[Problem Books in Mathematics] Exercises in Analysis || Smooth and Nonsmooth CalculusIn this chapter, X and Y are Banach spaces.doi:10.1007/978-3-319-27817-9_3Gasiński, LeszekPapageorgiou, Nikolaos S.
This is a preview of subscription content, log in via an institution to check access. Keywords Analysis Riemann integral Topologie calculus compactness Search within this book Search Table of contents (28 chapters) Front Matter Pages i-vii Download chapter PDF Analysis Front Matter Pages ix-ix...
10.9.6 Decaying Turbulence in a Box 479 10.9.7 Bubbles and the Gas–Liquid Interface 480 10.9.8 Shock and Vibration Events in Transportation 482 10.10 Conclusion and Some Final Thoughts 483 Problems 484 References 498 11 An Introduction to the Calculus of Variations and the Finite Element...
(Open in a new window)Google Scholar Haghjoo, S., Radmehr, F., & Reyhani, E. (2023). Analyzing the written discourse in calculus textbooks over 42 years: The case of primary objects, concrete discursive objects, and a realization tree of the derivative at a point. Educational Studies in...
The aim of this study is to investigate various qualitative properties of eigenvalues and corresponding eigenfunctions of one Sturm-Liouville problem with an interior singular point. We introduce a new Hilbert space and integral operator in it such a way
In this formula, t2is the square of the variable ‘t’, which is simply t * t, or t2. The pair of x(t) and y(t) equations are the required parametric equations that describe the path of the baseball in calculus. Tips: If the initial velocity is known with the unit of miles per...
In the next set of notes, we will combine the Gleason-Yamabe theorem with some topological analysis (and in particular, using the invariance of domain theorem) to establish some further control on locally compact groups, and in particular obtaining a solution to Hilbert’s fifth problem. To ...
Examples of this progress can be found in [42–46]. Numerical methods for solving optimal control problems are divided into two major classes: indirect methods and direct methods. In an indirect method, the calculus of variations, is used to determine the first-order optimality conditions of ...
The methods used in optimization vary depending on the type of problem and the variables involved. Optimization problems with discrete variables are known as combinatorial optimization problems. If the variables in the problem are continuous, we can use calculus to solve the problem....
We prove that positive solutions of the fractional Lane–Emden equation with homogeneous Dirichlet boundary conditions satisfy pointwise estimates in terms of the best constant in Poincaré’s inequality on all open sets, and are isolated in L^1 on smooth bounded ones, whence we deduce the isolatio...