Differentiation and integration by using matrix inversion

• Autorzy: Matlak D. , Matlak J. , Słota D. , Wituła R.
• Języki publikacji: EN

Abstrakty

EN

In the paper certain examples of applications of the matrix inverses for generating and calculating the integrals are presented.

Słowa kluczowe

EN

matrix inverse; integrals; generalized McLaurin’s formula

PL

odwrotność macierzy; całki; uogólniony wzór Maclaurina

• Wydawca: Wydawnictwo Politechniki Częstochowskiej
• Czasopismo: Journal of Applied Mathematics and Computational Mechanics
• Rocznik: 2014
• Tom: Vol. 13, nr 2
• Strony: 63--71
• Opis fizyczny: Bibliogr. 12 poz.

Twórcy

autor

Matlak D.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

autor

Matlak J.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

autor

Słota D.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

autor

Wituła R.

• Institute of Mathematics, Silesian University of Technology, Gliwice, Poland

Bibliografia

• [1] Swartz W., Integration by matrix inversion, Amer. Math. Monthly 1958, 65, 282-283.
• [2] Prudnikov A.P., Bryczkov J.A., Mariczev O.J., Integrals and Series, Elementary Functions,Vol. 1, Nauka Press, Moscov 1986 (in Russian).
• [3] Prudnikov A.P., Bryczkov J.A., Mariczev O.J., Integrals and Series, Complements Sections, Vol. 2, Nauka Press, Moscow 1986 (in Russian).
• [4] Kołodziej W., Mathematical Analysis, PWN, Warsaw 1979 (in Polish).
• [5] Eves H., An Introduction to the History of Mathematics, Holt, Rinehart and Winston, New York 1969.
• [6] Boyer C. (revised by Merzbach U.), A History of Mathematics, Wiley, New York 1991.
• [7] Olver F.W.J., Lozier D.W., Boisvert R.F., Clark C.W., NIST Handbook of Mathematical Functions, Cambridge Univ. Press, Cambridge 2010.
• [8] Wituła R., Number π, its History and Influence on Mathematical Creativeness, Wyd. Pracowni Komputerowej Jacka Skalmierskiego, Gliwice 2011 (in Polish).
• [9] Gawrońska N., Słota D., Wituła R., Zielonka A., Some generalizations of Gregory’s power series and their applications, J. Appl. Math. Comput. Mech. 2013, 12(3), 79-91.
• [10] Wituła R., Hetmaniok E., Pleszczyński M., Słota D., Generalized Gregory’s series (in review).
• [11] Redheffer R., Induced transformations of the derivative - vector, Amer. Math. Monthly 1976, 83, 255-259.
• [12] Wituła R., Matlak D., Matlak J., Słota D., Use of matrices in evaluation of całka sec2n+1 x dx in review.