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    Example and Directions
    Words (or words that have the same definition) The definition is case sensitive (Optional) Image to display with the definition [Not displayed in Glossary, only in pop-up on pages] (Optional) Caption for Image (Optional) External or Internal Link (Optional) Source for Definition
    (Eg. "Genetic, Hereditary, DNA ...") (Eg. "Relating to genes or heredity") The infamous double helix CC-BY-SA; Delmar Larsen
    Glossary Entries



    Image Caption Link Source
    Abacus Calculator based of stones moving on rods or in grooves        
    Aberration A departure from the normal operation of a device or an optical element        
    Acoustic Science of sound         
    Accuracy Proximity to true value. Accuracy is a consistent error from true value, but it is not necessarily a good or precise error.        
    Adjacent side In a right triangle, the side between a given angle and the right angle        
    Ailerons The small flaps on the back of wings on airplanes        
    Allotrope Different forms of the same chemical element. Some allotropes of carbon are graphite, graphene, diamond, and buckyballs.        
    Angle of depression The angle between the horizontal and the line from the object to the observer’s eye, assuming the object is positioned lower than the observer        
    Angle of elevation The angle between the horizontal and the line from the object to the observer’s eye, assuming the object is positioned higher than the observer        
    ANOVA Analysis of variance (ANOVA) is statistical models for estimations        
    Antiderivative The opposite of a derivative which leads to a indefinite integral. Through the fundamental theorem of calculus an antiderivative can be made into a definite integral.        
    Apatite A mineral group that consists of calcium phosophate minerals        
    Arc length The arc length of a curve can be thought of as the distance a person would travel along the path of the curve        
    Arithmetic sequence A sequence in which the difference between every pair of consecutive terms is the same is called an arithmetic sequence.        
    Aspheric Slightly off from spherical (usually used to correct spherical aberration)        
    AFM Atomic force microscope is a microscope that uses a cantilever with a nanometer-size tip to "feel" the surface of the specimen. AFMs can "see" in the nanometer realm and has many different interchangable probes to investigate many different properties.        
    Bandgap The gap in insulators and semiconductors between the valance band (the nucleus energy area) and the conduction bands (the electron shell energy area). Note: This is actually more complex than this.        
    Bellows A device that has a bag and two flats plates that is used to squeeze air out at a fast pace for various purposes. Also, flexible structures that expand and compress for various purposes.        
    Binomial series A series given by \( (1+x)^r=\sum_{n=0}^∞(^r_n)x^n=1+rx+\dfrac{r(r−1)}{2!}x^2+⋯+\dfrac{r(r−1)⋯(r−n+1)}{n!}x^n+⋯\) for \( |x|<1\); from the Maclaurin series for \( f(x)=(1+x)^r\)        
    Boat keel The long structure directly on the bottom of a boat that is used to support the hull. Can have hydrodynamics purpose or counterbalance purpose as well as support purpose.        
    Bounded above (sequences) A sequence \(\displaystyle {a_n}\) is bounded above if there exists a constant \(\displaystyle M\) such that \(\displaystyle a_n≤M\) for all positive integers \(\displaystyle n\)        
    Bounded below (sequences) A sequence \(\displaystyle {a_n}\) is bounded below if there exists a constant \(\displaystyle M\) such that \(\displaystyle M≤a_n\) for all positive integers \(\displaystyle n\)        
    Bounded sequence A sequence \(\displaystyle {a_n}\) is bounded if there exists a constant \(\displaystyle M\) such that \(\displaystyle |a_n|≤M\) for all positive integers \(\displaystyle n\)        
    Catenary A curve in the shape of the function \(y=a\cdot\cosh(x/a)\) is a catenary; a cable of uniform density suspended between two supports assumes the shape of a catenary. Catenary comes from the Latin word meaning "chain" as a catenary is often observed with free hanging chains. In engineering a catenary arch is known to be a strong self sustaining structure. catenary_real_world_smaller.png An electric wire between two poles is a catenary    
    Center of mass The point at which the total mass of the system could be concentrated without changing the moment        
    Centroid The centroid of a region is the geometric center of the region; laminas are often represented by regions in the plane; if the lamina has a constant density, the center of mass of the lamina depends only on the shape of the corresponding planar region; in this case, the center of mass of the lamina corresponds to the centroid of the representative region        
    Ceramic Hard brittle material made from inorganic substances and metals. Typically non-conductive, heat resistant, chemical resistant, and corrosion resistant        
    Change of variables The process in mathematics of substituting variables with another expression to simplify a problem.        
    Cipher Encoded words to make a message secret. Used is "spycraft". Evidence of using ciphers first appear in antiquity (Ancient Egypt, Ancient Greece, Ancient Rome)        
    Codex A manuscript usually hand written and on material other then paper        
    Cold finger A strip of metal intended to transfer temperature from a cold plate to a device like a detector        
    Confidence Interval A range of values that represents the confidence of a true value that is a function of one variable (kinda like an error bar)        
    Confidence Contour A contour that represents the confidence of a true value that is a function of two or more variables (kinda like a 3D error bar)        
    Contour Contour lines (isoline or isoarithm) which represent the path of a constant value        
    Convergence of a series A series converges if the sequence of partial sums for that series converges.        
    Convergent sequence A convergent sequence is a sequence \(\displaystyle {a_n}\) for which there exists a real number \(\displaystyle L\) such that \(\displaystyle a_n\) is arbitrarily close to \(\displaystyle L\) as long as \(\displaystyle n\) is sufficiently large        
    Cryocooler A mechanical cooling system that goes to cryogenic temperatures        
    Cryostat Cooling system that goes to cryogenic temperatures by means of a cryogenic liquid (LH or LHe)        
    Cryogenic temperature Temperatures below 124 K, though in practical terms it is usually 77K and below        
    Cubit A length unit used in antiquity        
    Demoiselle An ultralight aircraft in the context of this book. Young lady in general terms.        
    Density function (mass density) A density function describes how mass is distributed throughout an object; it can be a linear density, expressed in terms of mass per unit length; an area density, expressed in terms of mass per unit area; or a volume density, expressed in terms of mass per unit volume; weight-density is also used to describe weight (rather than mass) per unit volume.        
    Diffusion (physics) Movement of particles to a high concentration area to a low concentration area        

