Step-by-Step BS to PhD Math/Physics
by Alex Alaniz
Publisher: UC Riverside 2013
Number of pages: 323
These are step-by-verifiable-step notes which are designed to help students with a year of calculus based physics who are about to enroll in ordinary differential equations go all the way to doctoral foundations in either mathematics and more so in physics with much reduced mystery. Abstract algebra, topology (local and global) folds into a useful, intuitive toolset for ordinary differential equations and partial differential equations, be they linear or nonlinear.
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by Roy McWeeny - Learning Development Institute
Contents: Linear vector spaces; Elements of tensor algebra; The tensor calculus (Volume elements, tensor densities, and volume integrals); Applications in Relativity Theory (Elements of special relativity, Tensor form of Maxwell's equations).
by Nikos Theodorakopoulos - Universitaet Konstanz
This set of lectures describes some of the basic concepts mainly from the angle of condensed matter / statistical mechanics, an area which provided an impressive list of nonlinearly governed phenomena over the last fifty years.
by Cathleen S. Morawetz - Tata Institute Of Fundamental Research
Introduction to certain aspects of gas dynamics concentrating on some of the most important nonlinear problems, important not only from the engineering or computational point of view but also because they offer great mathematical challenges.
by Solomon I. Khmelnik - MiC
In this book we formulate and prove the variational extremum principle for viscous incompressible and compressible fluid, from which principle follows that the Navier-Stokes equations represent the extremum conditions of a certain functional.