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Methods Of Solving Nonstandard Problems

Author: Ellina Grigorieva
Publisher: Birkhäuser
ISBN: 3319198874
Size: 36.67 MB
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This book, written by an accomplished female mathematician, is the second to explore nonstandard mathematical problems – those that are not directly solved by standard mathematical methods but instead rely on insight and the synthesis of a variety of mathematical ideas. It promotes mental activity as well as greater mathematical skills, and is an ideal resource for successful preparation for the mathematics Olympiad. Numerous strategies and techniques are presented that can be used to solve intriguing and challenging problems of the type often found in competitions. The author uses a friendly, non-intimidating approach to emphasize connections between different fields of mathematics and often proposes several different ways to attack the same problem. Topics covered include functions and their properties, polynomials, trigonometric and transcendental equations and inequalities, optimization, differential equations, nonlinear systems, and word problems. Over 360 problems are included with hints, answers, and detailed solutions. Methods of Solving Nonstandard Problems will interest high school and college students, whether they are preparing for a math competition or looking to improve their mathematical skills, as well as anyone who enjoys an intellectual challenge and has a special love for mathematics. Teachers and college professors will be able to use it as an extra resource in the classroom to augment a conventional course of instruction in order to stimulate abstract thinking and inspire original thought.

Spectral Methods For Non Standard Eigenvalue Problems

Author: Călin-Ioan Gheorghiu
Publisher: Springer Science & Business
ISBN: 3319062301
Size: 18.45 MB
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This book focuses on the constructive and practical aspects of spectral methods. It rigorously examines the most important qualities as well as drawbacks of spectral methods in the context of numerical methods devoted to solve non-standard eigenvalue problems. In addition, the book also considers some nonlinear singularly perturbed boundary value problems along with eigenproblems obtained by their linearization around constant solutions. The book is mathematical, poising problems in their proper function spaces, but its emphasis is on algorithms and practical difficulties. The range of applications is quite large. High order eigenvalue problems are frequently beset with numerical ill conditioning problems. The book describes a wide variety of successful modifications to standard algorithms that greatly mitigate these problems. In addition, the book makes heavy use of the concept of pseudospectrum, which is highly relevant to understanding when disaster is imminent in solving eigenvalue problems. It also envisions two classes of applications, the stability of some elastic structures and the hydrodynamic stability of some parallel shear flows. This book is an ideal reference text for professionals (researchers) in applied mathematics, computational physics and engineering. It will be very useful to numerically sophisticated engineers, physicists and chemists. The book can also be used as a textbook in review courses such as numerical analysis, computational methods in various engineering branches or physics and computational methods in analysis.

Methods Of Solving Complex Geometry Problems

Author: Ellina Grigorieva
Publisher: Springer Science & Business Media
ISBN: 331900705X
Size: 49.48 MB
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This book is a unique collection of challenging geometry problems and detailed solutions that will build students’ confidence in mathematics. By proposing several methods to approach each problem and emphasizing geometry’s connections with different fields of mathematics, Methods of Solving Complex Geometry Problems serves as a bridge to more advanced problem solving. Written by an accomplished female mathematician who struggled with geometry as a child, it does not intimidate, but instead fosters the reader’s ability to solve math problems through the direct application of theorems. Containing over 160 complex problems with hints and detailed solutions, Methods of Solving Complex Geometry Problems can be used as a self-study guide for mathematics competitions and for improving problem-solving skills in courses on plane geometry or the history of mathematics. It contains important and sometimes overlooked topics on triangles, quadrilaterals, and circles such as the Menelaus-Ceva theorem, Simson’s line, Heron’s formula, and the theorems of the three altitudes and medians. It can also be used by professors as a resource to stimulate the abstract thinking required to transcend the tedious and routine, bringing forth the original thought of which their students are capable. Methods of Solving Complex Geometry Problems will interest high school and college students needing to prepare for exams and competitions, as well as anyone who enjoys an intellectual challenge and has a special love of geometry. It will also appeal to instructors of geometry, history of mathematics, and math education courses.

