{cases} $$     (Eq.2.8)
 * style="width:80%" |
 * style="width:80%" |
 *

 * }

Substituting equation 2.8 into the equation 2.1, we have,
 * {| style="width:100%" border="0"

$$  \displaystyle u(x,t)=\sum_{j=1}^{n}2\left [ \frac{(-1)^j-1}{\pi^3j^3} \right ]\cos \bigg(c \frac{j\pi}{L} \alpha \frac{2L}{c} \bigg) \sin \bigg(\frac{j\pi}{L}x \bigg)=\sum_{j=1}^{n}2\left [ \frac{(-1)^j-1}{\pi^3j^3} \right ]\cos (\alpha j2\pi) \sin \bigg(\frac{j\pi}{2}x \bigg) $$     (Eq.2.9)
 * style="width:80%" |
 * style="width:80%" |
 *

 * }

Expanding with n=5:
 * {| style="width:100%" border="0"

$$  \displaystyle u(x,t)=\bigg[\frac{-4}{\pi^3}\cos (2\pi \alpha) \sin \bigg(\frac{\pi x}{2}\bigg)\bigg]+\bigg[\frac{-4}{27\pi^3}\cos (6\pi \alpha) \sin \bigg(\frac{3\pi x}{2}\bigg)\bigg]+\bigg[\frac{-4}{125\pi^3}\cos (10\pi \alpha) \sin \bigg(\frac{5\pi x}{2}\bigg)\bigg] $$     (Eq.2.10)
 * style="width:80%" |
 * style="width:80%" |
 *

 * }

Plotting equation 2.10 from 0 to 2\pi,we have:

When \alpha=0.5:

When \alpha=1:

When \alpha=1.5:

When \alpha=2:

Author & Proofreaders
Author: Egm4313.s12.team17.Li 17:39, 24 April 2012 (UTC)

Proofreader: Egm4313.s12.team17.axelrod.a 12:30, 24 April 2012 (UTC)

Editor: Egm4313.s12.team17.deaver.md 09:32, 25 April 2012 (UTC)

=Problem R7.3 - Various Properties Derived from Functions=

Part 1 Given

 * {| style="width:100%" border="0"

$$  \displaystyle f(x) = cos(x) $$     (Eq.3.1.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

g(x) = x $$ (Eq.3.1.2)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle -2 \le x \le 10 $$     (Eq.3.1.3)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Part 1 Problem Statement
Find the scalar product of, the magnitude of, and the angle between $$f(x)$$ and $$g(x)$$.

Scalar Product

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle f,g \right \rangle = \int_b^a f(x)g(x)

$$     (Eq.3.1.4)
 *

 * }

Substituting the given functions gives:
 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle cos(x),x \right \rangle = \int_{-2}^{10} x cos(x)

$$     (Eq.3.1.5)
 *

 * }

Using integration by parts with:
 * {| style="width:100%" border="0"

$$  \displaystyle u = x $$
 * style="width:95%" |
 * style="width:95%" |

$$  \displaystyle du = dx $$

$$  \displaystyle dv = cos(x) $$

$$  \displaystyle v = sin(x) $$     (Eq.3.1.6)
 *

 * }

Yields the following result:
 * {| style="width:100%" border="0"

$$  \displaystyle \left \langle f,g \right \rangle=\bigg[x sin(x) + cos(x)\bigg]^{10}_{-2} $$     (Eq.3.1.7)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Therefore:
 * {| style="width:100%" border="0"

$$  \displaystyle \left \langle f,g \right \rangle=(10)sin(10) + cos(10) + (2)sin(-2) - cos(-2) $$     (Eq.3.1.8)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle \left \langle f,g \right \rangle= -7.68173 $$     (Eq.3.1.9)
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 *

 * }

Magnitude

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle f(x),f(x) \right \rangle ^\frac{1}{2} = \sqrt{\int_{-2}^{10} cos^2(x)}

$$     (Eq.3.1.10)
 *

 * }

Solving this integral gives:
 * {| style="width:100%" border="0"

$$  \displaystyle $$     (Eq.3.1.11)
 * style="width:95%" |
 * style="width:95%" |
 * f||=\sqrt{\frac{1}{4} ( 24 + sin(4) + sin(20)}
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle $$     (Eq.3.1.12)
 * style="width:95%" |
 * style="width:95%" |
 * f||=\sqrt{6.039}
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle $$     (Eq.3.1.13)
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * f||=2.45744
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle g(x),g(x) \right \rangle ^\frac{1}{2} = \sqrt{\int_{-2}^{10} x^2}

$$     (Eq.3.1.14)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

 * g||=\sqrt{336}

$$     (Eq.3.1.15)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * style="width:5%; padding:10px; border:2px solid #8888aa" |

