Laplace transform (Khan Academy)

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Transforms and the Laplace transform in particular. Convolution integrals. (1) Laplace transform Laplace transform 1 Laplace transform 2 L{sin(at)} – transform of sin(at) Part 2 of the transform of the sin(at) (2) Properties of the Laplace transform Laplace as linear operator and Laplace of derivatives Laplace transform of cos t and polynomials “Shifting” transform by […]

Derivative applications (Khan Academy)

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The reason we study calculus, and the reason it was invented, is for its many uses in real-world problems. In particular, derivatives let us optimize functions and study their rates of change. Here we cover optimization, rates of change, L’Hopital’s rule, the mean value theorem, and more! (1) Equations of normal and tangent lines Equation […]

Taking derivatives (Khan Academy)

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Calculating derivatives. Power rule. Product and quotient rules. Chain Rule. Implicit differentiation. Derivatives of common functions. (1) Introduction to differential calculus Newton, Leibniz, and Usain Bolt (2) Using secant line slopes to approximate tangent slope Slope of a line secant to a curve Slope of a secant line example 1 Slope of a secant line […]