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Brings together over one hundred different approaches from classrooms worldwide, exposing mathematicians to methods that they've never before encountered.
Joanne Morgan's fascinating and practical book presents a selection of mathematical methods for twenty topics in the secondary maths curriculum. Some of the methods featured are used widely in schools around the world, others are only used in a small number of countries. Some have been in use for generations and others have fallen out of fashion.Some of the very best maths teachers are those who take the time to research their subject in greater depth. Exploring new methods can help us make sense of things, even if we choose not to teach those methods. Read this book with an open mind and willingness to learn!
Annotation This text presents the various mathematical methods used in military operations research in one easy-to-use reference volume. The reader will find the calculations necessary to analyze all aspects of defense operations, from weapon performance to combat modeling. The text is so clearly written and organized that even newcomers to the field will find it useful. Included with the text is an updated version of Defense Analyses Software, a compendium of software subroutines that allow the reader to compute numerical values for functions or tables derived in the text. Each subroutine is provided with a detailed reference to the equation from which it was derived to ensure that its intended application is consistent with the assumptions used in the derivation. The third edition has a new chapter on theater missile defense based on the concept of layered defense with different strategies of allocating defense interceptors against short- or mid-range ballistic missiles.
This volume, a comprehensive survey and critical analysis of today's issues in mathematics education, distills research to build knowledge and capacity in the field. The compendium is a valuable new resource that provides the most comprehensive evidence about what is known about research in mathematics education. The 38 chapters present five sections that address research about (1) foundations, (2) methods, (3) mathematical processes and content, (4) students, teachers, and learning environments, and (5) futuristic issues. Each chapter offers a synthesis of research with an eye to the historical development of a research topic and, in particular, historical milestones of the research about the topic.
This completely revised edition provides a tour of the mathematical knowledge and techniques needed by students across the physical sciences. There are new chapters on probability and statistics and on inverse problems. It serves as a stand-alone text or as a source of exercises and examples to complement other textbooks.
Presents numerical methods and computer code in Matlab for the solution of ODEs and PDEs with detailed line-by-line discussion.
A clear, practical and self-contained presentation of the methods of asymptotics and perturbation theory for obtaining approximate analytical solutions to differential and difference equations. Aimed at teaching the most useful insights in approaching new problems, the text avoids special methods and tricks that only work for particular problems. Intended for graduates and advanced undergraduates, it assumes only a limited familiarity with differential equations and complex variables. The presentation begins with a review of differential and difference equations, then develops local asymptotic methods for such equations, and explains perturbation and summation theory before concluding with an exposition of global asymptotic methods. Emphasizing applications, the discussion stresses care rather than rigor and relies on many well-chosen examples to teach readers how an applied mathematician tackles problems. There are 190 computer-generated plots and tables comparing approximate and exact solutions, over 600 problems of varying levels of difficulty, and an appendix summarizing the properties of special functions.
Mathematical physics plays an important role in the study of many physical processes — hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical physics, this thorough advanced undergraduate- or graduate-level text considers only those problems leading to partial differential equations. Contents: I. Classification of Partial Differential Equations II. Evaluations of the Hyperbolic Type III. Equations of the Parabolic Type IV. Equations of Elliptic Type V. Wave Propagation in Space VI. Heat Conduction in Space VII. Equations of Elliptic Type (Continuation) The authors — two well-known Russian mathematicians — have focused on typical physical processes and the principal types of equations dealing with them. Special attention is paid throughout to mathematical formulation, rigorous solutions, and physical interpretation of the results obtained. Carefully chosen problems designed to promote technical skills are contained in each chapter, along with extremely useful appendixes that supply applications of solution methods described in the main text. At the end of the book, a helpful supplement discusses special functions, including spherical and cylindrical functions.