 * g||=18.33

$$     (Eq.3.1.16)
 *

 * }

Angle

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

cos(\theta) = \frac{\left \langle f(x),g(x) \right \rangle}{(||f||)(||g||)}

$$     (Eq.3.1.17)
 *

 * }

Substituting equations 3.1.9, 3.1.13, and 3.1.16 into equation 3.1.17:
 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

cos(\theta) = \frac{-7.68}{(2.45744)(18.33)}

$$     (Eq.3.1.18)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * style="width:5%; padding:10px; border:2px solid #8888aa" |

\theta = 99.817^o

$$     (Eq.3.1.19)
 *

 * }

Part 2 Given

 * {| style="width:100%" border="0"

$$  \displaystyle f(x) = \frac{1}{2} (3x^2 - 1) $$     (Eq.3.2.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

g(x) = \frac{1}{2} (5x^3 - 3x)

$$     (Eq.3.2.2)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle -1 \le x \le 1 $$     (Eq.3.2.3)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Part 2 Problem Statement
Find the scalar product of, the magnitude of, and the angle between $$f(x)$$ and $$g(x)$$.

Scalar Product

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle f,g \right \rangle = \int_b^a f(x)g(x)

$$     (Eq.3.2.4)
 *

 * }

Substituting the given functions gives:

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle \frac{3x^2 - 1}{2},\frac{5x^3 - 3x}{2} \right \rangle = \frac{1}{4} \int_{-1}^{1} 15x^5 - 14x^3 + 3x

$$     (Eq.3.2.5)
 *

 * }

Integrating gives:

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle f,g \right \rangle=\frac{1}{4} \bigg[ \frac{15}{6} x^6 - \frac{14}{4} x^4 + \frac{3}{2} x^2 \bigg]^{1}_{-1}

$$     (Eq.3.2.6)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle f,g \right \rangle=\frac{1}{4} \Bigg[ \bigg[ \frac{15}{6} (1^6) - \frac{14}{4} (1^4) + \frac{3}{2}(1^2) \bigg] - \bigg[ \frac{15}{6} (-1^6) - \frac{14}{4} (-1^4) + \frac{3}{2} (-1^2) \bigg] \Bigg]

$$     (Eq.3.2.7)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * style="width:5%; padding:10px; border:2px solid #8888aa" |

\left \langle f,g \right \rangle=0

$$     (Eq.3.2.8)
 *

 * }

Magnitude

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle f(x),f(x) \right \rangle ^\frac{1}{2} = \sqrt{\frac{1}{4} \int_{-1}^{1} (3x^2-1)^2dx}

$$     (Eq.3.2.9)
 *

 * }

Solving this integral gives:
 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

 * f||=\sqrt{\frac{1}{20} \bigg[ x(9x^4-10x^2+5) \bigg]^{1}_{-1} }

$$     (Eq.3.2.10)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * style="width:5%; padding:10px; border:2px solid #8888aa" |

 * f||=0.63246

$$     (Eq.3.2.11)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

\left \langle g(x),g(x) \right \rangle ^\frac{1}{2} = \sqrt{\frac{1}{4} \int_{-1}^{1} (5x^3-3x)^2dx}

$$     (Eq.3.2.12)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle $$     (Eq.3.2.13)
 * style="width:95%" |
 * style="width:95%" |
 * g||=\sqrt{\frac{1}{28} \bigg[ x^3(25x^4-42x^2+21) \bigg]^{1}_{-1} }
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle $$     (Eq.3.2.14)
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * g||=0.53452
 *

 * }

Angle

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

cos(\theta) = \frac{\left \langle f(x),g(x) \right \rangle}{(||f||)(||g||)}

$$     (Eq.3.2.15)
 *

 * }

Substituting equations 3.2.8, 3.2.11, and 3.2.14 into equation 3.2.15:

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:95%" |
 * style="width:95%" |

cos(\theta) = \frac{0}{(0.63256)(0.53452)}

$$     (Eq.3.2.16)
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle
 * style="width:5%; padding:10px; border:2px solid #8888aa" |
 * style="width:5%; padding:10px; border:2px solid #8888aa" |

\theta= 90^o

$$     (Eq.3.2.17)
 *

 * }

Author & Proofreaders
Author: Egm4313.s12.team17.hintz 17:51, 20 April 2012 (UTC)

Proofreader 1: Egm4313.s12.team17.wheeler.tw 16:00, 24 April 2012 (UTC)

Proofreader 2: Egm4313.s12.team17.deaver.md 09:40, 25 April 2012 (UTC)

Editor: Egm4313.s12.team17.deaver.md 09:40, 25 April 2012 (UTC)

=Problem R7.4 - Graphing Functions and Deriving Their Fourier Series=

Given
Information from problem 6,9,12,13 in Advanced Engineering Mathematics by Erwin Kreyszig on page 482.

