This textbook comprehensively introduces students and researchers to the application of continuous symmetries and their Lie algebras to ordinary and partial differential equations. Covering all the modern techniques in detail, it relates applications to cutting-edge research fields such as Yang-Mills theory and string theory.Aimed at readers in applied mathematics and physics rather than pure mathematics, the material is ideally suited to students and researchers whose main interest lies in finding solutions to differential equations and invariants of maps.A large number of worked examples...

Presents introductory and advanced topics in the field of computer graphics with mathematical descriptions and derivations. This book offers a balance of theory, applications, and code, and derives the underlying numerical methods and algorithms. It contains the classes in C# necessary for computer graphics, and offers an explanation of the code.

This work introduces computer graphics from a mathematical perspective, offering a balance of theory, applications, and code. The book begins with a discussion of basic graphics tools such as vectors, matrices, and quaternions, then builds up to more advanced topics such as the intersection of three-dimensional objects. Both classical and new topics are covered. Some topics discussed include basic transforms, curves, surfaces, and subdivision surfaces. New techniques such as wavelets, fractals, parameterization, and fluid simulation are also covered. Throughout a large portion of the book, a...

Offers various techniques and methods used in nonlinear dynamics. This book discusses the concepts and underlying mathematics. It contains more than 150 ready-to-run programs. It is intended for a one-year course at both the junior and senior levels in nonlinear dynamics.

Offers various techniques and methods used in nonlinear dynamics. This book discusses the concepts and underlying mathematics. It contains more than 150 ready-to-run programs. It is intended for a one-year course at both the junior and senior levels in nonlinear dynamics.

A collection of problems with detailed solutions which should be useful to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers should find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the...

A collection of problems with detailed solutions which should be useful to students and research workers in mathematics, physics, engineering and other sciences. The topics range in difficulty from elementary to advanced level. Almost all the problems are solved in detail and most of them are self-contained. All relevant definitions are given. Students can learn important principles and strategies required for problem solving. Teachers should find this text useful as a supplement, since important concepts and techniques are developed through the problems. The material has been tested in the...