1. 講者：許永昌 老師 1

2. Contents Preview of this Chapter 2. Basis used in a curved coordinate Distance Integrals Differential vector Operators 2

3. Preview of this Chapter Basis vectors Orthogonal Coordinates Integral & differential vector operators. Tensor (introduction) Pseudotensors, dual tensors 3

4. Basis vectors 4

5. q 1 =constant. q 2 =constant. q 3 =constant. Basis vectors (Continue) 5

6. Exercise If q 1 =x, q 2 =x+y, find out 畫出他們的等值線。 6

7. Basis vectors (final) 7

8. Exercise Find {h i } for spherical coordinate. 8

9. Some basic operations of vectors Vectors: V= Displacement: dr= Distance: ds 2 = 9

10. Some basic operations of vectors (Continue) Inner product: A  B= Cross product: A  B= 10

11. Integrals Line integral  V  dr= Surface integral Area element d  = 一般形式？ Volume integral Volume element d  = 11

12. Homework 2.1.1 (2.3.1e) 2.1.3 (2.3.3e) 2.1.6 (2.3.6e) 12

13. Gradient Main Concepts: df=dr  f df= We get 13

14. Exercise The  f in spherical coordinate. 先自行條列出基本概念。 14

15. Divergence Main Concepts: For orthonormal coordinate: 15 d1d1 d2d2

16. Exercise The  V in spherical coordinate. 先自行條列出基本概念。 16

17. Curl Main Concepts: If, we get 17

18. Exercise The curl V in Spherical Coordinate. 先自行條列出基本概念。 18

19. Stop to think Can we use: to find out  V and  V ? You can try to apply it for a cylindrical coordinate. 19 條件是：用的是 orthogonal basis.

20. Homework 2.2.2 (2.4.2e) 2.2.3 (2.4.3e) 2.2.4 (2.4.4e) 20

21. Nouns 21