Part 1 Problem Statement
Sketch or graph $$f(x)$$ which for $$-\pi<x<\pi$$ is given as follows:

 * {| style="width:100%" border="0"

$$  \displaystyle f(x)=\left | x \right | $$     (Eq.4.1.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Part 1 Solution

The Matlab code is included below:

Part 2 Problem Statement
Sketch or graph $$f(x)$$ which for $$-\pi<x<\pi$$ is given as follows:

 * {| style="width:100%" border="0"

$$  \displaystyle f(x)=\begin{cases} x & \text{ if }-\pi < x< 0 \\ \pi-x & \text{ if } 0<x<\pi \end{cases} $$     (Eq.4.2.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Part 2 Solution

The Matlab code is included below:

Part 3 Problem Statement
Find the Fourier series of the function $$f(x)$$, which is assumed to have the period 2 \pi. Show the details of your work. Sketch or graph the partial sums up to that including cos5x and sin5x.
 * {| style="width:100%" border="0"

$$  \displaystyle f(x)=\left | x \right | $$     (Eq.4.3.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Part 3 Solution
From Kreyszig 10th edition, 2011, page 476, for a Fourier series of period $$2\pi$$:
 * {| style="width:100%" border="0"

$$  \displaystyle f(x)=a_0+\sum_{n=1}^\infty[a_n\cos n x+b_n\sin n x] $$ (Eq.4.3.2)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle a_0=\frac{1}{2\pi}\int_{-\pi}^{\pi}f(x)dx $$     (Eq.4.3.3)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle a_n=\frac{1}{\pi}\int_{-\pi}^{\pi}f(x)\cos(nx)dx $$     (Eq.4.3.4)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle b_n=\frac{1}{\pi}\int_{-\pi}^{\pi}f(x)\sin(nx)dx $$     (Eq.4.3.5) Solving for $$a_{0}$$ using equations 4.3.3:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle a_0=\frac{1}{2\pi}\int_{-\pi}^{\pi}\left | x \right | dx = \frac{1}{\pi}\int_{0}^{\pi}x dx = \frac{1}{\pi}\bigg[ \frac{x^2}{2}\bigg]_{0}^{\pi}=\frac{\pi}{2} $$     (Eq.4.3.6) Solving for $$a_n$$ using equation 4.3.4:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle a_n=\frac{1}{\pi}\int_{-\pi}^{\pi}\left | x \right |\cos(nx)dx = \frac{2}{\pi}\int_{0}^{\pi} x \cos(nx)dx = \frac{2}{\pi}\bigg[\frac{nxsin(nx)+cos(nx)}{n^2}\bigg]_{0}^{\pi} $$     (Eq.4.3.7) Since $$n$$ is an integer, the sine term drops out of the equation, and equation 4.3.7 becomes: :{| style="width:100%" border="0" $$  \displaystyle a_n=\frac{2}{\pi}\bigg[\frac{cos(nx)}{n^2}\bigg]_{0}^{\pi} = \frac{2}{\pi}(\frac{cos(n \pi)-1}{n^2})=\frac{2}{\pi}(\frac{(-1)^{n}-1}{n^2})=\frac{2(-1)^n-2}{\pi n^2} $$     (Eq.4.3.8) Solving for $$b_n$$ using equation 4.3.5:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle b_n=\frac{1}{\pi}\int_{-\pi}^{\pi}\left | x \right |\sin(nx)dx $$     (Eq.4.3.9) Since $$\left | x \right |$$ is and even function and $$\sin(nx)$$ is an odd function, the result of equation 4.3.9 is 0:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle b_n=\frac{1}{\pi}\int_{-\pi}^{\pi}\left | x \right |\sin(nx)dx = 0 $$     (Eq.4.3.10) Plugging equations 4.3.6, 4.3.8, and 4.3.9 into equation 4.3.2:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle f(x)= \frac{\pi}{2}+\sum_{n=1}^\infty[\frac{2(-1)^n-2}{\pi n^2} \cos n x] $$ (Eq.4.3.11) Expanding equation 4.3.11 to $$\cos(5x)$$:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle f(x)= \frac{\pi}{2}- \frac{4}{\pi}\cos(x) - \frac{4}{9 \pi}\cos(3x)-\frac{4}{25 \pi} \cos(5x) $$     (Eq.4.3.12)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