    A rigid lighter-than-air aircraft that is steerable and powered by an engine. The Hindenburg was a dirigible. In contrast a Zeppelin is semi-rigid and a blimp is not rigid at all. So the Goodyear blimp is not a dirigible or Zeppelin.

    The dirigible was first demonstrated by a Brazilian in 1709. In 1785 a dirigible with bird-like steering and  hand-powered propellors crossed the  English channel with French balloonist Jean-Pierre-François Blanchard and American John Jeffries 

    Divergence of a series A series diverges if the sequence of partial sums for that series diverges.        
    Divine Proportion The Golden Ratio. This was detailed in the book illustrated by Leonardo da Vinci called "De Divina Proportione" by Luca Pacioli circa 1509.        
    Ductile The ease of which metal can be drawn out into a wire. Also, the degree to which a material can deform until failure.        
    Dynamics The study of objects in motion. This by its very nature suggests a study that is in the time domain. This differs from statics where time is not relevant. For fluids a hydro is attached to dynamics (hydrodynamics) but the idea is still the same.        
    eBird Citizen science site for bird observation.         
    Electron microscope Electron microscope is a microscope that uses electrons rather than light. Due to the wavelength of electrons, electron microscopes  can "see" in the nanometer realm.        
    Ethics A philosophy that is based off human morals that attempts to define right and wrong or good and evil        
    Frustum A portion of a cone; a frustum is constructed by cutting the cone with a plane parallel to the base        
    Geometric Sequence A sequence an in which the ratio an+1/an is the same for all positive integers, n, is called a geometric sequence.        
    Geometric series A geometric series is a series that can be written in the form \(\displaystyle \sum_{n=1}^∞ ar^{n−1}=a+ar+ar^2+ar^3+⋯\)        
    Getter Substance that absorbs unwanted residuals (like water) in a vacuum        
    Glassy carbon A carbon solid that has a glassy appearance that is also known as vitreous carbon         
    Golden Ratio A golden ratio is a ratio of two quantities, say a and b, that are equal to the ratio of the larger quantity and the sum of the quantities. It is said that this ratio defines a unique natural structure and hence it is sometimes called the divine proportion. Interestingly this quantity is used in numerical methods.        
    Handle (computer science) Abstract reference to a resources (similar to a pointer, but not). A pointer is an address to a resource, normally data, where as a handle references functions.        
    Harmonic series A geometric series is a series that can be written in the form \(\displaystyle \sum_{n=1}^∞ ar^{n−1}=a+ar+ar^2+ar^3+⋯\). This series is interesting in that it diverges albeit rather slowly.        
    Hydrophilic Tends to mix, dissolve, or be wetted in water        
    Hydrophobic Tends to repel water        
    Hydrostatic pressure The pressure exerted by water on a submerged object        
    Hydroxyapatite A phosphate material that forms bones and teeth but is rarely found in rocks        
    Hypotenuse The side of a right triangle opposite the right angle        
    Incompressible (fluid) A fluid that does not diverge but is the same density throughout the system        
    Indeterminate forms When evaluating a limit, the forms \(\dfrac{0}{0}\), \(∞/∞, 0⋅∞, ∞−∞, 0^0, ∞^0\), and \(1^∞\) are considered indeterminate because further analysis is required to determine whether the limit exists and, if so, what its value is.        
    Indefinite integral A primitive integral or an integral without an upper and lower limit. Sort of like a definition of a specific integral.        
    Index of refraction A unitless number that describes the speed of light in a material.        
