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Aimed at advanced undergraduates with background knowledge of
classical mechanics and electricity and magnetism, this textbook
presents both the particle dynamics relevant to general relativity,
and the field dynamics necessary to understand the theory. Focusing
on action extremization, the book develops the structure and
predictions of general relativity by analogy with familiar physical
systems. Topics ranging from classical field theory to minimal
surfaces and relativistic strings are covered in a homogeneous
manner. Nearly 150 exercises and numerous examples throughout the
textbook enable students to test their understanding of the
material covered. A tensor manipulation package to help students
overcome the computational challenge associated with general
relativity is available on a site hosted by the author. A link to
this and to a solutions manual can be found at
www.cambridge.org/9780521762458.
There is an increasing need for undergraduate students in physics
to have a core set of computational tools. Most problems in physics
benefit from numerical methods, and many of them resist analytical
solution altogether. This textbook presents numerical techniques
for solving familiar physical problems where a complete solution is
inaccessible using traditional mathematical methods. The numerical
techniques for solving the problems are clearly laid out, with a
focus on the logic and applicability of the method. The same
problems are revisited multiple times using different numerical
techniques, so readers can easily compare the methods. The book
features over 250 end-of-chapter exercises. A website hosted by the
author features a complete set of programs used to generate the
examples and figures, which can be used as a starting point for
further investigation. A link to this can be found at
www.cambridge.org/9781107034303.
Anchored in simple and familiar physics problems, the author
provides a focused introduction to mathematical methods in a
narrative driven and structured manner. Ordinary and partial
differential equation solving, linear algebra, vector calculus,
complex variables and numerical methods are all introduced and bear
relevance to a wide range of physical problems. Expanded and novel
applications of these methods highlight their utility in less
familiar areas, and advertise those areas that will become more
important as students continue. This highlights both the utility of
each method in progressing with problems of increasing complexity
while also allowing students to see how a simplified problem
becomes 're-complexified'. Advanced topics include nonlinear
partial differential equations, and relativistic and quantum
mechanical variants of problems like the harmonic oscillator.
Physics, mathematics and engineering students will find 300
problems treated in a sophisticated manner. The insights emerging
from Franklin's treatment make it a valuable teaching resource.
Classical field theory, which concerns the generation and
interaction of fields, is a logical precursor to quantum field
theory, and can be used to describe phenomena such as gravity and
electromagnetism. Written for advanced undergraduates, and
appropriate for graduate level classes, this book provides a
comprehensive introduction to field theories, with a focus on their
relativistic structural elements. Such structural notions enable a
deeper understanding of Maxwell's equations, which lie at the heart
of electromagnetism, and can also be applied to modern variants
such as Chern-Simons and Born-Infeld. The structure of field
theories and their physical predictions are illustrated with
compelling examples, making this book perfect as a text in a
dedicated field theory course, for self-study, or as a reference
for those interested in classical field theory, advanced
electromagnetism, or general relativity. Demonstrating a modern
approach to model building, this text is also ideal for students of
theoretical physics.
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