The Matlab code is included below:

Comparing the plot to the one in part 1:

The Matlab code is included below:

Part 4 Problem Statement
Find the Fourier series of the function $$f(x)$$, which is assumed to have the period 2 \pi. Show the details of your work. Sketch or graph the partial sums up to that including cos5x and sin5x.
 * {| style="width:100%" border="0"

$$  \displaystyle f(x)=\begin{cases} x & \text{ if }-\pi < x< 0 \\ \pi-x & \text{ if } 0<x<\pi \end{cases} $$     (Eq.4.4.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Part 4 Solution
Solving for $$a_{0}$$ using equations 4.3.3:
 * {| style="width:100%" border="0"

$$  \displaystyle a_0=\frac{1}{2\pi}\bigg(\int_{-\pi}^{0}x dx + \int_{0}^{\pi}(\pi -x) dx \bigg)=\frac{1}{2 \pi}\bigg( \bigg[\frac{x^2}{2}\bigg]_{-\pi}^{0} +\bigg[\pi x\bigg]_{0}^{\pi}-\bigg[\frac{x^2}{2}\bigg]_{0}^{\pi}\bigg)= \frac{1}{2 \pi}\bigg(\frac{-\pi^2}{2}+\pi^2-\frac{\pi^2}{2}\bigg)=0 $$     (Eq.4.4.2) Solving for $$a_n$$ using equation 4.3.4:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle a_n=\frac{1}{\pi}\int_{-\pi}^{0}x\cos(nx)dx + \frac{1}{\pi}\int_{0}^{\pi}(\pi-x)\cos(nx)dx =\frac{1}{\pi}\bigg(\bigg[\frac{nxsin(nx)+cos(nx)}{n^2}\bigg]\bigg|_{-\pi}^{0}+ \bigg[\frac{n(\pi-x)\sin(nx)-\cos(nx)}{n^2}\bigg]\bigg|_{0}^{\pi}\bigg) $$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle =\frac{1}{\pi}\bigg(\frac{1}{n^2}-\frac{(-1)^n}{n^2}+\frac{-(-1)^n}{n^2}+\frac{1}{n^2}\bigg) $$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle =\frac{1}{\pi}\bigg(\frac{2}{n^2}-\frac{2(-1)^n}{n^2}\bigg) $$     (Eq.4.4.3) $$a_n$$ can be simplified to:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle a_n=\begin{cases} \frac{4}{\pi n^2} & \text{ if }n \text{ is an odd integer} \\ 0 & \text{ if } n \text{ is an even integer} \end{cases} $$     (Eq.4.4.4) Solving for $$b_n$$ using equation 4.3.5:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle b_n=\frac{1}{\pi}\bigg(\int_{-\pi}^{0}x\sin(nx)dx+\int_{0}^{\pi}(\pi - x)\sin(nx)dx\bigg)= \frac{1}{\pi}\bigg(\bigg[\frac{\sin(nx)-nx\cos(nx)}{n^2}\bigg]\bigg|_{-\pi}^{0}-\bigg[\frac{sin(nx)+n(\pi-x)\cos(nx)}{n^2}\bigg]\bigg|_{0}^{\pi}\bigg) $$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle =\frac{-(\cos(\pi n)-1)}{n}=\frac{-((-1)^n-1)}{n} $$     (Eq.4.4.5) $$b_n$$ can be simplified to:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle b_n=\begin{cases} \frac{2}{n} & \text{ if }n \text{ is an odd integer} \\ 0 & \text{ if } n \text{ is an even integer} \end{cases} $$     (Eq.4.4.6) Plugging equations 4.4.2, 4.4.4, and 4.4.6 into equation 4.3.2:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle f(x)=0+\sum_{\text{odd n}}^{\infty}\frac{4}{\pi n^2}\cos(nx)+\frac{2}{n}\sin(nx) $$     (Eq.4.4.7) Expanding equation 4.4.7 to sin(5x) and cos(5x):
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle f(x)=\frac{4}{\pi}\cos(x)+2\sin(x)+\frac{4}{9 \pi}\cos(3x)+\frac{2}{3}\sin(3x)+\frac{4}{25 \pi}\cos(5x)+\frac{2}{5}\sin(5x) $$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle =\frac{4}{\pi}(\cos(x)+\frac{1}{9}\cos(3x)+\frac{1}{25}\cos(5x))+2(\sin(x)+\frac{1}{3}\sin(3x)+\frac{1}{5}\sin(5x)) $$     (Eq.4.4.8)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

