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| Author | : Alexandru Buium |
| Publisher | : American Mathematical Soc. |
| Total Pages | : 346 |
| Release | : 2005 |
| Genre | : Mathematics |
| ISBN | : 0821838628 |
For most of the book the only prerequisites are the basic facts of algebraic geometry and number theory."--BOOK JACKET.
| Author | : Steven G. Krantz |
| Publisher | : CRC Press |
| Total Pages | : 481 |
| Release | : 2015-10-07 |
| Genre | : Mathematics |
| ISBN | : 1498735029 |
Differential Equations: Theory, Technique, and Practice with Boundary Value Problems presents classical ideas and cutting-edge techniques for a contemporary, undergraduate-level, one- or two-semester course on ordinary differential equations. Authored by a widely respected researcher and teacher, the text covers standard topics such as partial diff
| Author | : Alexandru Buium |
| Publisher | : American Mathematical Society |
| Total Pages | : 357 |
| Release | : 2023-11-20 |
| Genre | : Mathematics |
| ISBN | : 1470475774 |
The aim of this book is to introduce and develop an arithmetic analogue of classical differential geometry. In this new geometry the ring of integers plays the role of a ring of functions on an infinite dimensional manifold. The role of coordinate functions on this manifold is played by the prime numbers. The role of partial derivatives of functions with respect to the coordinates is played by the Fermat quotients of integers with respect to the primes. The role of metrics is played by symmetric matrices with integer coefficients. The role of connections (respectively curvature) attached to metrics is played by certain adelic (respectively global) objects attached to the corresponding matrices. One of the main conclusions of the theory is that the spectrum of the integers is “intrinsically curved”; the study of this curvature is then the main task of the theory. The book follows, and builds upon, a series of recent research papers. A significant part of the material has never been published before.
| Author | : Kenneth B. Howell |
| Publisher | : CRC Press |
| Total Pages | : 907 |
| Release | : 2019-12-06 |
| Genre | : Mathematics |
| ISBN | : 1000701956 |
The Second Edition of Ordinary Differential Equations: An Introduction to the Fundamentals builds on the successful First Edition. It is unique in its approach to motivation, precision, explanation and method. Its layered approach offers the instructor opportunity for greater flexibility in coverage and depth. Students will appreciate the author’s approach and engaging style. Reasoning behind concepts and computations motivates readers. New topics are introduced in an easily accessible manner before being further developed later. The author emphasizes a basic understanding of the principles as well as modeling, computation procedures and the use of technology. The students will further appreciate the guides for carrying out the lengthier computational procedures with illustrative examples integrated into the discussion. Features of the Second Edition: Emphasizes motivation, a basic understanding of the mathematics, modeling and use of technology A layered approach that allows for a flexible presentation based on instructor's preferences and students’ abilities An instructor’s guide suggesting how the text can be applied to different courses New chapters on more advanced numerical methods and systems (including the Runge-Kutta method and the numerical solution of second- and higher-order equations) Many additional exercises, including two "chapters" of review exercises for first- and higher-order differential equations An extensive on-line solution manual About the author: Kenneth B. Howell earned bachelor’s degrees in both mathematics and physics from Rose-Hulman Institute of Technology, and master’s and doctoral degrees in mathematics from Indiana University. For more than thirty years, he was a professor in the Department of Mathematical Sciences of the University of Alabama in Huntsville. Dr. Howell published numerous research articles in applied and theoretical mathematics in prestigious journals, served as a consulting research scientist for various companies and federal agencies in the space and defense industries, and received awards from the College and University for outstanding teaching. He is also the author of Principles of Fourier Analysis, Second Edition (Chapman & Hall/CRC, 2016).
