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Topic: Equation solving

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	Equation solving - Wikipedia, the free encyclopedia
		In mathematics, equation solving is the problem of finding what values (numbers, functions, sets, etc.) fulfill a condition stated as an equality (an equation).
		However, depending on the function, the inverse may be difficult to be defined, or may not be a function on all of the set B (only on some subset), and have many values at some point.
		In certain circumstances, a root-finding algorithm can be used to find a numerical solution to an equation, which within some applications can be entirely sufficient to solve some problem.
	en.wikipedia.org /wiki/Equation_solving (690 words)

	Facts about topic: (Equation solving) (Site not responding. Last check: 2007-10-08)
		Usually, this condition involves expressions with variables (A quantity that can assume any of a set of values) (or unknowns), which are to be substituted by values in order for the equality to hold.
		However, it may not always be easy to graphically depict solutions sets - for example, the solution set to an equation in the form ax+by+cz+dw=k (with a, b, c, d, and k real-valued constants) is a hyperplane (additional info and facts about hyperplane).
		It is important to note that we can create even more complex equations, involving differential operator (additional info and facts about differential operator) s, matrices (additional info and facts about matrices), and so on.
	www.absoluteastronomy.com /encyclopedia/e/eq/equation_solving.htm (737 words)

	Hunt for Solving Equations (Site not responding. Last check: 2007-10-08)
		As you have seen,to solve equations, you add, subtract, multiply and divide both sides of the equation by numbers and variables as needed, so that you end up with a single variable on one side of the equation and a single number on the other side.
		Then, pretend you are a math teacher and make up four different equations to solve using the skills you have learned.The equations should show that you understand the key operations of adding, subtracting, multiplying and dividing to isolate the unknown variable to solve for its value to make the equation true.
		Solving equations is like a balance scale; what you do to one side you have to do to the other.
	www.kn.pacbell.com /wired/fil/pages/huntsolvingmr.html (712 words)

	Encyclopedia: Equation solving
		In mathematics, one often (not quite always) distinguishes between an identity, which is an assertion that two expressions are equal regardless of the values of any variables that occur within them, and an equation, which may be true for only some (or none) of the values of any such variables.
		Solving an equation means manipulating the expressions and finding the value of the variables.
		In order to solve this equation we would divide both sides by 8.
	www.nationmaster.com /encyclopedia/Equation-solving (642 words)

	Interactive Mathematics Dictionary - Equation Definitions (Site not responding. Last check: 2007-10-08)
		In the equation t = 5 + n, the coefficient of n is 1 and NOT 5 because 5 is being added to n and not being multiplied by n.
		The degree 2 indicates that the equation has 2 roots or solutions (i.e., points where the graph of the corresponding quadratic function crosses the axis of the second-degree variable).
		The solutions to a system of equations are called simultaneous because they satisfy all the equations in the system.
	www.intermath-uga.gatech.edu /tweb/gwin1-01/apley/Dictionary/Equations/equations.html (2220 words)

	All Elementary Mathematics - Study Guide - Algebra - Main ways used at solving of equations...
		Solving of equation is a process, consisting mainly in a replacement of the given equation by another, equivalent equation.
		This is very important, because a new equation can be not equivalent to previous, if the expression, by which we multiply or divide, can be equal to zero.
		It is possible to raise both sides of an equation to an odd power and to extract the odd degree root from both sides of an equation.
	www.bymath.com /studyguide/alg/sec/alg12.html (458 words)

	Solving an Equation with one Variable (Site not responding. Last check: 2007-10-08)
		An equation is a mathematical statement that has two expressions separated by an equal sign.
		The expression on the left side of the equal sign has the same value as the expression on the right side.
		to solve this equation we would add 4 and 8 and find that x = 12.
	www.aaamath.com /equ725-equation1.html (105 words)

	Equations and Inequalities - Addition and subtraction equations - In Depth (Site not responding. Last check: 2007-10-08)
		You can think of an equation like a balance scale—whatever you do to one side of the scale, you must also do to the other side, to keep it in balance.
		To solve the equation we must try to get the variable x alone on one side.
		To solve this equation we must try to get the variable y alone on one side.
	www.math.com /school/subject2/lessons/S2U3L1DP.html (386 words)

	Algebraic equation solving card game - Patent 5033754
		The gamemaster selects one of the equations 11-19 or writes his own equation on a piece of paper and places the selected equation on a playing surface in full view of all the players.
		The gamemaster of each equation-solving round is not eligible to win the pot but may be compensated from the bank for successfully monitoring the equation solving sequence of play in his round.
		And, the gamemaster should be compensated in accordance with the degree of difficulty of solution of the equation he selects because the more difficult the solution, the more difficult it is for him to monitor and determine the correctness of the several equation modifying operations.
	www.freepatentsonline.com /5033754.html (2244 words)

