대학 이공계 신입생을 위한 미분 적분학 과목에서는 변수가 한 개인 함수, 곧 일변수 함수의 미분과 적분을 다룬다. 이 책은 이런 과목을 이수한 학생들에게 변수가 두 개 이상인 함수, 곧 다변수 함수와 벡터 함수의 미분과 적분을 소개하기 위한 한 학기용 교재이다. 다변수 함수와 벡터 함수의 미분과 적분은 자연과학, 공학, 사회과학을 포함해서 많은 분야에서 널리 응용되고 있다. 이런 응용의 폭을 한정해서 제시하기 어렵고, 그 모든 내용을 이 책에 소개하는 것도 불가능하다. 이에 따라 이 책에서는 이공계 학문을 전공하는 데 필수적인 주제인 원기둥 좌표계, 구면 좌표계, 벡터, 벡터 함수와 곡선, 다변수 함수의 편미분과 그 응용, 다중 적분과 그 응용, 벡터 마당의 선 적분과 면적분,그린 정리, 스토크스 정리, 발산 정리 등을 다룬다. 그리고 각 주제와 관련된 기본적인 개념과 결과 및 간단한 응용을 소개한다. 일변수 함수의 미분과 적분을 배운 학생이면 누구나 이 책의 모든 내용을 큰 어려움 없이 이해할 수 있도록 본문의 내용은 상세하게 설명했고 많은 예제를 제시했으며, 직관적인 이해를 돕기 위해 적절한 그림도 충분히 넣었다. 몇 가지 중요한 정리에 대해서는 정확한 이해를 돕기 위해서 그 증명을 실었다. 부록에 행렬의 연산, 행렬식에 관한 기초 이론, 유용한 수학 공식 등을 실어서 학습에 참고할 수 있도록 했으며, 일부 연습문제의 해답 등을 실어서 풀이 결과를 확인할 수 있도록 했다.  -머리말 중에서-

제 1 장　벡터와 공간 기하 1

1.1 좌표 공간 ·································································································· 2

1.2 벡터 ·········································································································· 12

1.3 공간 기하 ································································································ 31

제 2 장　벡터 함수와 곡선 49

2.1 벡터 함수 ································································································ 50

2.2 곡선 ·········································································································· 57

제 3 장　다변수 함수 75

3.1 다변수 함수의 정의 ················································································ 76

3.2 다변수 함수의 극한과 연속 ··································································· 81

3.3 편도함수 ·································································································· 89

3.4 미분 가능한 함수와 전미분 ··································································· 98

3.5 연쇄 법칙 ······························································································ 109

3.6 물매와 방향 도함수 ·············································································· 121

3.7 다변수 함수의 극값 ·············································································· 131

3.8 다변수 벡터 함수 ···················································································143

제 4 장　다중 적분 155

4.1 이중 적분 ······························································································ 156

4.2 극 좌표계에서의 이중 적분 ································································· 175

4.3 삼중 적분 ······························································································ 187

4.4 치환 적분 ······························································································ 202

제 5 장　벡터 해석 209

5.1 벡터 마당과 선 적분 ············································································ 210

5.2 그린 정리 ······························································································ 235

5.3 면 적분 ·································································································· 245

5.4 스토크스 정리와 발산 정리 ································································· 255

부록 271

부록 A 행렬과 행렬식 ················································································ 272

부록 B 수학 공식과 평면 곡선 ·································································· 286

연습 문제 해답 309

찾아보기 331

김상목, 김영희, 김태균, 송영권, 이종우, 이진우, 이현근, 이호석, 이흥수, 최윤철, 최종성, 허민

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