CRISTINEL MORTICI. ABSTRACT. We describe here some  Mortici, C., Bazele Matematicii, Ed. Minus, Târgoviste,  Reiss, R.-D. and Thomas, M., . CRISTINEL MORTICI. ABSTRACT. We describe here some ..  Mortici, C., Bazele Matematicii, Ed. Minus, Târgoviste,  Reiss, R.-D. and Thomas, M., . M. Megan, Bazele Analizei Matematice, Ed. Eurobit, Timisoara, . W. Sierpinski, Sur Bucharest, Romania, and Cristinel Mortici, Valahia University of.
|Published (Last):||2 August 2009|
|PDF File Size:||18.57 Mb|
|ePub File Size:||16.20 Mb|
|Price:||Free* [*Free Regsitration Required]|
Thank you for interesting in our services. We are a non-profit group that run this website to share documents. We need your help to maintenance this website.
Please help us to share our service with your friends. David Hilbert That Cauchy had so much trouble proving the mean value theorem or coming to terms with the notion of uniform convergence should alert us to the fact that these ideas are not easily assimilated. The student needs time with them. The highly refined proofs that we know today leave the mistaken impression that the road of discovery in mathematics is straight and sure.
Experimentation and misunderstanding have been essential components in the growth of mathematics. Principalii operatori logici sunt: Expresiile de forma p x, y, z. Prin urmare avem tautologiile: A studiat la Trinity College Cambridge.
ASTRONAUTICA nr. 1/2008
Fie K un corp. Elementele lui V se numesc vectori, iar elementele lui K se numesc scalari. Definim adunarea pe R prin: Arhimede 62 a studiat, la Alexandria, cu succesorii lui Euclid. A fost prieten cu regele Hieron al doilea al Siracusei.
Matematicianul francez Augustin-Louis Cauchy a fost fondatorul Analizei Matematice moderne. Victor Buniakovski moryici fost profesor la St. Teorema Bolzano – Weierstrass. Iat a un alt exemplu: Este unul dintre fondatorii teoriei jocurilor. Cele mai importante opere ale lui Borel sunt: Fie I2 un astfel de interval.
Teorema de acoperire a lui Lebesgue. A fost un student eminent al liceului Lakanal. Denjoy a fost cel mai faimos student al lui Baire. Acest fapt contrazice teorema lui Baire. Acesta constituie unul dintre motivele care au condus la elaborarea teoriei integralei Lebesgue.
Well into the 19th century it was simply viewed as a descriptive term for curves that are unbroken. The preeminent calculus text of that era was S. It was first published in The sixth edition appeared in Unchanged throughout these editions was its definition of continuity: This intuitive notion of continuity is useless when one tries to prove anything. The first appearance of the modern definition of continuity was published by Bernhard Bolzano in in the Proceedings of the Prague Scientific Society under the title Rein analytischer Beweis des Lehrsatzes dass zwieschen je zwey [sic] Werthen, die ein entgegengesetztes Resultat gewaehren, wenigstens eine reele Matemaitcii der Gleichung liege.
This roughly translates as Purely analytic proof cristniel the theorem that between any two values that yield results of opposite sign there will be at least one real root of the equation.
The title says it all. Bolzano was proving that mateematicii continuous function has the intermediate mmatematicii problem. If he has to prove that continuity implies the intermediate value property, then he is not using the intermediate value property to define continuity.
Such a definition would agree with the morrici notion of continuity. If a function is defined at every point on the interval [a, b], then to say it has the intermediate property is equivalent to saying that it has no jumps or breaks. There are several problems with choosing this definition of continuity. A function that has the intermediate value property on [0, 1] is not necessarily bounded on that interval. Another problem with using the intermediate value problem property to define continuity is that two functions can have it while their sum does not.
Perhaps the most important aspect of continuity that the intermediate value property lacks, and the one that may have suggested the modern definition, is that if f is continuous in a neighborhood of a and if there is a small error in the matematicii so that instead of evaluating f at a we evaluate it at something very close to a, then we want the output to be very close to f a. We want to be able to control the variation in the output by setting a tolerance on the input.
Teorema lui Bolzano a valorilor intermediare. A murit la Bonn, Germania, la 7 octombrie A first course, Prentice Hall, Inc. Atunci f are un unic punct fix. Rezultatele de mai sus au mayematicii avantaje: Banach ingineria, iar Wilkosz limbile orientale. Teorema de punct fix a lui Brouwer. Mogtici we have seen, we can be much more precise. The mstematicii is clear in most cases, but the phrase “gets closer” mayematicii still to ambiguous.
What is important is that we can make the absolute value of our error matematocii small as it needs to be by controlling the distance of x from a. We now present notation that was introduced by Cauchy in Oxtoby, Measure and Category, Springer-Verlag,capitolul A criistinel unul dintre matematicienii de frunte ai vremilor sale a avut chiar unele controverse cu Descartes. A trimis rezultatele sale lui Euler, care a fost impresionat de noile metode elaborate de Lagrange.
A murit la 3 aprilie Una dintre aceste tehnici este metoda lui Newton sau mai exact metoda lui Newton-Raphson. Exemple Un prim exemplu: Spre exemplu, pentru f: Teorema lui Lagrange-cazul multidimensional.
ASTRONAUTICA nr. 1/ – PDF Free Download
Teorema lui Taylor-cazul multidimensional. Prin urmare f U: Cu alte cuvinte, orice punct din Rq care este suficient de apropiat de cristinle c este imaginea, prin fa unui punct apropiat de c.
Similar Dy F matematucii, b: Teorema lui Fermat-cazul multidimensional. Generalizare a teoremei lui Rolle. Contrar lui Newton, G. If we have waited this long before defining integration, it is because we have not needed a careful definition. For more than a hundred years, it was enough to define integration as the inverse process to differentiation.
As we saw in the last section, this is no longer sufficient when we start using Fourier series. We need a broader and clearer definition. As the nineteenth century progressed, it became increasingly evident that the right way to define matematciii was in terms of integration.
If we are to avoid circular reasoning, then we must look elsewhere for our definition. It was Cauchy who first proposed the modern solution to bazeel problem. He defined the integral as the limit of approximating sums. He was first to unlink the definitions of the integral and derivative. We have seen that Archimedes calculated areas by using approximating sums. Leibniz and his successors used these sums to approximate integrals they could not evaluate precisely.
But these were approximation techniques, not definitions. Part of the reason that no one used this definition before Cauchy is that it is ungainly. Following Cauchy, we shall assume that we are working with a continuous function jatematicii on a closed and bounded interval [a, b]. We choose a positive integer n and an arbitrary partition of [a, b] into n subintervals: It is significant that he does not merely take the limit as n approaches infinity.
Its purpose was nothing less than to find necessary and matematciii conditions for a function to have a representation as a trigonometric series. Riemann never published it, probably because it raises many new questions that he was hoping to answer. It appeared inafter his death. It was also sufficient for a demonstration that any bounded piecewise continuous function is integrable. Riemann wished to consider even more general functions, functions with infinitely many discontinuities within any finite interval.
Like Cauchy, he uses approximating sums: Because of this extra freedom, it appears more difficult to guarantee convergence of these series. Crisyinel wanted to be able to prove that any continuous function is matematiciii.
Riemann was interested in seeing how discontinuous a function could be and still remain integrable. In particular, it enables him to establish necessary and sufficient conditions for the existence of the integral.