derivative is no longer the slope of a tangent line.

In this chapter, we will describe the curves in $\mathbb{R}^2$ or $\mathbb{R}^{3}$ as the image of a function. $$\vec{r}(t) = \big(r_{1}(t), r_{2}(t),\dots ,r_{n}(t ...

The Lebesgue-Nikodym Theorem states that for a Lebesgue measure an additive set function which is -absolutely continuous is the integral of a Lebegsue integrable a measurable function ; that is, for ...

Calculus of functions of several variables. Differentiation; partial derivatives of implicit and explicit functions, applications including optimizations. Integration; multiple integrals in various co ...

This course is designed to develop the topics of multivariate calculus. Emphasis is placed on multivariate functions, partial derivatives, multiple integration, solid analytical geometry, vector ...

This is a preview. Log in through your library . Abstract With respect to a partial ordering $\ll$, the functional inequality $F(s) + tG(s) \ll F(s + t)$ arises ...