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MATHEMATICS EDUCATION
Study Guide DIFFERENTIAL EQUATIONS AND THEIR APPLICATIONS
Analysis from a Physicist’s Viewpoint
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by Noboru Nakanishi (Kyoto University, Japan) & Kenji Seto (Hokkai-Gakuen University, Japan) This book is written for students and researchers who are fond of mathematics and the natural sciences. It consists of two parts. Part I presents the theory of analysis in which the mathematical theory is described not as an accomplished palace, but as a building under construction. It uncovers how a theory has been or is being constructed. In Part II, the theory of differential equations is applied to interesting practical problems, such as pursuit-line and tractrix, attack on an object from an airplane, an insect crawling along a stretching rubber rod, the SIR model of a virus infection, string vibration, circular membrane vibration, as well as the wind ripple, sand dune and wave phenomena on a highway. Furthermore, the problems of a one-dimensional lattice vibration, the keyboard percussion vibration and the eigenvalue problems in quantum mechanics, such as the Aharonov – Bohm effect, are also investigated in detail. Contents: Theories: Introduction to the Theory of Analysis; Differential Equations; Differential Operators; Applications: Ordinary Differential Equations; Partial Differential Equations; Problems Encountering Bessel Functions; Potential Problems in Quantum Mechanics.
Readership: Undergraduate students, postgraduate students and researchers interested in the theory and applications of differential equations in mathematics and the natural sciences.
300pp Apr 2022 978-981-124-745-3 US$88 £75
Problem Solving in Mathematics and Beyond
MATHEMATICS: ITS HISTORICAL ASPECTS, WONDERS AND BEYOND
by Alfred S Posamentier & Arthur D Kramer (City University of New York, USA) The book offers 101 mathematical gems, some of which may require a modicum of high school mathematics and others, just a desire to carefully apply oneself to the ideas. Many folks have spent years encountering mathematical terms, symbols, relationships and other esoteric expressions. Their origins and their meanings may never have been revealed, such as the symbols +, -, =, π. ∞, √, ∑, and many others. This book provides a delightful insight into the origin of mathematical symbols and popular theorems such as the Pythagorean Theorem and the Fibonacci Sequence, common mathematical mistakes and curiosities, intriguing number relationships, and some of the different mathematical procedures in various countries. The book uses a historical and cultural approach to the topics, which enhances the subject matter and greatly adds to its appeal. The mathematical material can, therefore, be more fully appreciated and understood by anyone who has a curiosity and interest in mathematics, especially if in their past experience they were expected to simply accept ideas and concepts without a clear understanding of their origins and meaning. Contents: Introduction; Numbers and Symbols; Arithmetic Curiosities; Aspects of Measurement; Geometric Novelties; Probability; A Potpourri of Mathematical Topics. Readership: General readership as well as to teachers and students of mathematics at the secondary level.
