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Calculus: blah (Part 1 of x)

This series is aimed at providing tools for an electrical engineer to analyze data and solve problems in design. The focus is on applying calculus to equations or physical systems.

This article will introduce functions.

There are many calculus references, the one I like to use is Calculus by Larson, Edwards and Hostetler.

This also assumes you are familiar with Python or can stumble your way through it.

Variable: a symbol used to hold a value or coordinate.
Coordinate: a set of numbers used to indicate the position of a point, line, or plane. In the form of (a,b,c,...,n) and usually (x,y) and (x,y,z).
Function: a real-valued function f of a real variable x from X to Y is a correspondence that assigns to each number x in X exactly one number y in Y; where X and Y are sets (of anything) and x and y are variables.
Intercept: a coordinate at which one coordinate value in the set is zero.
Intersection: a coordinate at which two sets of data (or functions) intercept.
Graph: a visual representation of coordinate sets, most often in 2 to 4 variables.
Slope: rate of change of a function
m=(y2-y1)/(x2-x1), x1 != x2

Linear Functions

General Form Ax+By+C=0
Vertical Line x=a
Horizontal Line y=b
Point-slope Form y-y1=m(x-x1)
Slope-intercept Form y=mx+b

Where A, B, C, y1, x1a and b are coordinates; m is a the slope; x and y are variables.

Function Transformations

Original Graph (Reference) y=f(x)
Horizontal Shift y=f(x±c)
Vertical Shift y=f(x)±c
Reflection (about x) y=-f(x)
Reflection (about y) y=f(-x)
Reflection (about origin) y=-f(-x)

Next Up
Continuity and Limits of functions.

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