    Infinite series An infinite series is an expression of the form \(\displaystyle a_1+a_2+a_3+⋯=\sum_{n=1}^∞ a_n\)        
    Inflection point If f(x) is continuous at c and f(x) changes concavity at c, the point (c, f(c)) is an inflection point of f        

    Integral has a number of meanings in mathematics, but they all relate to the standard definition of integral: the sum of the necessary parts that creates a whole. 

    This leads to the most common use of integral in mathematics which is the sum of infinitesimal areas within a range.

    Integration by substitution A technique for integration that allows integration of functions that are the result of a chain-rule derivative        
    Interval of convergence The set of real numbers, x, for which a power series converges        
    Iso Equal as in equal temperature in isothermal, etc.        
    Iterative process Process in which a list of numbers x0, x1, x2, x3, … is generated by starting with a number x0 and defining xn=F(xn−1) for n≥1        
    Jerk Change of acceleration with respect to time. The names implies jerk as the feeling of being thrust suddenly in one direction. This is also sometimes called jolt (also aptly named).        
    Kinetics In mechanics the effects of force on a body and in chemistry the rate of reaction. Kinetics implies a dynamic situation (time varying).        
    Koch curve A fractal curve        
    Lamina A thin sheet of material; laminas are thin enough that, for mathematical purposes, they can be treated as if they are two-dimensional        
    Limestone Soft sedimentary rock made of calcium carbonate. Densities can vary from rather hard limestone to chalk like limestone.        
    Mastaba A tomb that has slanted sides and a flat roof; stone bench        
    Metal Crystal that conducts electricity and heat well. Ductile and malleable. Made of the metallic and semi-metallic elements.        
    Method of cylindrical shells A method of calculating the volume of a solid of revolution by dividing the solid into nested cylindrical shells; this method is different from the methods of disks or washers in that we integrate with respect to the opposite variable.        
    Nabla An ancient stringed harp        
    Newton’s method Method for approximating roots of \(f(x)=0;\) using an initial guess \(x_0\); each subsequent approximation is defined by the equation \(x_n=x_{n−1}−\frac{f(x_{n−1})}{f'(x_{n−1})}\)        
    Nonelementary integral An integral for which the antiderivative of the integrand cannot be expressed as an elementary function        
    Ostracon A piece of pottery or stone that has writings scratch on it.        
    Partial sum The kth partial sum of the infinite series \(\displaystyle \sum^∞_{n=1}a_n\) is the finite sum \(\displaystyle S_k=\sum_{n=1}^ka_n=a_1+a_2+a_3+⋯+a_k\)        
    Periodic function A function is periodic if it has a repeating pattern as the values of \(x\) move from left to right        
    Phase change Change for one state of matter to another state of matter through "symmetry breaking" (except in some iso instances)        
    Polymer Materials made of large molecules that are made of many subunits like DNA. Organic. Usually flexible.        
    Portmanteau A combination word        
    Power series A series of the form \(\displaystyle \sum_{n=0}^∞c_nx^n\) is a power series centered at \(x=0\); a series of the form \(\displaystyle \sum_{n=0}^∞c_n(x−a)^n\) is a power series centered at \(x=a\)        
    Precision A consistent result with a small error, but not necessarily anywhere near a true value        
    Principle of least action A variation principle that is used to derive the equation of motions. It has nothing to do with the general accepted meaning of action or least action.         
    Probability Distribution Function (PDF)

