Differential-algebraic system of equationsIn electrical engineering, a differential-algebraic system of equations (DAE) is a system of equations that either contains differential equations and algebraic equations, or is equivalent to such a system. In mathematics these are examples of differential algebraic varieties and correspond to ideals in differential polynomial rings (see the article on differential algebra for the algebraic setup).
Differential equationIn mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, and the differential equation defines a relationship between the two. Such relations are common; therefore, differential equations play a prominent role in many disciplines including engineering, physics, economics, and biology.
Ordinary differential equationIn mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives of those functions. The term "ordinary" is used in contrast with partial differential equations which may be with respect to one independent variable. A linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a_0(x), .
Linear differential equationIn mathematics, a linear differential equation is a differential equation that is defined by a linear polynomial in the unknown function and its derivatives, that is an equation of the form where a0(x), ..., an(x) and b(x) are arbitrary differentiable functions that do not need to be linear, and y′, ..., y(n) are the successive derivatives of an unknown function y of the variable x. Such an equation is an ordinary differential equation (ODE).
EquationIn mathematics, an equation is a mathematical formula that expresses the equality of two expressions, by connecting them with the equals sign . The word equation and its cognates in other languages may have subtly different meanings; for example, in French an équation is defined as containing one or more variables, while in English, any well-formed formula consisting of two expressions related with an equals sign is an equation. Solving an equation containing variables consists of determining which values of the variables make the equality true.
Partial differential equationIn mathematics, a partial differential equation (PDE) is an equation which computes a function between various partial derivatives of a multivariable function. The function is often thought of as an "unknown" to be solved for, similar to how x is thought of as an unknown number to be solved for in an algebraic equation like x2 − 3x + 2 = 0. However, it is usually impossible to write down explicit formulas for solutions of partial differential equations.
ToolA tool is an object that can extend an individual's ability to modify features of the surrounding environment or help them accomplish a particular task. Although many animals use simple tools, only human beings, whose use of stone tools dates back hundreds of millennia, have been observed using tools to make other tools. Early human tools, made of such materials as stone, bone, and wood, were used for the preparation of food, hunting, the manufacture of weapons, and the working of materials to produce clothing and useful artifacts and crafts such as pottery, along with the construction of housing, businesses, infrastructure, and transportation.
Master of Business AdministrationA Master of Business Administration (MBA; also Master in Business Administration) is a postgraduate degree focused on business administration. The core courses in an MBA program cover various areas of business administration such as accounting, applied statistics, human resources, business communication, business ethics, business law, strategic management, business strategy, finance, managerial economics, management, entrepreneurship, marketing, supply-chain management, and operations management in a manner most relevant to management analysis and strategy.
Master of ScienceA Master of Science (Magister Scientiae; abbreviated MS, M.S., MSc, M.Sc., SM, S.M., ScM or Sc.M.) is a master's degree in the field of science awarded by universities in many countries or a person holding such a degree. In contrast to the Master of Arts degree, the Master of Science degree is typically granted for studies in sciences, engineering and medicine and is usually for programs that are more focused on scientific and mathematical subjects; however, different universities have different conventions and may also offer the degree for fields typically considered within the humanities and social sciences.
Garden toolA garden tool is any one of many tools made for gardening and landscaping, which overlap with the range of tools made for agriculture and horticulture. Garden tools can be divided into hand tools and power tools. Hand tool Today's garden tools originated with the earliest agricultural implements used by humans. Examples include the hatchet, axe, sickle, scythe, pitchfork, spade, shovel, trowel, hoe, fork, and rake. In some places, the machete is common. The earliest tools were made variously of wood, flint, metal, tin, and bone.
Master of FinanceThe Master of Finance is a master's degree awarded by universities or graduate schools preparing students for careers in finance. The degree is often titled Master in Finance (M.Fin., MiF, MFin), or Master of Science in Finance (MSF in North America, and MSc in Finance in the UK and Europe). In the U.S. and Canada the program may be positioned as a professional degree. Particularly in Australia, the degree may be offered as a Master of Applied Finance (MAppFin). In some cases, the degree is offered as a Master of Management in Finance (MMF).
