Module-5

 

1. Vectors –

2. Unit vector,

3. collinear vectors,

4. coplanar vectors,

5. like and unlike vectors,

6. orthogonal triads

7. (i, j, k) Dot product,

8. cross product- properties.

9. Vector differentiation-

   1. unit tangent vector,

   2. unit normal vector,

10. curvature,

11. torsion,

12. vector fields,

13. scalar fields,

14. gradient divergence,

15. curl,

16. directional derivatives.

17. Vector Integration –

    1. Line Integrals,

    2. conservative fields,

    3. Green’s Theorem,

    4. Surface Integrals,

    5. Stoke’s Theorem,

    6. Divergence Theorem.

18. Differential Equations –

    1. Order and degree of differential equations.

    2. First order differential equations-

    3. solution of Linear equations,

    4. separable equations and exact equations.

19. Second order differential equations-

    1. Solution of homogeneous equations with constant coefficients –

20. various types non-homogeneous equations,

21. solutions by undetermined coefficients.