    This is a general term that describe the probability distribution of a system or experiment. There are three types of probability distribution functions:

    • Probability Mass Function (PMF) for discrete systems
    • Probability Density Function (PDF) for continuous systems
    • Cumulative Distribution Function (CDF) is the cumulation of probabilities for discrete and continuous systems
    Pseudocode A plain language text of an algorithm to be translated into a computer program with appropriate syntax. Useful for thinking out ideas before implementing them.        
    QED "Quad erat demonstrandum." Sometimes hollow square ◻ is used for this. Sometimes a filled in square is used ◼. These squares are sometimes referred to as a tombstone.         
    Quadrature Integration        
    Quarks Elementary particle that make up protons and neutrons        
    Radians For a circular arc of length \(s\) on a circle of radius 1, the radian measure of the associated angle \(θ\) is \(s\). This contrasts to degrees where a full circle is 360 degrees but \(2 \pi \) radians.         
    Radius of convergence If there exists a real number \(R>0\) such that a power series centered at \(x=a\) converges for \(|x−a|<R\) and diverges for \(|x−a|>R\), then \(R\) is the radius of convergence; if the power series only converges at \(x=a\), the radius of convergence is \(R=0\); if the power series converges for all real numbers \(x\), the radius of convergence is \(R=∞\)        
    Raman scattering The basis of Raman spectroscopy which is the inelastic scattering of photons into a material.         
    Raman spectroscopy Uses Raman scattering to determine the vibrational modes of a material. This will allow not only an identification of a substance but what allotrope it might be as well.        
    Read noise The noise associated with reading an element of a detector. Includes all sources of noise but primarily due to ADC of a detector.        
    Recurrence relation A recurrence relation is a relationship in which a term an in a sequence is defined in terms of earlier terms in the sequence        
    Recursion (computer) A function that calls itself (typical example is a factorial)        
    Regression Statistical model comparing dependent variables with independent variables usually using a mean value and the actual value in some fashion        
    Register (computer) Quick memory usually associated with the CPU        
    Regula Falsi  False position        
    Sequence An ordered list of numbers of the form a1,a2,a3,…is a sequence        
    Small angle approximation An approximation used extensively in engineering and physics. In this approximation when we have a small angle in our problem we can say that \(\cos(\theta) = 1 - \frac{\theta^2}{2}\) and/or \(\sin(\theta) = \theta\).        
    Surface area The surface area of a solid is the total area of the "skin" of the object; for objects such as bricks, the surface area of the object is the sum of the areas of all of its faces; for a sphere is the sum of infinitesimal area slices of the surface of the sphere.        
    Telescoping series A telescoping series is one in which most of the terms cancel in each of the partial sums        
    Theorem of Pappus for volume This theorem states that the volume of a solid of revolution formed by revolving a region around an external axis is equal to the area of the region multiplied by the distance traveled by the centroid of the region        
    Theremin A modern electronic instrument that does not require physical contact        
    Tuples Ordered set        
    Unix An operating system philosophy of modularity; also the operating system itself        
    Variable A representation of a changing value        
    Vitreous Substance that resembles glass        
    Work In science work is an energy transfer descriptor otherwise it means effort either physical or intellectually        
    x-ray x-radiation which is high energy radiation        
    Yeast A fungus that people use to make bread, beer, wine, and root beer among other uses         
    Zooniverse Citizen science web portal. Citizen science goes back to antiquity. Recently with the advent of computers and clouds citizen science has become more popular and important to science.        
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