Bøger i Chapman & Hall/CRC Applied Mathematics & Nonlinear Science serien

Offers an account of a rudimentary core of theoretical results that should be understood by those studying evolution equations. This text gradually builds readers' intuition and the material culminates in a discussion of an area of active research. It sets the stage for the next step of theoretical development, allowing you to see the big picture.

Presents the developments in differential quadrature methods for applied mathematics, computational mechanics and engineering.

Mathematical Methods in Physics and Engineering with Mathematica clearly demonstrates how to use Mathematica 4.x to solve difficult problems involving ordinary and partial differential equations and boundary value problems. Avoiding mathematical theorems and numerical methods and requiring no prior experience with the software, the author helps readers learn by doing with step-by-step recipes useful in both new and classical applications. The author's clear explanations of each Mathematica command along with a wealth of examples and exercises make this book an outstanding choice. Mathematica and FORTRAN codes used in the book's examples and exercises are available for download from the Internet.

With many examples and exercises, this book describes the control behavior of mechanical objects like wave equations, plates, and shells. It presents a complete and updated account of important advances in modeling and control of vibrational and structural dynamics. It also applies the differential geometric approach to waves, plates, shells, etc.

A Shock-Fitting Primer presents the proper numerical treatment of shock waves and other discontinuities. It comprehensively covers various shock-fitting techniques and describes the historical path that has led to the accepted theory of shock waves. The author introduces key techniques using a simple scalar equation and then ext

This text provides an introductory understanding of stochastic evolution equations for those with minimal formal training in mathematics. It develops all necessary prerequisite material in real analysis, probability theory, and functional analysis. The author presents examples of 20 different models spanning chemical kinetics, pharmacokinetics, neural networks, mathematical physics, epidemiology, environmental issues, and more. He also covers recent research areas, including functional and Sobolev-type stochastic evolution equations. More than 500 questions and exercises are included throughout, with hints at the end of each chapter.

Presents many approaches to solve a range of engineering problems. This book develops underlying approximation theory from first principles, building a foundation on which modern approximation methods can be broadly formulated. It compares competing solutions of benchmark problems to provide a qualitative appreciation of several approaches.

Updated throughout, this second edition of a bestseller illustrates the usefulness of PDEs through numerous applications and helps students appreciate the beauty of the underlying mathematics. It shows students how PDEs can model diverse problems, including the flow of heat, the propagation of sound waves, the spread of algae along the ocean¿s surface, the fluctuation in the price of a stock option, and the quantum mechanical behavior of a hydrogen atom. The text also contains many exercises, including standard ones and graphical problems using MATLAB®.

This book presents a deep, wide-ranging introduction to the mathematical theory of the optimal control of processes governed by ODEs and certain types of differential equations with memory. Many examples illustrate the mathematical issues that need to be addressed when using optimal control techniques in diverse areas. By providing a sufficient and rigorous treatment of finite dimensional control problems, the book equips readers with the foundation to deal with other types of control problems, such as those governed by stochastic differential equations, PDEs, and differential games.

This book illustrates the usefulness of estimation in engineering and science. It uses dynamic models to provide immediate results of estimation concepts with minimal reliance on mathematics. This second edition discusses a number of new topics, including higher order nonlinear filters, inertial navigation, and nonlinear stochastic processes. The authors cover prototype algorithms to stimulate the development and intelligent use of efficient computer programs. MATLAB is used throughout, with the code on a supporting website. In the appendices, the authors review statistics, optimization, probability, and matrix analysis.

This text provides an introductory understanding of stochastic evolution equations for those with minimal formal training in mathematics. It develops all necessary prerequisite material in real analysis, probability theory, and functional analysis. The author presents examples of 20 different models spanning chemical kinetics, pharmacokinetics, neural networks, mathematical physics, epidemiology, environmental issues, and more. He also covers recent research areas, including functional and Sobolev-type stochastic evolution equations. More than 500 questions and exercises are included throughout, with hints at the end of each chapter.

This self-contained text provides a sufficient theoretical basis to understand Green¿s function method, which is used to solve initial and boundary value problems involving linear ODEs and PDEs. It presents a variety of approaches, including classical and general variations of parameters, Wronskian method, Bernoulli¿s separation method, integral transform method, method of images, conformal mapping method, and interpolation method. The text also covers applications of Green¿s functions and contains numerous examples and exercises from diverse areas of mathematics, applied science, and engineering.

Demonstrates how to use Mathematica 4.x to solve difficult problems involving ordinary and partial differential equations and boundary value problems. This book helps readers learn by doing with step-by-step recipes useful in both new and classical applications. It includes explanations of various Mathematica commands with examples and exercises.

Part of a series on hp-adaptive finite elements, this book describes 1D and 2D finite element codes and automatic hp-adaptivity strategies that are designed to deliver meshes in the full range of error levels. It considers standard 1D elliptic problems and a 1D wave propagation problem.

Offers training in the analytic theory and rigorous design of fuzzy systems. This work provides guidance on designing and analyzing fuzzy intelligent and control systems. It explains fuzzy sets, fuzzy logic, fuzzy inference, approximate reasoning, fuzzy rule base and basic fuzzy PID control systems.

Presents the theoretical foundations of the 3D hp algorithm and provides numerical results using the 3Dhp code. Focusing on the 3D theory of hp methods as well as coding issues, this book also presents the 3D version of the automatic hp-adaptivity package, and a two-grid solver for highly anisotropic hp meshes and goal-oriented Krylov iterations.

A reference on nonlinear second-order parabolic partial differential equations that are used as models to help solve a broad class of engineering and physical problems. It uses analytical ideas that are geometric as opposed to super-sub solution methods that have limited application in the physical world.