The Matlab code is included below:

Comparing the plot to the one in part 2:

The Matlab code is included below:

Author & Proofreaders
Author: Egm4313.s12.team17.wheeler.tw 03:38, 17 April 2012 (UTC)

Proofreader 1: Egm4313.s12.team17.ying 04:10, 18 April 2012 (UTC)

Proofreader 2: Egm4313.s12.team17.deaver.md 11:35, 25 April 2012 (UTC)

Editor: Egm4313.s12.team17.deaver.md 11:35, 25 April 2012 (UTC)

=Problem R7.5 - Odd-Periodic dot Odd-Periodic Exact Solution=

Given

 * {| style="width:100%" border="0"

$$  \displaystyle \int_0^p \sin j \omega x \cdot \sin k \omega x\, dx = 0 $$     (Eq.5.1)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

$$  \displaystyle p = 2 \pi, \ j = 2, \ k = 3 $$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Part 1 Problem Statement
Find the exact integration of equation 5.1 with the given values as data.

Part 1 Solution
With the given values, equations 5.1 becomes:
 * {| style="width:100%" border="0"

$$  \displaystyle \int_0^{2 \pi} \sin 2 \omega x \cdot \sin 3 \omega x\, dx = 0 $$     (Eq.5.2)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Using the following identities given below, it is:
 * {| style="width:100%" border="0"

$$  \displaystyle \sin 2 \omega x = 2 \sin \omega x \cos \omega x $$ (Eq.5.3)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle \sin 3 \omega x = 3 \sin \omega x - 4 \sin^3 \omega x $$ (Eq.5.4)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Substituting equations 5.4 and 5.3 into equation 5.2 yields:
 * {| style="width:100%" border="0"

$$  \displaystyle \int_0^{2 \pi} 2 \sin \omega x \cos \omega x (3 \sin \omega x - 4 \sin^3 \omega x) = 0 $$     (Eq.5.5)
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

Realizing that $$\cos$$ is the only different term, u substitution is used:
 * {| style="width:100%" border="0"

$$  \displaystyle u = \sin \omega x $$
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle du = \frac{\cos \omega x}{\omega} $$ Equation 5.5 then becomes:
 * style="width:95%" |
 * style="width:95%" |
 *

 * }
 * {| style="width:100%" border="0"

$$  \displaystyle \frac{1}{\omega}\int_0^{0} 2u(3u-4u^3) $$     (Eq.5.6) Where the interval that is being integrated has been changed by substituting $$2 \pi$$ into u.
 * style="width:95%" |
 * style="width:95%" |
 *

 * }

 * {| style="width:100%" border="0"

Therefore the final value of the integral then becomes 0.
 * style="width:25%; padding:10px; border:2px solid #8888aa" |
 * style="width:25%; padding:10px; border:2px solid #8888aa" |
 *

 * }

Part 2 Problem Statement
Confirm the result with matlab's trapz command for the trapezoidal rule.

Part 2 Solution
Below is the matlab code used to generate the answer:

where Z = -4.2785e-17 approximating to 0, confirming part 1 solution.

Author & Proofreaders
Author: Egm4313.s12.team17.ying 16:41, 15 April 2012 (UTC)

Proofreader: Egm4313.s12.team17.Li 04:18, 17 April 2012 (UTC)

Editor: Egm4313.s12.team17.deaver.md 14:06, 25 April 2012 (UTC)

= Contributing Team Members = {| border="1" cellspacing="0" cellpadding="5" align="center" ! Team Member ! Contribute ! Proofread
 * Allan Axelrod
 * Problem 1
 * Problem 2
 * Michael Deaver
 * Formatting
 * Problem 3 and 4
 * Max Hintz
 * Problem 3
 * Problem 1
 * Kelvin Li
 * Problem 2
 * Problem 5
 * Thomas Wheeler
 * Problem 4
 * Problem 3
 * Chen Ying
 * Problem 5
 * Problem 4
 * Problem 4
 * Problem 3
 * Chen Ying
 * Problem 5
 * Problem 4
 * Problem 4

title: User:Egm4313.s12.team17/Report 7


text:
Computer hardware and software

This is a lesson in the course Introduction to Computers, which is a part of The School of Computer Science

Hardware
The term "Hardware" refers to the physical elements of a computer; the machinery or the electronics in a computer.A basic computer consists of 4 components:
 * Input unit
 * CPU
 * Memory unit
 * Output unit

Examples of hardware in a computer are the keyboard (Input unit), the monitor (output unit), the mouse (Input unit),the printer (output unit),the speaker (output unit),the memory and the CPU. Like the CPU, most of a computer's hardware cannot be seen; It's inside the computer case.

