1. ECE 305 Electromagnetic Theory
Fall 2016
ECE 305 Electromagnetic Theory
Lecture 3: Chapter 3
Qiliang Li
Dept. of Electrical and Computer Engineering, George Mason University, Fairfax, VA

2. 3 Vector Calculus (Chapter 3 in the book)
3.1 Introduction
3.2 Differential length, area and volume
A. Cartesian coordinate system

3. It is a vector

5. B.

7. C.

8. FIGURE 3.6 Differential normal surface areas in spherical coordinates: (a) dS = r2 sin θ dθ dɸ ar , (b) dS = r sin θ dr dɸ aθ, (c) dS = r dr dθ aɸ.

9. E.g. 3.1 Solve: Obviously, it is easier to solve it
in cylindrical coordinate

10. (note: for (b), what happen if you choose Cartesian coordinates?)

12. 3.3 Line, surface and volume integrals

13. Surface integral (or the flux of A through S)

15. E.g. 3.2

16. 3.4 Del Operator
Cylindrical Coordinate
Spherical Coordinate

17. - The gradient of a scalar field V is a vector
dl is differential displacement from P1 to P2 (see Fig. 3.13)

19. In the three coordinate systems

20. 3.6 Divergence of a Vector and Divergence Theorem

21. Divergence of a Vector in 3 coordinate systems
Note:

22. Divergence Theorem
E.g. 3.6

23. (E.g. 3.6)

24. 3.7 Curl of a Vector and Stokes’s Theorem

25. Cylindrical coordinate
Spherical coordinate

26. Note: Stokes’s Theorem

27. 3.8 Laplacian of a Scalar