Mathematical Physics

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
34. 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