Memory is what allows a computer to remember things (data and information). Similar to human memory, there's long term memory (a hard disc or optical media (like a CD)) and short term memory (Random Access Memory (RAM)). When a computer is turned off, it forgets everything in the RAM, so the computer saves everything it knows it will need later on in the long term memory. The short term memory is easier to use because it can do I/O faster, so when data is needed by the CPU, it's sent from the hard disk drive (HDD) to the RAM. The short term memory lives on RAM, while the long term memory is in the hard disk drive (HDD). Optical disks let you change certain parts of the memory, it's kind of like having a book or notebook that you might read and get information from.

The motherboard is the home of I/O in a computer. The motherboard is a piece of hardware that makes connections in the right places between all of the other components in a computer.

It tells data where it should go. It is sometimes necessary to add functionality to a computer to keep it up to date, or make it better.

The amount of I/O a computer has can be changed, by adding expansion cards to the motherboard.

Sometimes functionality can be added through a universal port, a port that supports multiple kinds of I/O to a motherboard. USB, FireWire, and Thunderbolt (types of I/O) support multiple data types; Your keyboard and mouse typically connect to your computer's motherboard via USB.

CPUs or processors perform computations. They do the math for your calculator application, they compare the size of numbers; people have likened the CPU to the "brain" of a computer.

1. Monitor

2. Motherboard

3.CPU (Microprocessor)

4. Random access memory (RAM)

5. Expansion cards

6. Power supply unit

7. Optical disc drive

8. Hard disk drive (HDD)

9. Keyboard

10. Mouse

What next?

 * On to the next lesson: Numeral systems
 * Back to the lesson before: Types of computers
 * Go back to course: Introduction to Computers

title: Computer hardware and software


text:
User:AmieKim

My main user page is on Vietnamese Wikibooks

title: User:AmieKim


text:
Wikipedia and Nupedia

“It's a strange feeling to realize you're helping make history.”

Introduction
This case study looks at how the Wikimedia Movement, centred around Wikipedia, grew from being originally a side project of Nupedia, to holding its current position as the 6th most popular website in the world. The first free online encyclopaedia was launched in October 1999 by Encyclopedia Britannica, which could trace back its origins to Edinburgh in 1768. Jimmy Wales founded Nupedia in 2000 and Larry Sanger was appointed editor in chief. Wikipedia was added in January 2001. However in July 2001, Encyclopedia Britannica decided to start charging anyone who wanted to read more than a few lines. Faced with the current economic slow-down, their representative, Tom Panelas said “The economics of the all-free model has changed”. However, Sanger challenged this view: “The grandest days of free content have not yet begun. Britannica and other proprietary encyclopedias will be hopelessly obsolete within ten years – small, out-of-date, and generally irrelevant – by comparison with Nupedia, Wikipedia, and the many other non-proprietary reference works that are being and will be developed.”. Sanger went on to speculate that by 2008 Wikipedia might have 84,000 articles – he was way out: In April 2008 there were 10 million articles. His article also concentrated on Nupedia: he was wrong on this as well. Nupedia closed in September 2003. However CNET did classify Nupedia as one of “The greatest defunct Web sites and dot-com disasters”.

