Mathematical Physics: The Basics

Preface / Coordinate Transformations, Vectors and Cartesian Tensors / Lorentz Transformation, 4-Vectors and 4-Tensors / Curvilinear Coordinates / Linear Vector Spaces – I / Linear Vector Spaces – II: Linear Operators / Complex Variables – I / Complex Variables – II / Complex Variables – III / Index

Mathematical Physics: The Basics is the first of the two-volume set on Mathematical Physics written for the postgraduate students (M. Sc./ Ph.D.) of Physics and Chemistry. Engineering students (BE/ME) will also find the book useful . This book covers the basic topics such as vectors and Cartesian tensors, vector calculus, Lorentz tensors, curvilinear coordinates, linear vector spaces and linear operators, eigenvalues and eigenvectors, matrix representations and diagonalization of matrices, complex variables, analytic functions, Taylor and Laurent series, contour integrals, residue theorem and applications, method of steepest descent, etc. The highlights of the book are • many solved problems, • a large number of exercises in each chapter, • connection with Physics elaborated, • concepts introduced and results elaborated intuitively, at the same time maintains rigor. Advanced topics including ordinary differential equations, gamma (factorial) and beta functions , Bessel functions, special functions and spherical harmonics, partial differential equation, generalized functions, the Dirac delta function, the Fourier transform, group theory, etc. are covered in the companion volume Mathematical Physics: Advanced Topics by the author (This will be ready by March 2005). Together these books will comprehensively cover all the aspects necessary for a postgraduate course in mathematical physics.