Bernoulli Polynomials and Applications
by Omran Kouba
Publisher: arXiv 2013
Number of pages: 48
In this lecture notes we try to familiarize the audience with the theory of Bernoulli polynomials; we study their properties, and we give, with proofs and references, some of the most relevant results related to them. Several applications to these polynomials are presented, including a unified approach to the asymptotic expansion of the error term in many numerical quadrature formulae, and many new and sharp inequalities, that bound some trigonometric sums.
Home page url
Download or read it online for free here:
by Ian Craw - University of Aberdeen
Introductory calculus course, with some leanings to analysis. It covers sequences, monotone convergence, limits, continuity, differentiability, infinite series, power series, differentiation of functions of several variables, and multiple integrals.
by Eckhard Hitzer - arXiv
This paper treats the fundamentals of the multivector differential calculus part of geometric calculus. The multivector differential is introduced, followed by the multivector derivative and the adjoint of multivector functions.
by Martin J. Osborne - University of Toronto
This tutorial covers the basic mathematical tools used in economic theory. The main topics are multivariate calculus, concavity and convexity, optimization theory, differential and difference equations. Knowledge of elementary calculus is assumed.
by E. Goursat, O. Dunkel, E.R. Hedrick - Ginn & company
Goursat's three-volume 'A Course in Mathematical Analysis' remains a classic study and a thorough treatment of the fundamentals of calculus. As an advanced text for students with one year of calculus, it offers an exceptionally lucid exposition.