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Provides a complete overview of the concept of symmetries in applied mathematics, engineering and especially mechanics
Intended for graduate and PhD students willing to discover the interest of symmetries, but also for researchers willing to apply modern and new symmetry techniques or to efficiently solve boundary value problems in engineering
Written by experts in the field
The principle aim of the book is to present a self-contained, modern account of similarity and symmetry methods, which are important mathematical tools for both physicists, engineers and applied mathematicians. The idea is to provide a balanced presentation of the mathematical techniques and applications of symmetry methods in mathematics, physics and engineering.
That is why it includes recent developments and many examples in finding systematically conservation laws, local and nonlocal symmetries for ordinary and partial differential equations.
The role of continuous symmetries in classical and quantum field theories is exposed at a technical level accessible even for non specialists. The importance of symmetries in continuum mechanics and mechanics of materials is highlighted through recent developments, such as the construction of constitutive models for various materials combining Lie symmetries with experimental data.
As a whole this book is a unique collection of contributions from experts in the field, including specialists in the mathematical treatment of symmetries, researchers using symmetries from a fundamental, applied or numerical viewpoint.
The book is a fascinating overview of symmetry methods aimed for graduate students in physics, mathematics and engineering, as well as researchers either willing to enter in the field or to capture recent developments and applications of symmetry methods in different scientific fields.
Content Level »Research
Keywords »Conservation Laws - Constitutive Modeling and Symmetries - Continuous Symmetries - Geometric Mechanics - LagrangianMechanics, Field Theories and Symmetries - Similarity Methods - Solution Methods for ODE’s and PDE’s