This paper studies the applicability of the Taylor method for the sensibility analysis of ODEs and DAEs. Extended automatic differentiation rules are introduced for the calculus of partial derivatives of Taylor series. The numerical method is implemented using an efficient variablestep variable-order scheme. Finally, some numerical tests are presented showing the benefits of the formulation.

introduction here we report an unusual case of massive stone formation in augmented urinary bladder. case presentation a 25-year-old man presented with recurrent urinary tract infection ten years after augmentation cystoplasty after a complex pelvic fracture urethral distraction defect. on evaluation by ultrasonography, x-ray, and computed tomography of abdomen showed large burden of stones in ...

When a function’s value is known at several distinct points, there exist “numerical differentiation” formulas which provide estimates for the first derivative, and with various error bounds. In fact, many times the numerical differentiation formula chosen must be complex to avoid intolerable error as shown below. However, in computer simulations, as well as in real-time programming, while sever...

introdouction: overhang refers to the extension of restoration material from the cavity. it has an important role in decay, plaque accumulation and periodontal disease, so the aim of this study is determining the frequency of restoration overhang in patients in anzali, guilan. materials and methods: this descriptive cross-sectional study was completed using 293 patients who visited for routine ...

This paper develops a discontinuous Galerkin (DG) finite element differential calculus theory for approximating weak derivatives of Sobolev functions and piecewise Sobolev functions. By introducing numerical one-sided derivatives as building blocks, various first and second order numerical operators such as the gradient, divergence, Hessian, and Laplacian operator are defined, and their corresp...

Abstract. The paper summarised arguments and counterarguments within the scientific discussions on financial, socio-economic, environmental, public health patterns of creating regional roadmaps to prevent spread COVID-19 epidemic. main goals were develop anti-epidemiological road map with markers using instruments differential calculus. results analysis core care (financial, social, economic, e...

Based upon the mathematical formulas of Lattice gauge theory and non-commutative geometry differential calculus, we developed an approach of generalized gauge theory on a product of the spacetime lattice and the two discrete points(or a Z2 discrete group). We introduce a differentiation for non-nearest-neighbour points and find that this differentiation may lead to the introduction of Wilson te...

We introduce a typed lambda calculus in which real numbers, real functions, and in particular continuously differentiable and more generally Lipschitz functions can be defined. Given an expression representing a real-valued function of a real variable in this calculus, we are able to evaluate the expression on an argument but also evaluate the generalised derivative, i.e., the L-derivative, equ...


 Preparing K-12 students to gear up for higher mathematics and sciences, be more mathematically college-ready, teachers were given the essential role in bridging learning gaps. One way address this was utilization of modules. The researcher developed Enhancing Mastery & Expertise Mathematics (EM&EM) module Basic Calculus. objective quasi-experimental research evaluate effectivenes...