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MA 128: Lecture – //02
MA 128: Lecture – //02

Document
Document

... be given and suppose that we would like to determine (approximating) values of the solution function in the finite interval [ a b ] . (It is well known that this problem is correctly given if f ( x y ) and f y ( x y) are continuous in a large enough neighbourhood of the point (a A) . The basic ...
General o Keep an organized notebook o Be a good note taker o
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Ch3-Sec 3.1

... can be written in the form Ax + By = C, where A, B, and C are real numbers and A and B are not both 0. Note Other linear equations in two variables, such as y = 4x + 5 and 3x = 7 – 2y, are not written in standard form but could be. We discuss the forms of linear equations in Section 3.4. Copyright © ...
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... the y-axis. (To grab a point, press /a and use the Touchpad arrows to move. Press d to release the point when the ordered pairs show.) Note: If you make a mistake, or are not happy with where the point is placed, immediately ...
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ACP Algebra II Summer Review Packet

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Equation



In mathematics, an equation is an equality containing one or more variables. Solving the equation consists of determining which values of the variables make the equality true. In this situation, variables are also known as unknowns and the values which satisfy the equality are known as solutions. An equation differs from an identity in that an equation is not necessarily true for all possible values of the variable.There are many types of equations, and they are found in all areas of mathematics; the techniques used to examine them differ according to their type.Algebra studies two main families of equations: polynomial equations and, among them, linear equations. Polynomial equations have the form P(X) = 0, where P is a polynomial. Linear equations have the form a(x) + b = 0, where a is a linear function and b is a vector. To solve them, one uses algorithmic or geometric techniques, coming from linear algebra or mathematical analysis. Changing the domain of a function can change the problem considerably. Algebra also studies Diophantine equations where the coefficients and solutions are integers. The techniques used are different and come from number theory. These equations are difficult in general; one often searches just to find the existence or absence of a solution, and, if they exist, to count the number of solutions.Geometry uses equations to describe geometric figures. The objective is now different, as equations are used to describe geometric properties. In this context, there are two large families of equations, Cartesian equations and parametric equations.Differential equations are equations involving one or more functions and their derivatives. They are solved by finding an expression for the function that does not involve derivatives. Differential equations are used to model real-life processes in areas such as physics, chemistry, biology, and economics.The ""="" symbol was invented by Robert Recorde (1510–1558), who considered that nothing could be more equal than parallel straight lines with the same length.
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