The fifth edition of this classic book continues its excellence in teaching numerical analysis and techniques. Interesting and timely applications motivate an understanding of methods and analysis of results. Suitable for students with mathematics and engineering backgrounds, the breadth of topics (partial differential equations, systems of nonlinear equations, and matrix algebra), provide comprehensive and flexible coverage of all aspects of all numerical analysis.
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Existence and Uniqueness of Periodic Solutions for a Class of Nonlinear Equations with p-Laplacian-Like Operators
Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Equivalent Solutions of Nonlinear Equations in a Topological Vector Space with a Wedge
It has been a great pleasure for me to have prepared the latest edition of my
book on nonlinear optics. My intrigue in the subject matter of this book is as
strong as it was when the first edition was published in 1992.
The principal changes present in the third edition are as follows: (1) The
book has been entirely rewritten using the SI system of units. I personally
prefer the elegance of the gaussian system of units, which was used in the first
two editions, but I realize that most readers would prefer the SI system, and
the change was made for this reason. (2) In...
Many mechanics and physics problems have variational formulations making them appropriate for numerical treatment by finite element techniques and efficient iterative methods. This book describes the mathematical background and reviews the techniques for solving problems, including those that require large computations such as transonic flows for compressible fluids and the Navier-Stokes equations for incompressible viscous fluids.
Computers are one of the most important tools in any field of science and
especially in physics. A student in an undergraduate lab will appreciate the
help of a computer in calculating a result from a series of measurements.
The more advanced researcher will use them for tasks like simulating an
experiment, or solving complex systems of equations. Physics is deeply
connected to mathematics and requires a lot of calculational skills. If one is
only interested in a conceptual understanding of the field, or an estimate of
the outcome of an experiment, simple calculus will probably suffice.
The emergence of a new paradigm in science offers vast perspectives for future
investigations, as well as providing fresh insight into existing areas of knowledge,
discovering hitherto unknown relations between them. We can observe
this kind of process in connection with the appearance of the concept of solitons
This article is concerned with local well-posedness of the Cauchy problem for second order quasilinear hyperbolic equations with rough initial data. The new results obtained here are sharp in low dimension. 1. Introduction 1.1. The results. We consider in this paper second order, nonlinear hyperbolic equations of the form (1.1) gij (u) ∂i ∂j u = q ij (u) ∂i u ∂j u
on R × Rn , with Cauchy data prescribed at time 0, (1.2) u(0, x) = u0 (x) , ∂0 u(0, x) = u1 (x) .
Nonlinearity, Bifurcation and Chaos - Theory and Application is an edited book focused on introducing both theoretical and application oriented approaches in science and engineering. It' contains 12 chapters, and is recommended for university teachers, scientists, researchers, engineers, as well as graduate and post-graduate students either working or interested in the field of nonlinearity, bifurcation and chaos.
Computational Physics is now a multidisciplinary line of research. A long time
ago, it was not like that, computers were used by physicists only in order to solve
classical problems resistant to the analytical approach: One is able to model the
problem at hands through, say, a set of coupled differential equations, but the
analytical solution for these equations is not available. The solace is the numerical
solution, and the old branch of Computational Physics consists in providing fast
and precise numerical methods to be applied to these cases....
This book contains the lectures given at the Centro Internazionale Matematico
Estivo (CIME), during the session Direct and Inverse Method in Non
Linear Evolution Equations, held at Cetraro in September 1999.
The lecturers were R. Conte of the Service de physique de l’´etat condens´e,
CEA Saclay, F. Magri of the University of Milan, M. Musette of Dienst
Theoretical Naturalness, Verite Universities Brussels, J. Satsuma of the Graduate
School of Mathematical Sciences, University of Tokyo and P. Winternitz
of the Centre de recherches math´ematiques, Universit´e de Montr´eal....
Wave-Equation Description of Nonlinear Optical Interactions
Các phương trình sóng cho truyền thông quang học phi tuyến
Chúng ta đã thấy trong chương cuối cùng như thế nào phi tuyến trong phản ứng của một hệ thống vật chất vào một lĩnh vực laser cường độ cao có thể gây ra sự phân cực của môi trường để phát triển các thành phần tần số mới không có mặt trong lĩnh vực bức xạ nhiệt.
The study of electromagnetic radiation (EM) can be divided into two distinct areas: full
solution of Maxwell's Equations relevant to the specific boundary conditions in a
special general case and into application of EM radiation that results in modern life
e.g. medicine, telecommunication, electromagnetic compatibility (EMC) etc. The
reader should have a specific scientific background and must be familiar with the
fundamental ideas of EM theory for the first area. Basic understanding of applying the
radiation techniques in modern life is needed for the second.
Basic properties of numbers Factors, multiples, and divisibility Prime numbers and prime factorization Exponents (powers) Exponents and the real number line Roots and radicals Roots and the real number line Linear equations with one variable Linear equations with two variables Linear equations that cannot be solved Factorable quadratic expressions with one variable The quadratic formula Nonlinear equations with two variables Solving algebraic inequalities Weighted average problems Currency problems Mixture problems Investment problems Problems of rate of production or work Problems of rate...
We now consider that most basic of tasks, solving equations numerically. While most equations are born with both a right-hand side and a left-hand side, one traditionally moves all terms to the left, leaving f(x) = 0 (9.0.1)
whose solution or solutions are desired. When there is only one
Hindawi Publishing Corporation Advances in Diﬀerence Equations Volume 2011, Article ID 154742, 10 pages doi:10.1155/2011/154742
Research Article On a Nonlinear Integral Equation with Contractive Perturbation
Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, China Correspondence should be addressed to Huan Zhu, firstname.lastname@example.org Received 19 December 2010; Accepted 19 February 2011 Academic Editor: Jin Liang Copyright q 2011 Huan Zhu.