講者：許永昌 老師 1

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

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

Basis vectors 4

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

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

Basis vectors (final) 7

Exercise Find {h i } for spherical coordinate. 8

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

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

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

Homework (2.3.1e) (2.3.3e) (2.3.6e) 12

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

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

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

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

Curl Main Concepts: If, we get 17

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

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.

Homework (2.4.2e) (2.4.3e) (2.4.4e) 20

Nouns 21