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Mathematics

Calculus

Calculus Review of Trigonometric Identities

Calculus Theorems

Calculus Basics

Calculus Symbols and Notations

Chain Rule Variations

Conic Sections and Quadratic Equations

Implicit Differentiation

Hyperbolic Functions

Infinite Series Convergence Tests

Laplace Transforms

Parametric Equations

Partial Derivatives

Polar Coordinates and Graphs

Taylor and Maclaurin Series

Stokes' Theorem and Surface Integrals

Laplace Transforms

Flashcards

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Natural logarithm, $\ln(t)$

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

Heaviside step function, $u(t)$

$\frac{1}{s}$

Exponential decay, $e^{-at}$

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

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

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

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

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

$\frac{1}{t}$

$-\ln(s)$

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

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

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

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

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

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

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

Unit impulse, $\delta(t)$

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

$s$

$\cosh(at)$

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

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

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

$\sinh(at)$

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

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