벡터의 기초 및 심화과정

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

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