Hand toolA hand tool is any tool that is powered by hand rather than a motor. Categories of hand tools include wrenches, pliers, cutters, , striking tools, struck or hammered tools, screwdrivers, vises, clamps, snips, hacksaws, drills, and knives. Outdoor tools such as garden forks, pruning shears, and rakes are additional forms of hand tools. Portable power tools are not hand tools. Hand tools have been used by humans since the Stone Age when stone tools were used for hammering and cutting.
Master of LawsA Master of Laws (M.L. or LL.M.; Latin: Magister Legum or Legum Magister) is an advanced postgraduate academic degree, pursued by those either holding an undergraduate academic law degree, a professional law degree, or an undergraduate degree in a related subject. In most jurisdictions, the LL.M. is the advanced professional degree for those usually already admitted into legal practice. To become a lawyer and practice law in most states and countries, a person must first obtain a law degree.
Master of ArtsA Master of Arts (Magister Artium or Artium Magister; abbreviated MA, M.A., AM, or A.M.) is the holder of a master's degree awarded by universities in many countries. The degree is usually contrasted with that of Master of Science. Those admitted to the degree have typically studied subjects within the scope of the humanities and social sciences, such as history, literature, languages, linguistics, public administration, political science, communication studies, law or diplomacy; however, different universities have different conventions and may also offer the degree for fields typically considered within the natural sciences and mathematics.
Power toolA power tool is a tool that is actuated by an additional power source and mechanism other than the solely manual labor used with hand tools. The most common types of power tools use electric motors. Internal combustion engines and compressed air are also commonly used. Tools directly driven by animal power are not generally considered power tools. Power tools are used in industry, in construction, in the garden, for housework tasks such as cooking, cleaning, and around the house for purposes of driving (fasteners), drilling, cutting, shaping, sanding, grinding, routing, polishing, painting, heating and more.
Master of Public AdministrationA Master of Public Administration (MPA) is a specialized professional graduate degree in public administration, similar or equivalent to a Master of Business Administration but with an emphasis on the issues of public services. The MPA program is a higher professional degree and a post graduate degree for the public sector and it prepares individuals to serve as managers, executives and policy analysts in the executive arm of local, state/provincial, and federal/national government, and increasingly in non-governmental organization (NGO) and nonprofit sectors; it places a focus on the practices of executive organization and management.
Machine toolA machine tool is a machine for handling or machining metal or other rigid materials, usually by cutting, boring, grinding, shearing, or other forms of deformations. Machine tools employ some sort of tool that does the cutting or shaping. All machine tools have some means of constraining the workpiece and provide a guided movement of the parts of the machine. Thus, the relative movement between the workpiece and the cutting tool (which is called the toolpath) is controlled or constrained by the machine to at least some extent, rather than being entirely "offhand" or "freehand".
Power-flow studyIn power engineering, the power-flow study, or load-flow study, is a numerical analysis of the flow of electric power in an interconnected system. A power-flow study usually uses simplified notations such as a one-line diagram and per-unit system, and focuses on various aspects of AC power parameters, such as voltages, voltage angles, real power and reactive power. It analyzes the power systems in normal steady-state operation. Power-flow or load-flow studies are important for planning future expansion of power systems as well as in determining the best operation of existing systems.
Electric machineIn electrical engineering, electric machine is a general term for machines using electromagnetic forces, such as electric motors, electric generators, and others. They are electromechanical energy converters: an electric motor converts electricity to mechanical power while an electric generator converts mechanical power to electricity. The moving parts in a machine can be rotating (rotating machines) or linear (linear machines).
Iterative methodIn computational mathematics, an iterative method is a mathematical procedure that uses an initial value to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones. A specific implementation with termination criteria for a given iterative method like gradient descent, hill climbing, Newton's method, or quasi-Newton methods like BFGS, is an algorithm of the iterative method.
