Concise Modular Calculus 97 97

(5/6 on Integration of Multivariable Functions) Derives the formula for integration in polar coordinates. Explains how to compute ...

Derives Green's Theorem as a two-dimensional version of Stokes' Theorem. Shows how Green's Theorem enables us to use line ...

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Derives Snell's law of refraction as an application of parameter dependent optimization. All videos and slides for single variable ...

(3/6 on Integration of Multivariable Functions) Justifies how the integration over regions other than rectangles is accomplished ...

Shows how integrals are used to compute the work that is required to lift a mass to the international space station, the work that is ...

Discusses improper integrals over infinite intervals. Computes the escape velocity from the Earth. Computes and estimates ...

Introduces the standard equations of a plane (parametric, vector and scalar). Explains how to compute intersections between ...

Explains how the graph of a multivariable function is analogous to the graph of a function of one variable. Shows how a ...

Introduces definite integrals as limits of Riemann sums. Shows how definite integrals are used to compute areas, displacements ...

(2/6 on Integration of Multivariable Functions) Introduces Fubini's Theorem as a much needed tool to avoid constant use of ...

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Justifies the power rule and shows how it abbreviates the computation of derivatives. Computes tangent lines, growth behavior ...

Visually illustrates the typical ways in which limits are used: Divisions by zero, defining derivatives, defining integrals and ...

2/2 on Change of Variables & Surface Area) Discusses the multivariable change of variable formula. Explains how to encode a ...

Introduces power series as a way to represent functions. Explains the radius of convergence, the algebra, derivatives and ...

Defines improper integrals near vertical asymptotes. Finishes the discussion of the Gamma function. Introduces convergence tests ...