Concise Modular Calculus 37 97

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 ...

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

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

Explains what

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

Justifies how a derivative can be found implicitly when we cannot solve for y. Computes tangent lines via implicit differentiation ...

Illustrates the derivative as the formal concept behind instantaneous velocities, tangent lines and general instantaneous rates of ...

Demonstrates that the Mean Value Theorem is the tool that connects slopes (a microscopic concept) with growth behavior (a ...

Presents the derivative form of the fundamental theorem of

Computes areas under curves and areas between curves with the Fundamental Theorem of

Introduces the alternating series test and the limit comparison test. Shows how, for the partial sums of certain series, to estimate ...

Justifies l'Hospital's rule graphically. Computes limits of indeterminate forms that are quotients, products, differences and powers.

Explains the comparison test and the ratio test. Presentation deliberately kept short to allow quick transition to power series.