Wiki Technology
Before analysing the different business models, it is useful to look at the technological innovation which led to the Wikipedia phenomenon. The first Wiki was created by Ward Cunningham in 1995. Basing it on his previous experience developing information stacks on Apple Computers HyperCard, Cunningham developed a website which enabled visitors to edit the material they found there in a comparatively straightforward way. In an interview in 2006 Cunningham commented that he had considered patenting his technology but “if I got a patent then I'd have to go out and sell people on the idea that anyone could edit. That just sounded like something that no one would want to pay money for.”. He also wanted to get it used by software developers and people into the study of patterns. His business model consisted of providing it as open source software, so as to raise his profile: “I also thought, well, if it is more widely used it'll just be a calling card and a way for people to know me. It certainly worked in that regard.” Cunningham invited people he knew interested in Design Patterns (a term used in software design to describe the application of a solution in a wide range of circumstances, independent of the specific coding used) to get involved. Over the next five years his wiki developed: by 1997 he was getting about 70,000 hits a month. However in 1998 tensions arose between partisans of Extreme Programming (a methodology developed by Kent Beck – currently working for Facebook – for computer programming which involves frequent small changes using users feedback to adjust errors) and those more interested in Design Patterns, as outlined by the “Gang of Four”. The two communities parted ways. In 2000 wikis were still largely unknown outside the computer programming communities.

Nupedia
In 1996 Jimmy Wales and Tim Shell set up Bomis. Wales had studied finance before becoming a player on the Chicago stock market. After six years he had made enough money that he would not need to work again. Having come across the Open Source movement he wondered if the same technique of mass user involvement could be used to develop an encyclopedia. He had met Larry Sanger through a shared interest in the philosophy of Ayn Rand. In February 2000 Bomis took Sanger on as Nupedia's Editor in Chief. They adopted the “One Best Way” model. This approach is most readily associated with Frederick Taylor – and indeed is the title of Robert Kanigel's biography. The model which Nupedia developed was that they aimed to attract academically qualified volunteers generally possessing a PhD in the area they covered. These would either act as editors or peer reviewers. Just as most academic publishing has no financial reward for the author, Nupedia hoped that by becoming a recognised repository of reliable information rigourously peer-reviewed, this would provide academics with suitable social capital, in terms of being recognised as the author of the relevant piece (Nupedia 2000). The articles were published under the GNU Free Document License. This had been designed by the Free Software Foundation for Richard Stallman's GNU Project. Bomis supplied free hosting and was using a business model they had developed around hosting web rings on topics aimed at young men: soft porn, sports, entertainment. These web-rings generated income through direct advertising and affiliate marketing. Sanger and Wales have subsequently disagreed about how the matter of advertising was to be handled. Sanger says that he was nervous about having his job paid for by the work of volunteers in a profit-based company (Sanger 2011). Originally the procedures being developed were a rather clumsy adaptation of the hard-copy academic publishing model. Nupedia a seven step process and an advisory body drawn from its editors and reviewers. By January 2001, when Wikipedia was launched, they had 2,000 members. However by July 2001 they had only been able to produce 20 articles.

In autumn 2000 Wales and Sanger had been concerned about the slow progress. They discussed various options which would allow a more open editing process, but these all turned out to require too much investment in software development to be viable. Then Sanger met Ben Kovitz – who both he and Wales knew from their shared participation in internet postings lists. Kovitz told Sanger about Cunningham's wiki. Sanger took the idea to Wales and the first wiki was soon installed on Nupedia on 10 January 2001. However when the matter was discussed by the Nupedia Advisory Board, a clear majority wanted to have nothing to do with the wiki. Thus Wikipedia was established on 15th January 2001.

Wikipedia
Wikipedia's business model has evolved as it has grown. Within a year it had attracted 350 users and generated 15,000 articles with 200 characters or more. By that time Nupedia was up to 25 articles with several dozen in preparation. Sanger proposed developing a simpler process to get articles up to standard. Originally Wikipedia was conceived as a way of allowing a pool of contributors to work together on articles which could then be transcluded to Nupedia. This did not have much of an impact on the productivity of Nupedia. Sanger was drawn into spending more and more time on Wikipedia, with little time for Nupedia. As Wikipedia grew, Sanger started a page on “What Wikipedia Is Not” where he and the community defined the limits if the project. Having a “Neutral Point Of View” soon became one of key criteria by which contributions were judged. The community started out managing disagreements within a consensual framework. Sanger refused the job title “Editor-in-Chief”, preferring “Chief Organizer”. But then a conflict arose between Sanger and an editor who used the nom de plume Cunctator or Cunc for short. Cunc advocated absence of hierarchy and removal of content limitation. Sanger was too busy to challenge Cunc's views effectively, but things got worse when an edit-war developed between the two men – this means they spent time removing each others contributions. Sanger then issued an appeal to the community requesting that they recognise him as the leader. However, he also deleted a number of pages – by Cunc and others – leading to criticism from across the community. In his response, he suggested that the irresponsibility of others meant that he was in fact being trained to act like an autocrat. The situation deteriorated: the social relations created by the new form of the wiki meant that Sanger did not have any suitable sanctions with which to control Cunc. Today an editor who misbehaves can be banned, a process handled by volunteer administrators complete with appeal process and variations of period, from 24 hours to a life-time ban. It has taken a decade to organically develop a self-organising community of volunteers. Wales saw that Sanger could not “manage' the project and citing financial difficulties, Sanger was made redundant in January 2002. However writing in 2008 Sanger attributed Wikipedia's success to: These were the features which provided a supportive environment to a world-wide community of 100,000 volunteers editing in over 280 languages. In 2003 Wales transferred ownership of Wikipedia to the Wikimedia Foundation. A recent fund-raising drive raised £9 million from 500,000 donations
 * Open content license
 * Clear Focus on purpose: an encyclopedia
 * Openness: everyone would be encouraged to contribute
 * Ease of editing – much easier than using html code
 * Radical collaboration – no article has an individual's signature, but all contributions can be seen from an attached “History” page
 * Unedited, unapproved content ready for further development
 * Neutrality
 * A core of good people to start with
 * High rating on Google – which happened without being planned.

