Principles and Methods of Applied Mathematics

Principles And Methods Of Applied Mathematics book cover

Principles And Methods Of Applied Mathematics

Author(s): Michael (misha) Chertkov (Author)

  • Publisher finelybook 出版社: WSPC
  • Publication Date 出版日期: August 7, 2025
  • Language 语言: English
  • Print length 页数: 506 pages
  • ISBN-10: 9819808243
  • ISBN-13: 9789819808243

Book Description

This textbook aims to equip readers with a deep understanding of mathematical techniques essential for modeling, analyzing, and solving real-world problems across diverse disciplines. Written for graduate students and professionals, the book emphasizes practical applications of applied mathematics in the context of modern challenges, especially in the age of artificial intelligence and data-driven sciences. The text is structured around core areas including complex analysis, differential equations, variational calculus, optimal control, stochastic processes, statistical inference and learning. These foundational topics are developed through a balance of theoretical principles and practical methods, with examples drawn from physics, engineering, and data science to illustrate each technique's relevance and application. Throughout the book, exercises are proposed to help readers practice and refine these techniques, and the appendices include a collection of past midterm and final exam papers from the University of Arizona's Math 581 course, offering students a valuable resource for further study and self-assessment.

About the Author

Dr Michael (Misha) Chertkov is a Professor of Mathematics and Chair of the Graduate Interdisciplinary Program in Applied Mathematics at the University of Arizona. His research addresses foundational challenges in mathematics, statistics, machine learning, and artificial intelligence, particularly as they apply to and are inspired by physical systems like fluid mechanics. He also works on applications in the control of engineered systems, such as energy grids, and bio-social systems. Dr Chertkov received his PhD in physics from the Weizmann Institute of Science in 1996. After obtaining his PhD, he spent three years as an R H Dicke Fellow in the Department of Physics at Princeton University. In 1999, he joined the Los Alamos National Laboratory, first as a J R Oppenheimer Fellow, later becoming a Technical Staff Member in the Theory Division. He transitioned to the University of Arizona in 2019. Throughout his career, Dr Chertkov has contributed to about 300 research papers. He holds the title of Fellow in both the AAAS and the American Physical Society and is a Senior Member of IEEE.

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