Mathematical Physics

Contents: Unit I: 1. Review of vector algebra. 2. Differentiation of vectors. 3. Integration of vectors. 4. Orthogonal curvilinear coordinates. 5. Double integrals. 6. Application of the double integrals. 7. Triple integration. 8. Application of triple integration. 9. Gamma, beta function. 10. Theory of errors. 11. Fourier series. Unit II: 12. Differential equations of first order. 13. Linear differential equations of second order. 14. Cauchy-euler equations, method of variation of parameters. 15. Differential equation of other types. 16. Coupled differential equations. 17. Applications to differential equations. 18. Calculus of variation. 19. Maxima and minima of functions (two variables). Unit III: 20. Complex numbers. 21. Expansion of trigonometric functions. 22. Functions of complex variable, analytic function. 23. Conformal transformation. 24. Complex integration. 25. Taylor's and Laurent's series. 26. The calculus of residues (integration). 27. Series solutions of second order differential equations. 28. Legendre's functions. 29. Bessel's functions. 30. Hermite function. 31. Laguerres functions. Unit IV: 32. Abstract vector spaces. 33. Vectors in RN. 4. Linear transformations. 35. Basis of null space, row space and column space. 36. Real inner product spaces. 37. Determinants. 38. Algebra of matrices. 39. Rank of matrix. 40. Consistency of linear system of equations and their solution (linear dependence). 41. Eigen values, eigen vector, cayley hamilton theorem, diagonalisation (complex and unitary matrices). 42. First order lagrange's linear and non-linear partial differential equations. 43. Linear and non-linear partial differential equations with constant coefficients of 2nd order. 44. Applications of partial differential equations. 45. Integral transforms. 46. Laplace transform. 47. Inverse laplace transforms (solution of differential equations). 48. Dirac-delta function. 49. Tensor analysis. "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 endeavour 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.…