Application to applied sciences
Rich of exercises with a set of selected solutions
Concise, rigorous, clear in analyzing the solutions
This book offers readers a primer on the theory and applications of Ordinary Differential Equations. The style used is simple, yet thorough and rigorous. Each chapter ends with a broad set of exercises that range from the routine to the more challenging and thought-provoking. Solutions to selected exercises can be found at the end of the book. The book contains many interesting examples on topics such as electric circuits, the pendulum equation, the logistic equation, the Lotka-Volterra system, the Laplace Transform, etc., which introduce students to a number of interesting aspects of the theory and applications. The work is mainly intended for students of Mathematics, Physics, Engineering, Computer Science and other areas of the natural and social sciences that use ordinary differential equations, and who have a firm grasp of Calculus and a minimal understanding of the basic concepts used in Linear Algebra. It also studies a few more advanced topics, such as Stability Theory and Boundary Value Problems, which may be suitable for more advanced undergraduate or first-year graduate students. The second edition has been revised to correct minor errata, and features a number of carefully selected new exercises, together with more detailed explanations of some of the topics.
A complete Solutions Manual, containing solutions to all the exercises published in the book, is available. Instructors who wish to adopt the book may request the manual by writing directly to one of the authors.
Springer Proceedings in Mathematics & Statistics
Presents papers on a wide range of topics, along with two mini-courses intended to introduce the topics in a smooth, accessible manner
This book focuses on mathematical problems concerning different applications in physics, engineering, chemistry and biology. It covers topics ranging from interacting particle systems to partial differential equations (PDEs), statistical mechanics and dynamical systems.
The purpose of the second meeting on Particle Systems and PDEs was to bring together renowned researchers working actively in the respective fields, to discuss their topics of expertise and to present recent scientific results in both areas. Further, the meeting was intended to present the subject of interacting particle systems, its roots in and impacts on the field of physics and its relation with PDEs to a vast and varied public, including young researchers.
The book also includes the notes from two mini-courses presented at the conference, allowing readers who are less familiar with these areas of mathematics to more easily approach them.
The contributions will be of interest to mathematicians, theoretical physicists and other researchers interested in interacting particle systems, partial differential equations, statistical mechanics, stochastic processes, kinetic theory, dynamical systems and mathematical modeling aspects.
Includes a tutorial overview on random graphs, with rigorous mathematical results
Applies statistical physics methods to distributed algorithms
Introduces the reader to graphical models and message-passing algorithms
Presents the information theoretic aspects of wireless communication networks
Presents the information theoretic aspects of wireless communication networks
Introducing the reader to the mathematics beyond complex networked systems, these lecture notes investigate graph theory, graphical models, and methods from statistical physics. Complex networked systems play a fundamental role in our society, both in everyday life and in scientific research, with applications ranging from physics and biology to economics and finance.
The book is self-contained, and requires only an undergraduate mathematical background.
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Theoretical and Mathematical Physics
Presents an ab initio quantum mechanical treatment of few-body systems
like light nuclei, few-electron atoms, small molecules and clusters
Useful reference material for research workers starting from advanced graduate level students to senior scientists
Provides a detailed treatment of the trinucleon system
The book provides a generalized theoretical technique for solving the fewbody Schrodinger equation. Straight forward approaches to solve it in terms of position vectors of constituent particles and using standard mathematical techniques become too cumbersome and inconvenient when the system contains more than two particles. The introduction of Jacobi vectors, hyperspherical variables and hyperspherical harmonics as an expansion basis is an elegant way to tackle systematically the problem of an increasing number of interacting particles. Analytic expressions for hyperspherical harmonics, appropriate symmetrisation of the wave function under exchange of identical particles and calculation of matrix elements of the interaction have been presented. Applications of this technique to various problems of physics have been discussed. In spite of straight forward generalization of the mathematical tools for increasing number of particles, the method becomes computationally difficult for more than a few particles. Hence various approximation methods have also been discussed. Chapters on the potential harmonics and its application to Bose-Einstein condensates (BEC) have been included to tackle dilute system of a large number of particles. A chapter on special numerical algorithms has also been provided. This monograph is a reference material for theoretical research in the few-body problems for research workers starting from advanced graduate level students to senior scientists.
Undergraduate Texts in Mathematics
Concepts such as continuity, differentiation and integration, are approached via sequences
Contains carefully selected, clearly explained examples and counterexamples to help the reader understand and apply concepts
Approach taken has simplicial merit and places students in a position to understand more sophisticated concepts that play central in more advanced fields
This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating definitions, results and proofs. Simple examples are provided to illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallisfs formula and Stirlingfs formula, proofs of the irrationality of Î and e and a treatment of Newtonfs method as a special instance of finding fixed points of iterated functions.
Undergraduate Texts in Mathematics
Provides a polished and tuned-up version of the same core text that has proved successful with students and instructors for 15 years
Includes around 150 new exercises, in addition to around 200 of the best exercises from the first edition
Presents three new self-guided projects exploring Eulerfs sum, the factorial function, and the Weierstrass Approximation Theorem
This lively introductory text exposes the student to the rich rewards of a rigorous study of functions of a real variable. In each chapter, informal discussions of questions that give analysis its inherent fascination are followed by precise, but not overly formal, developments of the techniques needed to make sense of them. By focusing on the unifying themes of approximation and the resolution of paradoxes that arise in the transition from the finite to the infinite, the text turns what could be a daunting cascade of definitions and theorems into a coherent and engaging progression of ideas. Acutely aware of the need for rigor, the student is then much better prepared to understand what constitutes a proper mathematical proof and how to write one.
Fifteen years of classroom experience with the first edition of Understanding Analysis have solidified and refined the central narrative of the second edition. Roughly 150 new exercises now join a selection of the best exercises from the first edition and three more project-style sections have been added. Investigations of Eulerfs computation of Ä(2), the Weierstrass Approximation Theorem and the gamma function are now among the bookfs cohort of seminal results serving as motivation and payoff for the beginning student to master the methods of analysis.
gThis is a dangerous book. Understanding Analysis is so well-written and the development of the theory so well-motivated that exposing students to it could well lead them to expect such excellence in all their textbooks. c Understanding Analysis is perfectly titled; if your students read it, thatfs whatfs going to happen. c This terrific book will become the text of choice for the single-variable introductory analysis course c h
Steve Kennedy, MAA Reviews
Compact Textbooks in Mathematics
New arrangement of the subject matter with hands-on examples
The Lebesgue integral is an essential tool in the fields of analysis and stochastics and for this reason, in many areas where mathematics is applied. This textbook is a concise, lecture-tested introduction to measure and integration theory. It addresses the important topics of this theory and presents additional results which establish connections to other areas of mathematics. The arrangement of the material should allow the adoption of this textbook in differently composed Bachelor programmes.