This section attempts to answer some of the questions you might formulate when you turn the first page: What does this toolbox do? Can I use it? What problems can I solve?, etc.
What Does this Toolbox Do?
The Partial Differential Equation (PDE) Toolbox provides a powerful and flexible environment for the study and solution of partial differential equations in two space dimensions and time. The equations are discretized by the Finite Element Method (FEM). The objectives of the PDE Toolbox are to provide you with tools that:
• Define a PDE problem, i.e.
A complete introduction to partial differential equations, this textbook provides a rigorous yet accessible guide to students in mathematics, physics and engineering. The presentation is lively and up to date, with particular emphasis on developing an appreciation of underlying mathematical theory. Beginning with basic deﬁnitions, properties and derivations of some fundamental equations of mathematical physics from basic principles, the book studies ﬁrst-order equat
This text is intended to provide an introduction to the standard methods that are used for the solution of first-order partial
differential equations. Some of these ideas are likely to be introduced, probably in a course on mathematical methods
during the second year of a degree programme with, perhaps, more detail in a third year. The material has been written
to provide a general – but broad – introduction to the relevant ideas, and not as a text closely linked to a specific module
or course of study. Indeed, the intention is to present the material so that it can be used as an...
n mathematics, an ordinary differential equation (abbreviated ODE) is an equation containing a function of one independent variable and its derivatives. There are many general forms an ODE can take, and these are classified in practice (see below). The derivatives are ordinary because partial derivatives only apply to functions of many independent variables (see Partial differential equation).
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.
Computational fluid dynamics (CFD) is concerned with the efficient numerical solution of the partial differential equations that describe fluid dynamics. CFD techniques are commonly used in the many areas of engineering where fluid behavior is an important factor. Traditional fields of application include aerospace and automotive design, and more recently, bioengineering and consumer and medical electronics.
The numerical treatment of partial differential equations is, by itself, a vast subject. Partial differential equations are at the heart of many, if not most, computer analyses or simulations of continuous physical systems, such as ﬂuids, electromagnetic ﬁelds, the human body, and so on.
Tuyển tập các báo cáo nghiên cứu về y học được đăng trên tạp chí y học quốc tế cung cấp cho các bạn kiến thức về ngành y đề tài: Modelling of oedemous limbs and venous ulcers using partial differential equations
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 Integral Inequality and Exponential Stability for Neutral Stochastic Partial Differential Equations with Delay
Finance is one of the fastest growing areas in the modern banking and corporate world. This, together with the sophistication of modern financial products, provides a rapidly growing impetus for new mathematical models and modern mathematical methods. Indeed, the area is an expanding source for novel and relevant "real-world" mathematics. In this book, the authors describe the modeling of financial derivative products from an applied mathematician's viewpoint, from modeling to analysis to elementary computation.
A differential equation is an ordinary differential equantion if the unknown function depends on only one independent variable. If the unknown function depends on two or moer indenpendent variable, the differential equation is a partial differential equation.
The goal of this book is to expose the reader to modern computational tools for
solving differential equation models that arise in chemical engineering, e.g.,
diffusion-reaction, mass-heat transfer, and fluid flow. The emphasis is placed
on the understanding and proper use of software packages. In each chapter we
outline numerical techniques that either illustrate a computational property of
interest or are the underlying methods of a computer package. At the close of
each chapter a survey of computer packages is accompanied by examples of
The three texts in this one cover, entitled ‘The series solution of second order, ordinary differential equations and special
functions’ (Part I), ‘An introduction to Sturm-Liouville theory’ (Part II) and ‘Integral transforms’ (Part III), are three of
the ‘Notebook’ series available as additional and background reading to students at Newcastle University (UK).
This book is based on lectures delivered over the years by the author at the
Universit´e Pierre et Marie Curie, Paris, at the University of Stuttgart, and at
City University of Hong Kong. Its two-fold aim is to give thorough introductions
to the basic theorems of differential geometry and to elasticity theory in
The treatment is essentially self-contained and proofs are complete.
Basic principles underlying the transactions of financial markets are tied to
probability and statistics. Accordingly it is natural that books devoted to
mathematical finance are dominated by stochastic methods. Only in recent
years, spurred by the enormous economical success of financial derivatives,
a need for sophisticated computational technology has developed. For example,
to price an American put, quantitative analysts have asked for the
numerical solution of a free-boundary partial differential equation.
Partial differential equations (PDEs) are very important in modelling as their solutions
unlock the secrets to a range of important phenomena in engineering and
physics. The PDE known as the wave equation models sound waves, light waves
and water waves. It arises in fields such as acoustics, electromagnetics and fluid