In this section we introduce the step or Heaviside function. We illustrate how to write a piecewise function in terms of Heaviside functions. We also work a variety of examples showing how to take Laplace transforms and inverse Laplace transforms that involve Heaviside functions. We also derive the formulas for taking the Laplace transform of functions which involve Heaviside functions.
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Solving Differential Equations with Piecewise. We can solve differential equations with piecewise functions in the coefficients. The type of equations that one can solve include all first-order methods using integration, Riccati, and higher-order methods including linear, Bernoulli, and Euler. Some examples are included in the sections that follow.
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How To: Given a piecewise function, write the formula and identify the domain for each interval. Identify the intervals for which different rules apply. Determine formulas that describe how to calculate an output from an input in each interval. Use braces and if-statements to write the function.
PiecewiseExpand converts nested piecewise functions into a single piecewise function: Min, Max, UnitStep, and Clip are piecewise functions of real arguments: Abs, Sign, and Arg are piecewise functions when their arguments are assumed to be real.
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LaTeX is very flexible. Although it is not WYSIWYG you can write it in a very logical way. So if you want to have to have f(x) precede your cases, just write it that way. Here with the example of the linked question.
A piecewise function is a function defined by two or more equations. A step functions is a piecewise function defined by a constant value over each part of its domain.
How Do You Write an Equation for a Translation of an Absolute Value Function? Want to write an equation to translate the graph of an absolute value equation? This tutorial takes you through that process step-by-step! Take an absolute value equation and perform a vertical and horizontal translation to create a new equation.