東華大學圖書館 |

語系: 繁體中文

說明(常見問題)

回圖書館首頁

手機版館藏查詢

登入

回首頁 到查詢結果 [ author_sort:"bouleau, nicolas." ]

切換: 標籤 | MARC模式 | ISBD

The mathematics of errors

Bouleau, Nicolas.

FindBook

Google Book

Amazon

博客來

The mathematics of errors

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	The mathematics of errors/ by Nicolas Bouleau.
作者:	Bouleau, Nicolas.
出版者:	Cham :Springer International Publishing : : 2021.,
面頁冊數:	1 online resource (xii, 448 p.) :ill., digital ;24 cm.
內容註:	I. Error computations à la Gauss -- 1. The different approaches -- 2. Finite dimensional examples -- 3. An intuitive introduction to error structures -- 4. Weakly and strongly random errors -- II. Probabilistic and Functional Models -- 5. Strongly continuous semi-groups and Dirichlet forms -- 6. Error structures -- 7. Images and products of error structures -- 8. The gradient and the sharp and other calculation tools -- 9. Error structures on fundamental spaces -- III. The subtleness of the notion of bias -- 10. Approximation and bias operators -- 11. Computations and simulation methods -- IV. Error structures and its applications -- 12. Statistical identification of error structures -- 13. The instantaneous structure of a stochastic process -- 14. Models inspired by finance -- 15. Examples in Physics -- 16. The principle of arbitrary functions and error structures -- V. Historical elements and research themes -- 17. Error calculations from Gauss and Laplace -- 18. Extensions and open questions -- Hints for exercises -- Pedagogical References -- Chronological Bibliography.
Contained By:	Springer Nature eBook
標題:	Error analysis (Mathematics) -
電子資源:	https://doi.org/10.1007/978-3-030-88575-5
ISBN:	9783030885755

The mathematics of errors
Bouleau, Nicolas.

The mathematics of errors[electronic resource] /by Nicolas Bouleau. - Cham :Springer International Publishing :2021. - 1 online resource (xii, 448 p.) :ill., digital ;24 cm.

I. Error computations à la Gauss -- 1. The different approaches -- 2. Finite dimensional examples -- 3. An intuitive introduction to error structures -- 4. Weakly and strongly random errors -- II. Probabilistic and Functional Models -- 5. Strongly continuous semi-groups and Dirichlet forms -- 6. Error structures -- 7. Images and products of error structures -- 8. The gradient and the sharp and other calculation tools -- 9. Error structures on fundamental spaces -- III. The subtleness of the notion of bias -- 10. Approximation and bias operators -- 11. Computations and simulation methods -- IV. Error structures and its applications -- 12. Statistical identification of error structures -- 13. The instantaneous structure of a stochastic process -- 14. Models inspired by finance -- 15. Examples in Physics -- 16. The principle of arbitrary functions and error structures -- V. Historical elements and research themes -- 17. Error calculations from Gauss and Laplace -- 18. Extensions and open questions -- Hints for exercises -- Pedagogical References -- Chronological Bibliography.

The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician. Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader's intuition. By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation. Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.

ISBN: 9783030885755

Standard No.: 10.1007/978-3-030-88575-5doiSubjects--Topical Terms:

549972
Error analysis (Mathematics)

LC Class. No.: QA275 / B68 2021

Dewey Class. No.: 511.43

The mathematics of errors
LDR:03916nmm a2200361 a 4500 001 2262409
003 DE-He213
005 20220223105943.0
006 m o d
007 cr nn 008maaau
008 220616s2021 sz s 0 eng d
020 $a 9783030885755 $q (electronic bk.)
020 $a 9783030885748 $q (paper)
024 7 $a 10.1007/978-3-030-88575-5 $2 doi
035 $a 978-3-030-88575-5
040 $a GP $c GP
041 1 $a eng $h fre
050 4 $a QA275 $b B68 2021
072 7 $a PBT $2 bicssc
072 7 $a PBWL $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 511.43 $2 23
090 $a QA275 $b .B763 2021
100 1 $a Bouleau, Nicolas. $3 749170
240 1 0 $a Theorie des erreurs. $l English
245 1 4 $a The mathematics of errors $h [electronic resource] / $c by Nicolas Bouleau.
260 $a Cham : $b Springer International Publishing : $b Imprint: Springer, $c 2021.
300 $a 1 online resource (xii, 448 p.) : $b ill., digital ; $c 24 cm.
505 0 $a I. Error computations à la Gauss -- 1. The different approaches -- 2. Finite dimensional examples -- 3. An intuitive introduction to error structures -- 4. Weakly and strongly random errors -- II. Probabilistic and Functional Models -- 5. Strongly continuous semi-groups and Dirichlet forms -- 6. Error structures -- 7. Images and products of error structures -- 8. The gradient and the sharp and other calculation tools -- 9. Error structures on fundamental spaces -- III. The subtleness of the notion of bias -- 10. Approximation and bias operators -- 11. Computations and simulation methods -- IV. Error structures and its applications -- 12. Statistical identification of error structures -- 13. The instantaneous structure of a stochastic process -- 14. Models inspired by finance -- 15. Examples in Physics -- 16. The principle of arbitrary functions and error structures -- V. Historical elements and research themes -- 17. Error calculations from Gauss and Laplace -- 18. Extensions and open questions -- Hints for exercises -- Pedagogical References -- Chronological Bibliography.
520 $a The Mathematics of Errors presents an original, rigorous and systematic approach to the calculus of errors, targeted at both the engineer and the mathematician. Starting from Gauss's original point of view, the book begins as an introduction suitable for graduate students, leading to recent developments in stochastic analysis and Malliavin calculus, including contributions by the author. Later chapters, aimed at a more mature audience, require some familiarity with stochastic calculus and Dirichlet forms. Sensitivity analysis, in particular, plays an important role in the book. Detailed applications in a range of fields, such as engineering, robotics, statistics, financial mathematics, climate science, or quantum mechanics are discussed through concrete examples. Throughout the book, error analysis is presented in a progressive manner, motivated by examples and appealing to the reader's intuition. By formalizing the intuitive concept of error and richly illustrating its scope for application, this book provides readers with a blueprint to apply advanced mathematics in practical settings. As such, it will be of immediate interest to engineers and scientists, whilst providing mathematicians with an original presentation. Nicolas Bouleau has directed the mathematics center of the Ecole des Ponts ParisTech for more than ten years. He is known for his theory of error propagation in complex models. After a degree in engineering and architecture, he decided to pursue a career in mathematics under the influence of Laurent Schwartz. He has also written on the production of knowledge, sustainable economics and mathematical models in finance. Nicolas Bouleau is a recipient of the Prix Montyon from the French Academy of Sciences.
650 0 $a Error analysis (Mathematics) $3 549972
650 0 $a Stochastic analysis. $3 533923
650 1 4 $a Probability Theory. $3 3538789
650 2 4 $a Functional Analysis. $3 893943
650 2 4 $a Mathematical Modeling and Industrial Mathematics. $3 891089
650 2 4 $a Computational Mathematics and Numerical Analysis. $3 891040
710 2 $a SpringerLink (Online service) $3 836513
773 0 $t Springer Nature eBook
856 4 0 $u https://doi.org/10.1007/978-3-030-88575-5
950 $a Mathematics and Statistics (SpringerNature-11649)