Lagrangian

Different Faces of Geometry - edited by the world renowned geometers S. Donaldson, Ya. Eliashberg, and M. Gromov - presents the current state, new results, original ideas and open questions from the following important topics in modern geometry:

Advanced Quantum Mechanics: Materials and Photons is a textbook which emphasizes the importance of advanced quantum mechanics for materials science and all experimental techniques which employ photon absorption, emission, or scattering.

The present book contains chapters devoted to numerical models, experimental tools/results and conceptual aspects of fluid dynamics.

The objective of this monograph is to present some methodological foundations of theoretical mechanics that are recommendable to graduate students prior to, or jointly with, the study of more advanced topics such as statistical mechanics, thermodynamics, and elementary particle physics. A program of this nature is inevitably centered on the methodological foundations for Newtonian systems, with particular reference to the central equations of our theories, that is, Lagrange's and Hamilton's equations. This program, realized through a study of the analytic representations in terms of Lagrange's and Hamilton's equations of generally nonconservative Newtonian systems (namely, systems with Newtonian forces not necessarily derivable from a potential function), falls within the context of the so-called Inverse Problem, and consists of three major aspects: I. The study of the necessary and sufficient conditions for the existence of a Lagrangian or Hamiltonian representation of given equations of motion with arbitrary forces; 1. The identification of the methods for the construction of a Lagrangian or Hamiltonian from the given equations of motion; and 3. The analysis of the significance of the underlying methodology for other aspects of Newtonian Mechanics, e. g. , transformation theory, symmetries, and first integrals for nonconservative Newtonian systems. This first volume is devoted to the foundations of the Inverse Problem, with particular reference to aspects I and 2.

Authors: Nolting, Wolfgang
Targets deeper understanding of Hamilton and Lagrangian mechanics, giving a sturdy base for understanding quantum mechanics in later semesters
Offers a tried-and-tested approach reflecting the author's 40 years of teaching experience
Belongs to a multi-volume introduction to theoretical physics, in which one renowned textbook author covers the complete curriculum
Offers detailed explanations of the solutions to numerous problems

Authors: Helrich, Carl S.
Leaps directly into the variational approach, bypassing the Newtonian approach entirely, making this book stand out from its competitors
Applies a unique approach to teaching mechanics to advanced undergraduates with Lagrangian and Hamiltonian method that is far superior to that of Newton
Contains numerous exercises with concise solutions in the text and very detailed solutions in the manual

The book presents a state-of-the-art overview of current developments in the field in a way accessible to attendees coming from a variety of fields. Relevant examples are turbulence research, (environmental) fluid mechanics, lake hydrodynamics and atmospheric physics.