The Cathedral and the Bazaar
When Wales was originally discussing Nupedia with Sanger, he mentioned Eric S. Raymond's book The Cathedral and the Bazaar which had recently been published. Raymond was also an avid reader of Ayn Rand. Adam Curtis has commented on the role of Rand's libertarian views on the growth of what Richard Barbrook and Andy Cameron dubbed The Californian Ideology. This developed primarily amongst the open-source programmers during the dot-com bubble (1995–2000). Principally focusing on software development, Raymond argued against a top down approach – the cathedral model – where source code is available with each software release and in favour of the bazaar model – where the code is developed over the the internet in public view. In his text he discusses the implications of Beck's Extreme Programming and the Gang of Four's Design Patterns. Sanger and Wales adapted this analysis to developing an on-line encyclopedia. However, despite a number of initial problems in how the Wikipedia community should be managed, Wales' Wikipedia Bazaar model far out-stripped Sander's Nupedia Cathedral model. In 2006, Sanger launch Citizendium as a fork to Wikipedia after five years and all sorts of squabbles, Citizendium got bogged down just like its predecessor. However Sanger defended his model: "A lot of people are going to try to draw the conclusion that there's something about the model which meant that it couldn't take off. I really don't think that's the case. The model works very well in many ways." . However, Clay Sharky has provided a critique of Sander's model, suggesting that “Citizendium is based less on a system of supportable governance than on the belief that such governance will not be necessary, except in rare cases.”. Sharky goes on to place Nupedia/Citizendium at the bottom of a U curve between a functioning hierarchy and a functioning community. According to Sharky Wikipedia functions because of deference to specific piece of texts comprising individual editors edits, rather than deference to the individuals themselves, which can only be maintained through the upkeep of expensive institutions. It should come as no surprise that such an engaged approach to business modelling should emerge amongst the open source software development community. As they see problems of business modelling forming a subset of the problems they have to deal with as computer programmers, they adapt their skills learnt from the programming of computers to an understanding of how human beings as social beings use computers. However this cybernetic approach may act as restraint on considering other forms of business models.

title: Wikipedia and Nupedia


text:
Instructional design/Reducing cognitive load in multimedia instruction/Cognitive Theory of Multimedia Learning

The Cognitive Theory of Multimedia Learning model depicts all that dual-channel processing going in the learner's mind when using multimedia instruction. This model was created by Richard E. Mayer and Roxana Moreno and presented in their paper "Nine Ways to Reduce Cognitive Load in Multimedia Learning" in 2003. Keep in mind the three assumptions of Dual Channel, Limited Capacity and Active Processing, as we explore the cognitive theory of multimedia learning.
 * (Mayer & Moreno based their model, in part, on the The Dual-coding Theory by Allan Paivio).

The two rows of the model represent the two information-processing channels: the auditory/verbal channel and the visual/pictorial channel (dual-channel assumption). The five columns each represent the modes of knowledge representations or physical representations, such as words or pictures. Sensory representations are those that take place in the ears or eyes of the learner, while shallow working memory representations are the sounds or images a learner notices or attends to during the instruction. Deep working memory representations are verbal and pictorial models constructed by the learner, and lastly, long-term memory representations are what the learner already knows about this particular instruction.

Multimedia Learning requires a lot of cognitive processing in both channels. Working memory has to make representations of sounds and images. Deep working memory is busy making verbal and pictorial models, and long-term memory is searching for and retrieving relevant prior knowledge.

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