Mathematics The Darboux Integral This post describes the classical notion of an integral from calculus in terms of the Darboux integral, which is equivalent to the Riemann integral, but often more computationally tractable.
Mathematics The Mean Value Theorem This post describes the mean value theorem and several other theorems of real analysis.
Mathematics The Chain Rule This post is a detailed examination of the chain rule from differential calculus.
Mathematics The Fréchet and Gâteaux Derivatives This brief note explains the precise relationship between the two principal notions of derivatives on normed vector spaces, namely, the Fréchet and Gâteaux derivatives.
Mathematics Derivatives on Normed Vector Spaces This post explores the conception of derivatives as the best local linear approximation of a continuous function in the general setting of normed vector spaces, and generalizes classical results to spaces of functionals.
Mathematics Total Derivatives This post contains a detailed explanation of the concept of the total derivative of a continuous function. It attempts to explain the total derivative in a way which relates it to concepts from differential geometry (such as tangent spaces).
