Mathmetical Physics (Paperback)

PREFACE
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I have once again availed the opportunity of revising this work, designed to suit the requirements of students of Applied Mathematics, Physics and Technical courses at both. undergraduate and postgraduate levels. In the Third Edition, as required by the UGC syllabus as well as syllabi of several other universities of India many topics such as Conformal Mapping in Complex Analysis, Inversion of Complex Matrices, Error Functions, Factorial Functions, etc., and specially the solution of Schroedinger's Wave- equation in Quantum Mechanics, had been added. However a need was still felt to add some more useful topics to enhance the utility of the work, without going into competitive spirit to make it bulky as done at the primary levels, where there is almost a kind of competition to make the schoolbag heavier by putting into it, even bricks or rough and tough materials taken from any corner, without thinking whether the fabricated material matches the needs of the reader who may be an ordinary student or a researcher i.e., if the author himself is competant enough to undergo the research work.
In the present revised work, I have mainly touched upon the following topics for new additions and alterations:
(i) In Vectors: Transformation of Coordinates of a vector on a change of bases, Rankine's Theorem, Helmholtz Theorem (i.e., rigorous proof) and a few problems.
(ii) In Matrices: A criterion on Solutions of Simultaneous Equations, some more methods of Matrix Inversion, other elegant methods of matrix-inversion along with the general eigenvalue problem and a few problems.
(iii) In Tensors: Einstein Gravitational Equation and Equation of Planetary Orbits. (iv) In Complex Analysis: Natural Boundary Theorem (Lambert's Series), a new article on Convergence of Integrals, Series and Products along with uniform and Absolute Convergence, and a few problems.
(vi) In Differential Equations: Euler's Method with modifications, Taylor's Series Method and Runge's Method for solving First Order Differential Equations. (vii) In Harmonics: Some alternative approaches, Weber Bessel Functions, Neuman- Bessel Functions, Weber-Schlafli Functions, Lommet Theorem, Kelvin's Functions, Various Transformations, alternative solutions to Hermite Equation, other form of Hermite Polynomial along with Integral representation, Explanatory note on Integral Property of Laguerre Polynomials, altier to…