Methods Of Solving Sequence And Series Problems

Author: Ellina Grigorieva
Publisher: Birkhäuser
ISBN: 3319456865
Size: 10.57 MB
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This book aims to dispel the mystery and fear experienced by students surrounding sequences, series, convergence, and their applications. The author, an accomplished female mathematician, achieves this by taking a problem solving approach, starting with fascinating problems and solving them step by step with clear explanations and illuminating diagrams. The reader will find the problems interesting, unusual, and fun, yet solved with the rigor expected in a competition. Some problems are taken directly from mathematics competitions, with the name and year of the exam provided for reference. Proof techniques are emphasized, with a variety of methods presented. The text aims to expand the mind of the reader by often presenting multiple ways to attack the same problem, as well as drawing connections with different fields of mathematics. Intuitive and visual arguments are presented alongside technical proofs to provide a well-rounded methodology. With nearly 300 problems including hints, answers, and solutions, Methods of Solving Sequences and Series Problems is an ideal resource for those learning calculus, preparing for mathematics competitions, or just looking for a worthwhile challenge. It can also be used by faculty who are looking for interesting and insightful problems that are not commonly found in other textbooks.

Finite Mathematics For The Managerial Life And Social Sciences

Author: Soo T. Tan
Publisher: Cengage Learning
ISBN: 1337405787
Size: 58.44 MB
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Market-leading FINITE MATHEMATICS FOR THE MANAGERIAL, LIFE, AND SOCIAL SCIENCES, Twelfth Edition, balances contemporary applications, solid pedagogy, and the latest technology to provide students with content that motivates and keeps them interested in the course. Praised by users for its clarity, easy-to-follow writing style, and excellent applications, the text’s pedagogical features and exciting array of supplements equip students with the tools they need to make the most of their study time and succeed in the course. Using an intuitive approach, the text introduces mathematical concepts through real-life examples that students can relate to, and offers a clear and concise discussion of the mathematics involved, with numerous examples and applications that illustrate those concepts. Emphasis is placed on helping students formulate, solve, and interpret results of applied problems. Graphs and illustrations are used to help students visualize the concepts being presented. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.

Problem Solving Methods In Combinatorics

Author: Pablo Soberón
Publisher: Springer Science & Business Media
ISBN: 3034805977
Size: 68.94 MB
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Every year there is at least one combinatorics problem in each of the major international mathematical olympiads. These problems can only be solved with a very high level of wit and creativity. This book explains all the problem-solving techniques necessary to tackle these problems, with clear examples from recent contests. It also includes a large problem section for each topic, including hints and full solutions so that the reader can practice the material covered in the book.​ The material will be useful not only to participants in the olympiads and their coaches but also in university courses on combinatorics.

Applications Of Nonstandard Finite Difference Schemes

Author: Ronald E. Mickens
Publisher: World Scientific
ISBN: 9789810241339
Size: 72.31 MB
Format: PDF
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The main purpose of this book is to provide a concise introduction to the methods and philosophy of constructing nonstandard finite difference schemes and illustrate how such techniques can be applied to several important problems. Chapter I gives an overview of the subject and summarizes previous work. Chapters 2 and 3 consider in detail the construction and numerical implementation of schemes for physical problems involving convection-diffusion-reaction equations, that arise in groundwater pollution and scattering of electromagnetic waves using Maxwell's equations. Chapter 4 examines certain mathematical issues related to the nonstandard discretization of competitive and cooperative models for ecology. The application chapters illustrate well the power of nonstandard methods. In particular, for the same accuracy as obtained by standard techniques, larger step sizes can be used. This volume will satisfy the needs of scientists, engineers, and mathematicians who wish to know how to construct nonstandard schemes and see how these are applied to obtain numerical solutions of the differential equations which arise in the study of nonlinear dynamical systems modeling important physical phenomena.

Finite Mathematics

Author: Stefan Waner
Publisher: Cengage Learning
ISBN: 1337280429
Size: 15.98 MB
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Full of relevant, diverse, and current real-world applications that students can relate to, Waner and Costenoble's FINITE MATHEMATICS, Seventh Edition, helps your students see the relevance of mathematics in their lives. A large number of the applications are based on real, referenced data from business, economics, and the life and social sciences. Thorough, clearly delineated spreadsheet and TI Graphing Calculator instruction appears throughout the text, supplemented by an acclaimed author website that provides interactive tutorials, powerful utilities, conceptualization tools, review, and practice. The end-of-chapter Technology Notes and Technology Guides are optional, allowing you to include in your courses precisely the amount of technology instruction you choose. Acclaimed for accuracy and readability, FINITE MATHEMATICS appeals to, and is appropriate for, all types of teaching and learning styles. Important Notice: Media content referenced within the product description or the product text may not be available in the ebook version.