Mikusiński, Jan
Overview
Works:  90 works in 385 publications in 8 languages and 3,885 library holdings 

Roles:  Author, Honoree, Other, Editor, Contributor 
Classifications:  QA312, 515.43 
Publication Timeline
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Most widely held works about
Jan Mikusiński
 An extension of Mikusinski's algebraic theory of differential equations by James Francis Geer( Book )
Most widely held works by
Jan Mikusiński
Operational calculus by
Jan Mikusiński(
Book
)
69 editions published between 1953 and 1983 in 6 languages and held by 676 WorldCat member libraries worldwide
69 editions published between 1953 and 1983 in 6 languages and held by 676 WorldCat member libraries worldwide
The theory of Lebesgue measure and integration by
Stanisław Hartman(
Book
)
36 editions published between 1960 and 2014 in English and Undetermined and held by 589 WorldCat member libraries worldwide
The Theory of Lebesgue Measure and Integration
36 editions published between 1960 and 2014 in English and Undetermined and held by 589 WorldCat member libraries worldwide
The Theory of Lebesgue Measure and Integration
The Bochner integral by
Jan Mikusiński(
Book
)
32 editions published between 1978 and 2014 in 3 languages and held by 582 WorldCat member libraries worldwide
The theory of the Lebesgue integral is still considered as a difficult theory, no matter whether it is based the concept of measure or introduced by other methods. The primary aim of this book is to give an approach which would be as intelligible and lucid as possible. Our definition, produced in Chapter I, requires for its background only a little of the theory of absolutely convergent series so that it is understandable for students of the first undergraduate course. Nevertheless, it yields the Lebesgue integral in its full generality and, moreover, extends automatically to the Bochner integral (by replacing real coefficients of series by elements of a Banach space). It seems that our approach is simple enough as to eliminate the less useful Riemann integration theory from regular mathematics courses. Intuitively, the difference between various approaches to integration may be brought out by the following story on shoemakers. A piece of leather, like in Figure 1, is given. The task consists in measuring its area. There are three shoemakers and each of them solves the task in his own way. A B Fig. 1 The shoemaker R. divides the leather into a finite number of vertical strips and considers the strips approximately as rectangles. The sum of areas of all rectangles is taken for an approximate area of the leather (Figure 2). If he is not satisfied with the obtained exactitude, he repeats the whole procedure, by dividing the leather into thinner strips
32 editions published between 1978 and 2014 in 3 languages and held by 582 WorldCat member libraries worldwide
The theory of the Lebesgue integral is still considered as a difficult theory, no matter whether it is based the concept of measure or introduced by other methods. The primary aim of this book is to give an approach which would be as intelligible and lucid as possible. Our definition, produced in Chapter I, requires for its background only a little of the theory of absolutely convergent series so that it is understandable for students of the first undergraduate course. Nevertheless, it yields the Lebesgue integral in its full generality and, moreover, extends automatically to the Bochner integral (by replacing real coefficients of series by elements of a Banach space). It seems that our approach is simple enough as to eliminate the less useful Riemann integration theory from regular mathematics courses. Intuitively, the difference between various approaches to integration may be brought out by the following story on shoemakers. A piece of leather, like in Figure 1, is given. The task consists in measuring its area. There are three shoemakers and each of them solves the task in his own way. A B Fig. 1 The shoemaker R. divides the leather into a finite number of vertical strips and considers the strips approximately as rectangles. The sum of areas of all rectangles is taken for an approximate area of the leather (Figure 2). If he is not satisfied with the obtained exactitude, he repeats the whole procedure, by dividing the leather into thinner strips
Theory of distributions; the sequential approach by
Piotr Antosik(
Book
)
15 editions published in 1973 in English and Dutch and held by 433 WorldCat member libraries worldwide
15 editions published in 1973 in English and Dutch and held by 433 WorldCat member libraries worldwide
An introduction to analysis : from number to integral by
Jan Mikusiński(
Book
)
14 editions published between 1993 and 2017 in English and Italian and held by 218 WorldCat member libraries worldwide
Based on the lifetime work of leading teacher and researcher Jan Mikusinski, this classroomtested book provides a thorough grounding in mathematical analysis, calculus and mathematical proofing. It introduces natural numbers through a new mathematical approach; replaces the Riemann integral with the more general Lebesgue integral; and rigorously develops the real number system from four simple axioms of natural numbers. Additional features include a wider range of problems than other textsincluding simple and routine as well as problems requiring more in depth creativity, answers to common questions, a new approach to the concept of equivalence relation which simplifies the construction of real numbers, and a large number of computational applications.  Publisher description
14 editions published between 1993 and 2017 in English and Italian and held by 218 WorldCat member libraries worldwide
