|
Week - 1 |
Matrices |
|
Week - 2 |
Linear systems of equations |
|
Week - 3 |
Rank of a matrix. Linear independence. Vector spaces |
|
Week - 4 |
Solutions of linear systems. Determinants |
|
Week - 5 |
Inverse of a matrix. Gauss-Jordan elimination. Vector spaces, inner product spaces, linear transformations |
|
Week - 6 |
Eigenvalues and eigenvectors |
|
Week - 7 |
Some applications of eigenvalue problems |
|
Week - 8 |
First-order differential equations: separable differential equations, exact differential equations. Integrating factor. Bernoulli equation |
|
Week - 9 |
Orthogonal trajectories of curves. Existence and uniqueness of solutions. Picard iteration |
|
Week - 10 |
Homogeneous linear equations of second order. Second order homogeneous equations with constant coefficients |
|
Week - 11 |
Differential operators. Euler-Cauchy equation |
|
Week - 12 |
Wronskian. Nonhomogeneous equations. Solution by undetermined coefficients. Solution by variation of parameters |
|
Week - 13 |
Higher order linear differential equations. Higher order homogeneous equations with constant coefficients. Higher order nonhomogeneous equations |
|
Week - 14 |
Systems of differential equations, phase plane, qualitive methods |