| Author | : Galina Filipuk |
| Publisher | : Birkhäuser |
| Total Pages | : 471 |
| Release | : 2017-06-23 |
| Genre | : Mathematics |
| ISBN | : 3319528424 |
This volume consists of invited lecture notes, survey papers and original research papers from the AAGADE school and conference held in Będlewo, Poland in September 2015. The contributions provide an overview of the current level of interaction between algebra, geometry and analysis and demonstrate the manifold aspects of the theory of ordinary and partial differential equations, while also pointing out the highly fruitful interrelations between those aspects. These interactions continue to yield new developments, not only in the theory of differential equations but also in several related areas of mathematics and physics such as differential geometry, representation theory, number theory and mathematical physics. The main goal of the volume is to introduce basic concepts, techniques, detailed and illustrative examples and theorems (in a manner suitable for non-specialists), and to present recent developments in the field, together with open problems for more advanced and experienced readers. It will be of interest to graduate students, early-career researchers and specialists in analysis, geometry, algebra and related areas, as well as anyone interested in learning new methods and techniques.
| Author | : Mark H. Holmes |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 248 |
| Release | : 2007-04-05 |
| Genre | : Mathematics |
| ISBN | : 0387681213 |
This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.
| Author | : Walter A. Strauss |
| Publisher | : John Wiley & Sons |
| Total Pages | : 467 |
| Release | : 2007-12-21 |
| Genre | : Mathematics |
| ISBN | : 0470054565 |
Our understanding of the fundamental processes of the natural world is based to a large extent on partial differential equations (PDEs). The second edition of Partial Differential Equations provides an introduction to the basic properties of PDEs and the ideas and techniques that have proven useful in analyzing them. It provides the student a broad perspective on the subject, illustrates the incredibly rich variety of phenomena encompassed by it, and imparts a working knowledge of the most important techniques of analysis of the solutions of the equations. In this book mathematical jargon is minimized. Our focus is on the three most classical PDEs: the wave, heat and Laplace equations. Advanced concepts are introduced frequently but with the least possible technicalities. The book is flexibly designed for juniors, seniors or beginning graduate students in science, engineering or mathematics.
| Author | : Andrei D. Polyanin |
| Publisher | : CRC Press |
| Total Pages | : 1767 |
| Release | : 2017-11-15 |
| Genre | : Mathematics |
| ISBN | : 1351643916 |
The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.
| Author | : Victor Henner |
| Publisher | : CRC Press |
| Total Pages | : 647 |
| Release | : 2013-01-29 |
| Genre | : Mathematics |
| ISBN | : 1466515007 |
Covers ODEs and PDEs—in One Textbook Until now, a comprehensive textbook covering both ordinary differential equations (ODEs) and partial differential equations (PDEs) didn’t exist. Fulfilling this need, Ordinary and Partial Differential Equations provides a complete and accessible course on ODEs and PDEs using many examples and exercises as well as intuitive, easy-to-use software. Teaches the Key Topics in Differential Equations The text includes all the topics that form the core of a modern undergraduate or beginning graduate course in differential equations. It also discusses other optional but important topics such as integral equations, Fourier series, and special functions. Numerous carefully chosen examples offer practical guidance on the concepts and techniques. Guides Students through the Problem-Solving Process Requiring no user programming, the accompanying computer software allows students to fully investigate problems, thus enabling a deeper study into the role of boundary and initial conditions, the dependence of the solution on the parameters, the accuracy of the solution, the speed of a series convergence, and related questions. The ODE module compares students’ analytical solutions to the results of computations while the PDE module demonstrates the sequence of all necessary analytical solution steps.
| Author | : Kazumasa Mizumura |
| Publisher | : World Scientific Publishing Company |
| Total Pages | : 436 |
| Release | : 2011-05-26 |
| Genre | : |
| ISBN | : 9813107855 |
Applied Mathematics in Hydraulic Engineering is an excellent teaching guide and reference to treating nonlinear mathematical problems in hydraulic, hydrologic and coastal engineering. Undergraduates studying civil and coastal engineering, as well as analysis and differential equations, are started off applying calculus to the treatment of nonlinear partial differential equations, before given the chance to practice real-life problems related to the fields. This textbook is not only a good source of teaching materials for teachers or instructors, but is also useful as a comprehensive resource of mathematical tools to researchers.
