벡터의 기초 및 심화과정

제1부 벡터의 기초과정

1. 벡터 정의 ····································································································7

2. 벡터 연산 ····································································································7
2.1. 벡터의 합 ································································································ 7
2.2. 벡터의 뺄셈 ···························································································· 9
2.3. 힘의 벡터 합(2D) ·················································································· 10

3. 동일 평면에 작용하는 힘들의 합 (스칼라 표기법, 직교벡터 표기법) ········· 13
3.1. 스칼라 표기법 ······················································································ 13
3.2. 직교벡터 표기법 ··················································································· 14

4. 직교벡터(3차원, 3D) ················································································16

5. 위치벡터(r벡터) ························································································19

6. 벡터의 내적 ······························································································21
6.1. 직교성 / 수직성 ···················································································· 21
6.2. Cauchy-Schwarz 부등식 ··································································· 22

7. 벡터의 외적 ······························································································23

8. 벡터의 종합정리 ·······················································································24
8.1. 3차원 공간에서의 직선과 평면 ··························································· 24
8.2. 벡터 공간 ······························································································ 28

제2부 벡터의 심화과정

9. 벡터 해석(기초과정) ·················································································33
벡터 정리 ······································································································ 33

10. 벡터 해석(고급과정) ···············································································41
10.1. 벡터함수와 곡률 ················································································· 41
10.2. 벡터장과 기울기장 ············································································· 48
10.3. 선적분 ································································································· 53
10.4. Green의 정리 ····················································································· 55
10.5. 퍼텐셜 이론 / 경로의 독립성 ···························································· 56
10.6. 접평면과 면적분 ················································································· 57
10.7. Stokes 정리 ························································································ 61
10.8. Gauss 발산 정리 / Stokes 적분 정리 ··············································· 65