Course Summary

1. Properties of Vector Algebra, Vector space, subspace, basis, null and
   

2. range space, invertibility and matrix representation; Cartesian Tensor
   

3. notation and vector analysis; Matrices and Matrix algebra, Echelon
   

4. form, orthogonalization; Eigen values and eigenvectors of a linear
   

5. operator; First and second order ODEs, Linear Differential equations
   

6. with constant coefficients and equi dimensional equations; Second
   

7. order linear homogenous differential equations and their                    
   

8. solutions; Methods of Taylor and Frobenius, Laplace and Fourier
   

9. transforms, Fourier series; Legendre and Bessel functions; Sturm
   

10. Louville Problem; classification of PDEs; Analytical solution of linear
    

11. PDEs.