벡터의 기초 및 심화과정 > 공학

이 책은 벡터의 정의, 연산, 표기법, 직교벡터, 위치벡터, 벡터의 내적과 외적, 종합정리 등을 포함한 벡터의 기초과정과 벡터 해석을 다룬 벡터의 심화과정으로 구성되어 있다.

목차

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

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