Based on the lifetime work of leading teacher and researcher Jan Mikusinski, this classroomtested book provides a thorough grounding in mathematical analysis, calculus and mathematical proofing. It introduces natural numbers through a new mathematical approach; replaces the Riemann integral with the more general Lebesgue integral; and rigorously develops the real number system from four simple axioms of natural numbers. Additional features include a wider range of problems than other textsincluding simple and routine as well as problems requiring more in depth creativity, answers to common questions, a new approach to the concept of equivalence relation which simplifies the construction of real numbers, and a large number of computational applications.  Publisher description
Théorie élémentaire des distributions by
Jan Mikusiński(
Book
)
13 editions published in 1964 in 3 languages and held by 200 WorldCat member libraries worldwide
13 editions published in 1964 in 3 languages and held by 200 WorldCat member libraries worldwide
Operatorenrechnung by
Jan Mikusiński(
Book
)
11 editions published in 1957 in German and Undetermined and held by 157 WorldCat member libraries worldwide
11 editions published in 1957 in German and Undetermined and held by 157 WorldCat member libraries worldwide
The elementary theory of distributions by
Jan Mikusiński(
Book
)
20 editions published between 1957 and 1961 in English and Polish and held by 74 WorldCat member libraries worldwide
20 editions published between 1957 and 1961 in English and Polish and held by 74 WorldCat member libraries worldwide
Una introducción de la integral sin la noción de medida by
Jan Mikusiński(
Book
)
5 editions published in 1963 in Spanish and held by 51 WorldCat member libraries worldwide
5 editions published in 1963 in Spanish and held by 51 WorldCat member libraries worldwide
The elementary theory of distributions by
Jan Mikusiński(
Book
)
13 editions published in 1961 in English and held by 45 WorldCat member libraries worldwide
13 editions published in 1961 in English and held by 45 WorldCat member libraries worldwide
The elementary theory of distributions by
Jan Mikusiński(
Book
)
3 editions published in 1957 in English and held by 32 WorldCat member libraries worldwide
3 editions published in 1957 in English and held by 32 WorldCat member libraries worldwide
Operational calculus by
Jan Mikusiński(
Book
)
16 editions published between 1986 and 1987 in English and Undetermined and held by 25 WorldCat member libraries worldwide
16 editions published between 1986 and 1987 in English and Undetermined and held by 25 WorldCat member libraries worldwide
Operational calculus by
Jan Mikusiński(
Book
)
3 editions published in 1987 in English and held by 24 WorldCat member libraries worldwide
Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and nonho
3 editions published in 1987 in English and held by 24 WorldCat member libraries worldwide
Operational Calculus, Volume II is a methodical presentation of operational calculus. An outline of the general theory of linear differential equations with constant coefficients is presented. Integral operational calculus and advanced topics in operational calculus, including locally integrable functions and convergence in the space of operators, are also discussed. Formulas and tables are included.Comprised of four sections, this volume begins with a discussion on the general theory of linear differential equations with constant coefficients, focusing on such topics as homogeneous and nonho
Teorija obobščennych funkcij sekvencial'nyj podchod by
Piotr Antosik(
Book
)
8 editions published in 1976 in Russian and held by 16 WorldCat member libraries worldwide
8 editions published in 1976 in Russian and held by 16 WorldCat member libraries worldwide
Teoria miary i całki Lebėsgue'a by
Stanisław Hartman(
Book
)
3 editions published in 1957 in Polish and held by 15 WorldCat member libraries worldwide
3 editions published in 1957 in Polish and held by 15 WorldCat member libraries worldwide
Elementarna teoria dystrybucji by
Jan Mikusiński(
Book
)
5 editions published between 1961 and 1964 in Polish and Undetermined and held by 9 WorldCat member libraries worldwide
5 editions published between 1961 and 1964 in Polish and Undetermined and held by 9 WorldCat member libraries worldwide
Wstęp do analizy matematycznej by
Jan Mikusiński(
Book
)
4 editions published between 1957 and 1990 in Polish and held by 7 WorldCat member libraries worldwide
4 editions published between 1957 and 1990 in Polish and held by 7 WorldCat member libraries worldwide
Operational calculus by
Jan Mikusiński(
Book
)
3 editions published in 1983 in English and held by 5 WorldCat member libraries worldwide
3 editions published in 1983 in English and held by 5 WorldCat member libraries worldwide
Operational calculus by
Jan Mikusiński(
Book
)
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
Operational algebra. Sequences and series of operators. The operational differential calculus. Applications to chromotography
1 edition published in 1983 in English and held by 1 WorldCat member library worldwide
Operational algebra. Sequences and series of operators. The operational differential calculus. Applications to chromotography
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fewer
Audience Level
0 

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Kids  General  Special 
Related Identities
 Sikorski, Roman Other Author
 Hartman, Stanisław Author
 Antosik, Piotr Author Editor
 Mikusiński, Piotr
 Boehme, Thomas K. Other
 Mai, Brigitte
 Tesch, G.
 Boron, Leo F. Editor
 Klarsfeld, S. Translator
 Plesner, A. I. (Abram Iezekiilovich) 19001961 Translator
Useful Links
Alternative Names
Jan Mikusiński matemático polaco
Jan Mikusiński mathématicien polonais
Jan Mikusiński Polish mathematician
Jan Mikusiński polnischer Mathematiker
Jan Mikusiński polsk matematikar
Jan Mikusiński polsk matematiker
Jan Mikusiński Pools wiskundige (19131987)
Mikusiński, J.
Mikusiński, J. 19131987
Mikusinski, Jan 19131987
Mikusiński, Jan G.
Mikusiński, Jan Stefan.
Mikusiński, Jan Stefan 19131987
Mikusinskiĭ, I︠A︡
Mikusinskiĭ, I︠A︡n
Mikusinskij, Â.
Mikusinskij, Ja. 19131987
Микусинский, Я.
Микусинский, Я 19131987
Микусинский, Я. (Ян), 19131987
Микусинский, Ян
Микусинский, Ян 19131987
ミクシンスキー, J
ヤン・ミクシンスキー
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