Du 2

Nonlinear Functional Analysis and Its Applications, Part 2

Introduction to Engineering Mathematics Volume - II : For APJAKTU Lucknow

The book "Introduction to Engineering Mathematics II" has been conceptualized specifically according to the New Syllabus (2022 onwards) of A. P. J. Abdul Kalam Technical University (APJAKTU), Lucknow. It covers important topics such as Linear Differential Equations of nth Order with Constant Coefficients, Second Order Linear Differential Equations with Variable Coefficients, Method of Variation of Parameters, Cauchy-Euler Equation, Applications of Differential Equations in Solving Engineering Problems, Laplace Transform and Properties, Sequence and Series, Tests for Convergence of Series, Fourier Series, Functions of Complex Variable, Harmonic Function & Milne's Thompson Method, Conformal Mapping, Taylor's and Laurent's Series, Residue Theorem and Applications etc. for sound conceptual understanding of students. Latest Question papers have been solved and included in the book. Also, short questions have been added at the end of each chapter for better preparation of examinations.

General Relativity for Mathematicians

This is a book about physics, written for mathematicians. The readers we have in mind can be roughly described as those who: I. are mathematics graduate students with some knowledge of global differential geometry 2. have had the equivalent of freshman physics, and find popular accounts of astrophysics and cosmology interesting 3. appreciate mathematical elarity, but are willing to accept physical motiva tions for the mathematics in place of mathematical ones 4. are willing to spend time and effort mastering certain technical details, such as those in Section 1. 1. Each book disappoints so me readers. This one will disappoint: 1. physicists who want to use this book as a first course on differential geometry 2. mathematicians who think Lorentzian manifolds are wholly similar to Riemannian ones, or that, given a sufficiently good mathematical back ground, the essentials of a subject !ike cosmology can be learned without so me hard work on boring detaiis 3. those who believe vague philosophical arguments have more than historical and heuristic significance, that general relativity should somehow be "proved," or that axiomatization of this subject is useful 4. those who want an encyclopedic treatment (the books by Hawking-Ellis [1], Penrose [1], Weinberg [1], and Misner-Thorne-Wheeler [I] go further into the subject than we do; see also the survey article, Sachs-Wu [1]). 5. mathematicians who want to learn quantum physics or unified fieId theory (unfortunateIy, quantum physics texts all seem either to be for physicists, or merely concerned with formaI mathematics).