Mathematical Physics

Product Description

“Mathematical Physics” has been written to provide the readers a clear understanding of the mathematical concepts which are an important part of modern physics.

The textbook contains 49 chapters on all major topics in an exhaustive endeavor to cover syllabuses of all major universities.

Some of the important topics covered in these chapters are Vectors, Integration, Beta and Gamma functions, Differential Equations, Complex Numbers, Matrix and Determinants and the Laplace transforms.

Key Features :

• • Comprehensive: Coverage to cater to syllabuses of major universities.
• • On the Website: One will find solved question papers of 2016 and 2017 along with useful formulae for easy download.
• • Student friendly: In the way that the text goes in depth of the subject with as many as 49 chapters which contain over 1600 examples and over 225 exercise sets.

Table of Content :

Unit-I

• • Review of Vector Algebra
• • Differentiation of Vectors
• • Integration of Vectors
• • Orthogonal Curvilinear Coordinates
• • Double Integrals
• • Application of the Double Integrals
• • Triple Integration
• • Application of Triple Integration
• • Gamma, Beta Function
• • Theory of Errors
• • Fourier Series

Unit-II

• • Differential Equations of First Order
• • Linear Differential Equations of Second Order
• • Cauchy-Euler Equations, Method of Variation of Parameters
• • Differential Equation of other Types
• • Coupled Differential Equations
• • Applications to Differential Equations
• • Calculus of Variation
• • Maxima and Minima of Functions (Two Variables)

Unit-III

• • Complex Numbers
• • Expansion of Trigonometric Functions
• • Functions of Complex Variable, Analytic Function
• • Conformal Transformation
• • Complex Integration
• • Taylor’s and Laurent’s Series
• • The Calculus of Residues (Integration)
• • Series Solutions of Second Order Differential Equations
• • Legendre’s Functions
• • Bessel’s Functions
• • Hermite Function
• • Laguerres Functions

Unit-IV

• • Abstract Vector Spaces ]
• • Vectors in Rn
• • Linear Transformations
• • Basis of Null Space, Row Space and Column Space
• • Real Inner Product Spaces
• • Determinants
• • Algebra of Matrices
• • Rank of Matrix
• • Consistency of Linear System of Equations and their Solution (Linear Dependence)
• • Eigen Values, Eigen Vector, Cayley Hamilton Theorem, Diagonalisation (Complex and Unitary Matrices)
• • First Order Lagrange’s Linear and Non-Linear Partial Differential Equations
• • Linear and Non-linear Partial Differential Equations with Constant Coefficients of 2nd Order
• • Applications of Partial Differential Equations
• • Integral Transforms
• • Laplace Transform
• • Inverse Laplace Transforms (Solution of Differential Equations)
• • Dirac-Delta Function
• • Tensor Analysis.