Publisher finelybook 出版社: World Scientific Publishing Europe Ltd
Publication Date 出版日期: December 20, 2025
Language 语言: English
Print length 页数: 368 pages
ISBN-10: 1800617283
ISBN-13: 9781800617285
Book Description
This textbook provides a comprehensive exploration of mathematical modeling, emphasizing the limitations of pointwise analysis and highlighting the great potential of measure theory. Measure theory not only offers better representations of phenomena, such as distributions and continuous probabilities, but also facilitates the analysis of classical partial differential equation problems. Additionally, the book introduces new classes of problems that go beyond traditional pointwise and infinitesimal analysis, integrating random and deterministic aspects into a unified framework.
The narrative follows Bernard Namier, a young engineering apprentice, and Laurent Corps, a retired mathematics expert who tutors Bernard to tackle a challenging project assigned at work. Through their interwoven dialogue and the fictitious texts they study, readers are immersed in mathematical modeling as applied to engineering problems, with insights that extend to broader applications. This unique structure bridges two educational traditions: the abstract, Bourbaki-style approach common in France and the progressive, example-based learning prevalent in the Anglosphere. As a result, readers will master core concepts through rigorous proofs and applied examples and gain confidence in handling complex systems.
Editorial Reviews
About the Author
Erick Herbin, a former engineer who was specializing in random modeling and fundamental research on stochastic processes at Dassault Aviation from 1995 to 2011, is now a full professor in mathematics at CentraleSupélec, where he conducts research on the local and geometric properties of random objects. He headed the mathematics department at CentraleSupélec, a leading French engineering school, from 2011 to 2025. He designed and taught the "Probabilités" course for 500 students from 2006 to 2017. He then designed and has been teaching the extensive "Convergence, integration, probabilities" course since 2018. He was heavily involved in the creation of CentraleSupélec's current curriculum, which trains 1,000 students a year over a three-year period. Erick Herbin is the author of several articles in international peer-reviewed journals in mathematics and is a member of the Laboratoire de Mathématiques d'Orsay at the Université Paris-Saclay.
Pauline Lafitte, a full professor at Centrale- Supélec, specializes in mathematical modeling with partial differential equations. Her research focuses on performing the complete chain of modeling, from observation to validation using experimental data, through the analysis of mathematical models, the design of numerical schemes, their analysis, and their simulation. These models aim to reproduce phenomena appearing in various fields, including fluid mechanics, chemistry, and biology. She designed the "Partial Differential Equations (Theory and Numerics)" course at CentraleSupélec in 2012 and has been teaching it since.
Since 2016, she has been in charge of "Option Mathématiques Appliquées", which evolved into the "Dominante Mathématiques et Data Science", a key part of the mathematical studies in the third year of the CentraleSupélec curriculum.
Pauline Lafitte has authored several papers in international peerreviewed journals in mathematics and is a member of the Laboratoire de Mathématiques d'Orsay at the Université Paris-Saclay.
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