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Mathematics

Calculus

Parametric Equations

Partial Derivatives

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Calculus Review of Trigonometric Identities

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Polar Coordinates and Graphs

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Flashcards

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Heaviside step function, $u(t)$

$\frac{1}{s}$

Exponential decay, $e^{-at}$

$\frac{1}{s+a}$

Ramp Function, $t \cdot u(t)$

$\frac{1}{s^2}$

$\delta'(t)$ , the derivative of the unit impulse

$s$

$\frac{1}{t}$

$-\ln(s)$

$\sinh(at)$

$\frac{a}{s^2 - a^2}$

$\cosh(at)$

$\frac{s}{s^2 - a^2}$

Sine function, $\sin(\omega t)$

$\frac{\omega}{s^2 + \omega^2}$

Cosine function, $\cos(\omega t)$

$\frac{s}{s^2 + \omega^2}$

Natural logarithm, $\ln(t)$

$-\frac{\ln(s) + \gamma}{s}$ where $\gamma$ is the Euler-Mascheroni constant.

Unit impulse, $\delta(t)$

$t^n$ where $n$ is a positive integer

$\frac{n!}{s^{n+1}}$

$e^{at} \sin(\omega t)$

$\frac{\omega}{(s-a)^2 + \omega^2}$

$e^{at} \cos(\omega t)$

$\frac{s-a}{(s-a)^2 + \omega^2}$

$\frac{1}{s^2}$

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