Related papers: An Elementary but Logical Approach to Integration
Software tools of Automated Reasoning are too sophisticated for general use in mathematics education and respective reasoning, while Lucas-Interpretation provides a general concept for integrating such tools into educational software with…
Spingarn's method of partial inverses has found many applications in nonlinear analysis and in optimization. We show that it can be employed to solve composite monotone inclusions in duality, thus opening a new range of applications for the…
There is a substantial curricular overlap between calculus and physics, yet introductory physics students often struggle to connect the two. We introduce a quantity-based framing of the Fundamental Theorem of Calculus (FTC) to help unify…
In this article we present logarithmic methods for solving first order and second order ordinary differential equations. The essence of the method is that we apply the basic properties derivatives and logarithms to reduce the number of…
We study Lispchitz solutions of partial differential relations $\nabla u\in K$, where $u$ is a vector-valued function in an open subset of $R^n$. In some cases the set of solutions turns out to be surprisingly large. The general theory is…
This paper presents a systematic study of the calculus of interval-valued functions and its application to interval differential equations. To this end, first, we introduce new interval arithmetic operations. Under new operations, the space…
This paper presents a brief but comprehensive introduction to certain mathematical techniques in General Relativity. Familiar mathematical procedures are investigated taking into account the complications of introducing a non trivial…
A Lax operator algebra is constructed for an arbitrary semi-simple Lie algebra over $\mathbb C$ equipped with a $\mathbb Z$-grading, and arbitrary compact Riemann surface with marked points. In this set-up, a treatment of almost graded…
This note presents a new equivalence to the Riemann Hypothesis by means of the Salem integral equation.
Line integration of generalized functions is studied. Second order partial differential equations with piecewise continuous and generalized variable coefficients over Cayley-Dickson algebras are investigated. Formulas for integrations of…
We describe the development of a junior-senior level course for Physics majors designed to teach Mathematica skills in support of their undergraduate coursework, but also to introduce students to modern research level results. Standard…
Using a generalized Littlewood theorem concerning integrals of the logarithm of analytical functions, we have established a few equalities involving integrals of the logarithm of the Riemann Zeta-function and have rigorously proven that…
The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies.…
We introduce and study graphic lambda calculus, a visual language which can be used for representing untyped lambda calculus, but it can also be used for computations in emergent algebras or for representing Reidemeister moves of locally…
We present a systematic study of integrals over [0,1] where the integrand is of the form Q(x) log log 1/x. Here Q is a rational function.
In these lectures I will give an introduction to Feynman integrals. In the first part of the course I review the basics of the perturbative expansion in quantum field theories. In the second part of the course I will discuss more advanced…
Integration by parts is used to reduce scalar Feynman integrals to master integrals.
A logic calculus is presented that is a conservative extension of linear logic. The motivation beneath this work concerns lazy evaluation, true concurrency and interferences in proof search. The calculus includes two new connectives to deal…
We introduce a formalism to analyze partially defined functions between ordered sets. We show that our construction provides a uniform and conceptual approach to all the main definitions encountered in elementary real analysis including…
The rational Landen transformations are used to produce a highly efficient numerical method for the integration of rational functions.