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algebra
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A branch of math that uses known quantities to find unknown quantities. Algebra can be used for functions involving regular shapes and straight lines.
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calculus
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A type of mathematics that measures changes in one quantity in relation to another. Calculus is used for functions involving curves.
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closed-loop system
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A type of control system that automatically changes the output based on the difference between the feedback signal to the input signal.
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continuous function
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A function that can be compared to a bridge that connects a road on both sides. Just as a bridge allows you to drive along the road with no interruptions, obstacles, or detours, a continuous function allows you to draw a line or a curve without lifting your pencil.
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coordinate
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A number that indicates a location in 2- or 3-dimensional space. Two-dimensional graphs use x- and y-coordinates.
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delta
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A mathematical operator used to indicate a change in a value. It is represented by the Greek letter Δ.
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dependent variable
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A value that is typically the output of a function.
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derivative
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The rate of change.
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difference quotient
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The ratio of the change in y-values over the change in x-values. The difference quotient is simply a more complex variation of the formula for slope.
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differentiation
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The process of determining the rate of change of a curve.
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discontinuous function
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A function that has a break, hole, or jump in the graph.
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error
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The difference between the setpoint and the process variable. When errors are detected, the controller sends instructions to the control system to adjust the output to compensate.
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function
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A relationship between two things in which the value of one thing depends on the value of the other. Functions can be represented by graphs.
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graph
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A two-dimensional representation of a function on an x- and y-axis.
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independent variable
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A value that is typically used as input for a function.
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input
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The value or independent variable entered into a function.
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integral
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A small part of a larger whole.
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integration
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The process of summing up small areas under a curve to determine the total area.
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limit
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A value that you would expect the function to go to, or a value that gets extremely close to the value you want to reach.
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line
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A set of two or more points that extend endlessly in two directions. A line is the quickest way to get from one point to another.
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linear equation
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An equation of the form y = ax + b, where a and b can be any real number. Linear equations are a way to represent lines.
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negative slope
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When a line goes down and to the right.
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output
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The end result or dependent variable of a function.
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PID control
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One of the most common types of process control. Proportional, integral, derivative control adjusts system outputs when there is a difference between the setpoint and process variable.
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point
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A dot that indicates a definite position or location. A point has no width, depth, or length.
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positive slope
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When a line goes up and to the right
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process variable
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The actual value detected by a sensor as a process is taking place.
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rise
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The vertical movement of a line.
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run
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The horizontal movement of a line.
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secant line
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A line that intersects the graph at two points.
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setpoint
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A preset value such as a specific temperature, speed, or flow rate that the control system is supposed to reach.
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slope
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A measure of the slant or steepness of a line.
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substitution method
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The simplest method for evaluating limits. In the substitution method, you replace x with another value.
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summing junction
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The part of a PID control system in which the SP and PV are compared to each other. The difference between the SP and PV is called error.
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tangent line
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A line that touches the graph only once.
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