Related papers: An Elementary but Logical Approach to Integration

We remark a variant of the existence part of the fundamental theorem of calculus, which, together with the Lebesgue differentiation theorem, constitute a new proof that every Riemann-integrable function on a compact interval having limit…

A proposed solution to the Riemann Hypothesis

We state some elementary problems concerning the relation between difference calculus and differential calculus, and we try to convince the reader that, in spite of the simplicity of the statements, a solution of these problems would be a…

A variety of problems emerged investigating electronic circuits, computer devices and cellular automata motivated a number of attempts to create a differential and integral calculus for Boolean functions. In the present article, we extend…

We utilize a combination of integral transforms, including the Laplace transform, with some classical results in analytic number theory concerning the Riemann $\xi$-function, to obtain a new integral equation. We also provide a new proof of…

University students taking introductory physics are generally successful executing mathematical procedures in context, but often struggle with the use of mathematical concepts for sense making. Physics instructors note that their students…

Much effort and research has been invested into understanding and bridging the gaps which many students experience in terms of contents and expectations as they begin university studies with a heavy component of mathematics, typically in…

Using both fractional derivatives, defined in the Riemann-Liouville and Caputo senses, and classical derivatives of the integer order we examine different numerical approaches to ordinary differential equations. Generally we formulate some…

One of the essential questions of the theory of multidimensional integrals concerns the evaluation of integrals taken in given domains. In the simplest case, when integrating over parallelepipeds, evaluation can easily be performed by…

The reduction of Feynman integrals to master integrals is an algebraic problem that requires algorithmic approaches at the modern level of calculations. Straightforward applications of the classical Buchberger algorithm to construct…

After the language of module and theirs morphisms, this short course presents matricial calculus and determinants in a commutative ring as appliction of ``remarquable identities'' in the ring of polynomials with integer coefficients with…

This paper offers what seems at first to be a minor technical correction to the current practice of computing indefinite integrals, and introduces the idea of a "Kahanian constant of integration". However, the total impact of this minor…

This is an introduction to linear algebra and group theory. We first review the linear algebra basics, namely the determinant, the diagonalization procedure and more, and with the determinant being constructed as it should, as a signed…

An elementary proof of a quantitative version of the Riemann-Lebesgue lemma for functions supported on the half line is given. Applications to differential models with memory are discussed.

We introduce Riemannian Lie algebroids as a generalization of Riemannian manifolds and we show that most of the classical tools and results known in Riemannian geometry can be stated in this setting. We give also some new results on the…

This article exemplifies a novel approach to the teaching of introductory differential calculus using the modern notion of ``infinitesimal'' as opposed to the traditional approach using the notion of ``limit''. I illustrate the power of the…

In this article, we present an integration of any real finite-dimensional Leibniz algebra as a Lie rack which reduces in the particular case of a Lie algebra to the ordinary connected simply connected Lie group. The construction is not…

We introduce a new framework called linear algebraic number theory (LANT) that reformulates the number-theoretic problem as a regression model and solves it using matrix algebra. This framework restricts all computations to log space,…

This survey article is an introduction to Diophantine Geometry at a basic undergraduate level. It focuses on Diophantine Equations and the qualitative description of their solutions rather than detailed proofs.

Formalization of real analysis offers a chance to rebuild traditional proofs of important theorems as unambiguous theories that can be interactively explored. This paper provides a comprehensive overview of the Lebesgue Differentiation…