Topics not usually found in books at this level include but examined in this text: 
<li>the application of linear and nonlinear first-order PDEs to the evolution of population densities and to traffic shocks 
</li>
<li>convergence of numerical solutions of PDEs and implementation on a computer 
</li>
<li>convergence of Laplace series on spheres 
</li>
<li>quantum mechanics of the hydrogen atom 
</li>
<li>solving PDEs on manifolds The text requires some knowledge of calculus but none on differential equations or linear algebra.</li>

Basic Partial Differential Equations

Science & Math

David Bleecker

George Csordas

Mathematics

Chapman and Hall/CRC

This text provides a framework for describing and organizing the basic forces of nature and the interactions of subatomic particles. A detailed and self-contained mathematical account of gauge theory, it is geared toward beginning graduate students and advanced undergraduates in mathematics and physics. This well-organized treatment supplements its rigor with intuitive ideas. Starting with an examination of principal fiber bundles and connections, the text explores curvature; particle fields, Lagrangians, and gauge invariance; Lagrange's equation for particle fields; and the inhomogeneous field equation. Additional topics include free Dirac electron fields; interactions; calculus on frame bundle; and unification of gauge fields and gravitation. The text concludes with references, a selected bibliography, an index of notation, and a general index.

Gauge Theory and Variational Principles (Dover Books on Physics)

Dover Publications

Quantities which depend on space and/or time variables are often governed by differential equations which are based on underlying physical principles. Partial differential equations (PDEs) not only accurately express these principles, but also help to predict the behavior of a system from an initial state of the system and from given external influences. Thus, it is hard to overestimate the relevance of PDEs in all forms of science and engineering, or any endeavor which involves reasonably smooth, predictable changes of measurable quantities. Having taught from the material in this book for ten years with much feedback from students, we have found that the book serves as a very readable introduction to the subject for undergraduates with a year and a half of calculus, but not necessarily any more. In particular, one need not have had a linear algebra course or even a course in ordinary differential equations to understand the material. As the title suggests, we have concentrated only on what we feel are the absolutely essential aspects of the subject, and there are some crucial topics such as systems of PDEs which we only touch on. Yet the book certainly contains more material than can be covered in a single semester, even with an exceptional class. Given the broad relevance of the subject, we suspect that a demand for a second semester surely exists, but has been largely unmet, partly due to the lack of books which take the time and space to be readable by sophomores.

Springer

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Books by David Bleecker

See the best price to sell, buy, or rent books by David Bleecker. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Basic Partial Differential Equations

Gauge Theory and Variational Principles (Dover Books on Physics)

Basic Partial Differential Equations