A Sweep‐Type Differential and Integral Discriminator

The distributional Henstock-Kurzweil integral and measure differential equations

In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...

Differential and Integral Calculus

1. Historical survey 2. Convergence of Sequences 2.1 Definition of Convergence 2.2. The Basic Property of Real Numbers. 2.3. Real Line 3. Continuous Functions 3.1 Continuous Functions and Their Limits 3.2 Properties of Continuous Functions. 3.2.1 The Intermediate Value Theorem 3.2.2. Maxima and Minima of Continuous Functions 3.3. The graph of a function 4. Differential Calculus 4.1 Derivative 4...

Differential equations and integral geometry

be the operator of mean value over a radius r sphere centered at y ∈ R. The integral transform I is clearly injective. Let C be a compact hypersurface in R isotopic to a sphere. Theorem 1.1 Let f(x) be a smooth function vanishing near C. Then one can recover f from its mean values along the spheres tangent to C, and the inversion is given by an explicit formula. In fact we will show that this t...

POL502: Differential and Integral Calculus

We have come a long way and finally are about to study calculus. Many of you might have taken some courses in the past where you learned a number of formulas to calculate the derivatives and integrals of certain functions. The purpose of this course, however, is not to memorize these formulas mindlessly. Rather, our goals are to understand the mathematical concepts underlying such formulas and ...

Integral geometry and differential equations