Vector calculus

1. Vector Calculus

2. Cartesian Coordinates
● Vector:

3. Cylindrical Coordinates
● Vector:

4. Spherical Coordinates
● Vector:

5. Differential Length, Area, and
Volume

6. Cartesian

7. Cylindrical

8. Cylindrical

9. Spherical

10. Spherical

11. Line, Surface, and Volume Integrals

12. Drills

13. Ans

14. Drill
● Determine the total surface area enclosing a
cylinder.
● Determine the total surface area enclosing a
sphere.

15. Ordinary Derivative of Vectors
Let R(u) be a vector depending on a scalar variable u.

16. Ordinary Derivative of Vectors
Let R(u) be a vector depending on a scalar variable u.

17. Differentiation Formulas

18. Differentiation Formulas

19. Applications

20. Streamlines and Sketches of
Fields
Streamlines (flux lines or direction lines) are
short line segments drawn with arrows
pointing in the direction of E and the
spacing of lines is inversely proportional to
the strength of the field.

21. Streamlines and Sketches of
Fields

22. Illustration: Like charges

23. Illustration: Opposite Charges

24. Equation of Streamlines

25. Example
Consider the vector field
Find the equation of one particular
streamline passing through P(-2,7,10).

26. Example
Ans. y = -3.5x

27. Drill 2.7
Find the equation of the streamline that
passes through the point P(1,4,-2) in the
field E=: (a) -8x/y ax + 4x2/y2 ay;

28. Drill 2.7
Find the equation of the streamline that
passes through the point P(1,4,-2) in the
field E=: (a) -8x/y ax + 4x2/y2 ay;
Ans. x2 + 2y2 = 33 ;

29. END