Foundations of Abstract Analysis (Indian Ed)

The timeliness of a manuscript is more than its form, which may be unfinished or tentative. Thus, in some instances, proofs may be merely outlined and results presented which have been or will later be published elsewhere. If possible, a subject index should be included. Publication of Lecture Notes is intended as a service to the international mathematical community, in that a commercial publisher, Springer-Verlag, can offer a wide distribution of documents which would otherwise have a restricted readership. Once published and copyrighted, they can be documented in the scientific literature.

A good example is the proof that there is no projective plane of parameter 10. In that case the computations involved were not different in kind from those which have been done by human brains without electronic assistance; they were merely longer. Computers have also been useful in the study of combinatorial spec­ trum problems: if a class of design has certain parameters, what is the set of values that the parameters can realize? In many cases, there is a recursive construction, so that the existence of a small number of “starter” designs leads to the construction of infinite classes of designs, and computers have proven very useful in finding “starter” designs.

The authors discuss topics such as elasticity, thermo-elasticity, aero-elasticity, interactions between fluids and elastic structures, and fluid dynamics and the new challenges that they present. Other control theoretic problems include parabolic systems, dynamical Lame systems, linear and nonlinear hyperbolic equations, and pseudo-differential operators on a manifold. This is a valuable tool authored by international specialists in the field.

The book places the fundamental tenets of computer programming into the context of MATLAB, employing hands-on exercises, examples from the engineering industry, and a variety of core tools to increase programming proficiency and capability. With this knowledge, students are prepared to adapt learned concepts to other programming languages.

• Based on a decade’s worth of the authors lecture notes detailing the topic of applied mathematics for scientists and engineers
• Concisely writing with numerous examples provided including historical perspectives as well as a solutions manual for academic adopters