	Solving Equations (Site not responding. Last check: 2007-10-08)
		To keep both sides of an equation equal, we must do exactly the same thing to each side of the equation.
		First, add two to each side of the equation so that 8x-2+2=14+2 or 8x=16.
		It is possible to substitute the value of x back into the original equation 8*2-2=14.
	www.aaamath.com /B/equ725x6.htm (156 words)

	Polynomial Equation Solving
		While equations do exist for quadratic, cubic, and quartic equations, they do become significantly more complex with increasing powers of x and four powers higher than 4, no solutions are known.
		Rewrite the equation so that the largest power of the variable is isolated on the left side of the equation.
		In the cell B1, enter the equation you have derived, using the cell A1 for the value for x.
	www.chembio.uoguelph.ca /educmat/ips1200/iterative_solver.html (783 words)

	Solving Radical Equations Lesson - I
		A "radical" equation is an equation in which the variable is stuck inside a radical.
		But "solving radical equations" usually involves mostly or only square roots, so most of the examples in what follows use square roots as the radical.
		When you have solved equations before, you have solved them by "undoing" whatever had been done to the variable.
	www.purplemath.com /modules/solverad.htm (790 words)

	Solving Laplace's Equation
		As evidence of this we looked at a numerical solution to Laplace's Equation for the case of a grounded metal cylinder with a variable-sized opening in its side.
		Laplace's equation is a second order partial differential equation, and in order to solve it, you must find the unique function who derivatives satisfy (del squared) V = 0, and simultaneously satisfies the required boundary conditions.
		A brief examination of this equation shows that for any point (i,j), the value of V there must be the average of the values of its four nearest neighbors.
	www.physics.hmc.edu /courses/ph51/laplace.html (671 words)

	Solve equations with algebra
		An equation is a statement that two quantities are equivalent.
		To solve linear equations, you add, subtract, multiply and divide both sides of the equation by numbers and variables, so that you end up with a single variable on one side and a single number on the other side.
		You should already have a strategy in mind for solving the equation, so it's just a matter of doing the correct operations in the correct order.
	www.teacherschoice.com.au /Maths_Library/Algebra/Alg_21.htm (668 words)

	Math Forum - Ask Dr. Math (Site not responding. Last check: 2007-10-08)
		The most serious problem you have to begin with is that the x appears inside an expression in parentheses.
		If you subtract (ax) from the right side of the equation, there will be no x on the right side.
		But whatever you do to one side of an equation you must also do to the other.
	mathforum.org /library/drmath/view/53042.html (358 words)

	Algebra.Help -- Equation Simplifying Calculator
		TIP: To solve equations, try the Equation Solving Calculator.
		The calculator will simplify the equation step-by-step, and display the result.
		If you wish to solve the equation, use the Equation Solving Calculator.
	www.algebrahelp.com /calculators/equation/simplifying (226 words)

	Read about Equation solving at WorldVillage Encyclopedia. Research Equation solving and learn about Equation solving ... (Site not responding. Last check: 2007-10-08)
		In mathematics, equation solving is the problem of finding what values (numbers,
		functions, sets...) fulfill a condition stated as an equality (an equation).
		root-finding algorithm can be used to find a numerical solution to an equation, which within some applications can be entirely sufficient to solve some problem.
	encyclopedia.worldvillage.com /s/b/Equation_solving (668 words)

	Solving linear equation systems
		When dealing with non-linear networks the number of equation systems to be solved depends on the required precision of the solution and the average necessary iterations until the solution is stable.
		The Gaussian algorithm for solving a linear equation system is done in two parts: forward elimination and backward substitution.
		Equation systems with large and sparse matrices should rather be solved with iterative methods.
	qucs.sourceforge.net /tech/node16.html (1620 words)

	Complexity of Equation Solving and Algebra Home Page (Site not responding. Last check: 2007-10-08)
		Equation solving is at the core of several problems in science and technology.
		Understanding the complexity of different forms of equation solving is a key issue which has attracted the attention of mathematicians and computer scientists in the last few years.
		The Workshop on Complexity of Equation Solving and Algebra is organized by Felipe Cucker and Steve Smale.
	www.damtp.cam.ac.uk /user/na/FoCM/HK_Wshop2.html (93 words)

