18.095 Lecture Notes - Lecture 4: Continuous Function, Step Function, Oliver Heaviside
Document Summary
Steven johnson: delta functions and distributions: when functions have no value(s) A point charge is a hypothetical charge located at a single point in space. The dirac delta function is a generalized function, or distribution, on the real number line that is zero everywhere except at zero, with an integral of one over the entire real line. The heaviside step function, also known as the unit step function, is a discontinuous function whose value is zero for negative argument and one for positive arguments. The limit of a derivative is not the same as the derivative of a limit. Distributions, also known as general functions, are objects extending the notations of classical functions. Generalized functions are especially useful in making discontinuous functions more like smooth functions, and describing discrete physical phenomena such as point charges.
