The Book Is Intended As A Text For Students Of Physics At The Master S Level. It Is Assumed That The Students Pursuing The Course Have Some Knowledge Of Differential Equations And Complex Variables. In Addition, A Knowledge Of Physics Upto At Least The B.Sc. (Honours) Level Is Assumed. Throughout The Book The Applications Of The Mathematical Techniques Developed, To Physics Are Emphasized. Examples Are, To A Large Extent, Drawn From Various Branches Of Physics. The Exercises Provide Further Extensions To Such Applications And Are Often ``Chosen`` To Illustrate And Supplement The Material In The Text. They Thus Form An Essential Part Of The TextDistinguishing Features Of The Book: * Emphasis On Applications To Physics. The Examples And Problems Are Chosen With This Aspect In Mind. * More Than One Hundred Solved Examples And A Large Collection Of Problems In The Exercises. * A Discussion On Non-Linear Differential Equations-A Topic Usually Not Found In Standard Texts. There Is Also A Section Devoted To Systems Of Linear, First Order Differential Equations. * One Full Chapter On Linear Vector Spaces And Matrices. This Chapter Is Essential For The Understanding Of The Mathematical Foundations Of Quantum Mechanics And The Material Can Be Used In A Course Of Quantum Mechanics. * Parts Of Chapter-6 (Greens Function) Will Be Useful In Courses On Electrodynamics And Quantum Mechanics. * One Complete Chapter Is Devoted To Group Theory Within Special Emphasis On The Applications In Physics. The Subject Matter Is Treated In Fairly Great Detail And Can Be Used In A Course On Group Theory.
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analytic arbitrary axes basis Bessel functions Bessel's equation boundary conditions boundary value problem Cauchy-Riemann conditions commute complex numbers consider constant contour converges corresponding critical point curve defined definition denoted eigen functions eigen values eigen vectors evaluate Example finite Fourier transform given Green's function group Q Helmholtz equation Hermitian operator identity element inside integrand interval inverse irreducible representations known Laplace transform Laplace's equation Legendre equation Legendre polynomials linear operator linear vector space linearly independent linearly independent solutions mapping multiplication obtained orthogonal orthonormal physical potential prove quantum mechanics radius recurrence relations regular singular point residue right hand side rotation satisfies the boundary scalar product Similarly sin2 spherical polar coordinates subgroup Substituting surface symmetry group tensor of rank theorem tion unitary matrix variable vector space z-plane zero