	Math.com Online Solver Equations (Site not responding. Last check: 2007-10-08)
		The equations section allows you to solve virtually any equation or system of equations.
		We shall only be concerned with so-called conditional equations here, in which the expressions of both sides of the equation are equal for particular values of the pronumeral only.
		The solving of equations is really a part of algebra, but it is such a big topic that it has been given its own section in QuickMath.
	www.math.com /students/solvers/equations/equations.htm (253 words)

	Algebra.Help -- Equation Calculator
		When you enter an equation into the calculator, the calculator will begin by expanding (simplifying) the problem.
		Any lowercase letter may be used as a variable.
		Exponents may not currently be placed on numbers, brackets, or parentheses.
	www.algebrahelp.com /calculators/equation/solving (252 words)

	CS267: Notes for Lectures 15 and 16, Mar 5 and 7, 1996
		Solving the Discrete Poisson Equation using Jacobi, SOR, Conjugate Gradients, and the FFT
		This equation describes the steady-state temperature of a uniform square plate with the boundaries held at temperature u=0, and f(x,y) equaling the external heat supplied at (x,y).
		Recalling Lecture 13 again, we discretize this equation by using finite differences: We use an (n+1)-by-(n+1) grid on Omega = the unit square, where h=1/(n+1) is the grid spacing.
	www.cs.berkeley.edu /~demmel/cs267/lecture24/lecture24.html (6755 words)

	Solving Kepler's equation
		The benefit of this is that your "equation solver" can then be used for pretty much anything you want.
		In my case, this very particular equation was so important that I felt it worthwhile to sacrifice "generalness" to get a much faster solution.
		That equation can be solved or approximated analytically, and the result is a good enough solution to Kepler's equation that we can be sure of getting convergence.
	www.projectpluto.com /kepler.htm (1219 words)

	Solving Polynomial Equation Systems I - Cambridge University Press
		Polynomial equations have been long studied, both theoretically and with a view to solving them.
		It is a handbook covering the classical theory of finding roots of a univariate polynomial, emphasising computational aspects, especially the representation and manipulation of algebraic numbers, enlarged by more recent representations like the Duval Model and the Thom Codification.
		Mora aims to show that solving a polynomial equation really means finding algorithms that help one manipulate roots rather than simply computing them; to that end he also surveys algorithms for factorizing univariate polynomials.
	www.cambridge.org /uk/catalogue/catalogue.asp?isbn=0521811546 (247 words)

	[No title]
		To base a Solving Polynomial Equation Systems theory on a tautology is not a clever idea.
		When Abel-Ruffini Theorem proved the impossibility of solving univariate polynomials with the classical notion of ``solving'', the way of getting out of this impasse was Kronecker's solution to interpret ``solving'' via the theory of algebraic extensions as producing programs which compute with the roots of a polynomial equation.
		For the most advanced Computer Algebra research, the most effective way for solving polynomial equation systems is just to interpret such system as a tool for solving itself, by building programs which use this tool to manipulate its own roots.
	www.math.fsu.edu /~seppala/Symbolic/Classes/ComputerAlgebra.html (476 words)

	Exponential Equation Solving
		In the problem to the right we are close to having all elements of solving a logarithmic equation.
		In the problem to the right, notice we handle as much solving as possible before we rewrite to the exponential form.
		Solve for the variable using normal algebraic processes.
	fym.la.asu.edu /~tturner/MAT_117_online/Logarithms_files/Solving_Log_problems/Solving_Log_Problems.htm (518 words)

	Equation Solver - Solving Linear, Quadratic, Radical and Radical Equations, Systems of Equations and more!
		We have put together a large number of helpful tutorials on all aspects of equation solving - just click on the appropriate topic on the menu bar to display the tutorial.
		We know how frustrating the solving of algebraic equations can be - we hope that our site will provide you with some useful methods and simple hints in this area of algebra.
		Currently our help tutorials cover solving linear equations, solving quadratic equations, solving radical equations, solving equations involving fractions, solving systems of linear equations and solving rational equations.You will notice that some solution methods are covered more than once - different students find one approach to work better than another, so take your pick!
	www.equation-solver.com (300 words)

	Appendix: Use of Solutions Plus for equation solving and parameter estimation
		If a variable is first referred to in an algebraic equation, and then is listed as a variable in a differential equation, an error message will be returned.
		Experiments were conducted to assess the effect of temperature on the pressure of a fixed quantity of gas kept in a 2.0 L vessel.
		These parameter values may then be used to predict the experimental data, to confirm the goodness of the fit and ensure that the model equation is consistent with the trends in the data.
	www.chem-eng.toronto.edu /~cre/AppendixD.html (1837 words)

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