This book provides an introduction to Hilbert space theory, Fourier transform and wavelets, linear operators, generalized functions and quantum mechanics. Although quantum mechanics has been developed between 1925 and 1930 in the last twenty years a large number of new aspect and techniques have been introduced. The book also covers these new fields in quantum mechanics. In quantum mechanics the basic mathematical tools are the theory of Hilbert spaces, the theory of linear operators, the theory of generalized functions and Lebesgue inte gration theory. Many excellent textbooks have been...

Dieses Lehrbuch bietet eine grundlegende Einfuhrung in chaotische Systeme, welche keinerlei Abstriche an mathematischer Exaktheit macht. Der Text umfasst einerseits in ansprechender Tiefe die klassischen theoretischen Gesichtspunkte der dynamischen Systeme, wobei alle wesentlichen Beispiele der Literatur ausuhrlich behandelt werden. Daneben befasst er sich mit moderneren Fragestellungen, wie etwa nach der Natur der Berechenbarkeit oder der Verlasslichkeit des Computers. Die Abgrenzung zu fortgeschrittenen Methoden ist klar gegeben durch den Ausschluss statistischer Methoden.

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Solving problems in quantum mechanics is an essential skill and research activity for scientists, engineers and others. Nowadays, the labour of scientific computation has been greatly eased by the advent of computer algebra packages. These do not merely perform number-crunching, but enable users to manipulate algebraic expressions and equations symbolically. For example, differentiation and integration can now be carried out algebraically by the computer. This book collects standard and advanced methods in quantum mechanics and implements them using REDUCE, a popular computer algebra package....

This work offers an introduction to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. It should be suitable for students and research workers whose main interest lies in finding solutions to differential equations. It therefore caters for readers primarily interested in applied mathematics and physics rather than pure mathematics. The book provides an application-orientated text that is self-contained. Worked examples have been included to help readers working independently of a teacher.

The Kronecker product of matrices plays a central role in mathematics and in applications found in engineering and theoretical physics. These applications are signal processing, statistical physics, quantum groups and quantum computers. This book provides a comprehensive introduction to the Kronecker product of matrices together with its software implementation in C++ using an object-oriented design.

This book provides all the techniques and methods used in nonlinear dynamics. All the concepts are discussed in detail. The numerical and symbolic methods are implemented using C++, Java, Symbolic C++ and Reduce.

This book provides all the techniques and methods used in nonlinear dynamics. All the concepts are discussed in detail. The numerical and symbolic methods are implemented using C++, Java, Symbolic C++ and Reduce.

Object-oriented programming has been the most dramatic innovation in software development in the last decade. It offers a powerful way to cope with the complexity of programs. C++ is by far the most popular object-oriented language.

This book gives a complete introduction to C++ and object-oriented programming. Additionally, it provides a large collection of C++ programs which are useful in finance, administration and statistics. The book contains more than 20 fully developed classes and more than 200 ready-to-run programs. The Standard Template Library is also included.

The study of nonlinear dynamical systems has advanced tremendously in the last 15 years, making a big impact on science and technology. This book provides all the techniques and methods used in nonlinear dynamics. The concepts and underlying mathematics are discussed in detail. The numerical and symbolic methods are implemented in C++, SymbolicC++ and Java. Object-oriented techniques are also applied. The book contains more than 100 ready-to-run programs. The text has also been designed for a one-year course at both the junior and senior levels in nonlinear dynamics. The topics discussed in...

Quantum computing and quantum information are two of the fastest-growing and most exciting research areas in physics. The possibilities of using non-local behaviour of quantum mechanics to factorize integers in random polynomial time have added to this new interest. This invaluable book provides a collection of problems in quantum computing and quantum information together with detailed solutions. It consists of two parts: in the first part finite-dimensional systems are considered, while the second part deals with finite-dimensional systems. All the important concepts and topics are...