1 함수와 극한 / 1 1.1 함수와 그 표현 ······················································1 1.2 필수적인 함수 목록 ··············································11 1.3 함수의 극한 ···························································26 1.4 극한 셈 ···································································38 1.5 연속 ········································································49 1.6 무한대와 관련된 극한 ··········································61 1 복습 ············································································75 2 도함수 / 79 2.1 미분 계수와 변화율 ·············································79 2.2 도함수 ····································································90 2.3 기본적인 미분법 ···················································102 2.4 곱과 몫의 미분법 ··················································114 2.5 연쇄 법칙 ·······························································122 2.6 음함수의 미분법 ···················································131 2.7 서로 관련된 변화율 ··············································137 2.8 선형 근사와 미분 ··················································144 2 복습 ············································································150 3 역함수: 지수․로그․역삼각 함수 / 155 3.1 지수 함수 ·······························································155 3.2 역함수와 로그 ·······················································161 3.3 로그 함수와 지수 함수의 도함수 ·······················174 3.4 지수적 증가와 감소 ··············································182 3.5 역삼각 함수 ···························································190 3.6 쌍곡선 함수 ···························································196 3.7 부정형과 로피탈의 법칙 ······································203 3 복습 ············································································211 4 미분의 활용 / 215 4.1 최댓값과 최솟값 ···················································215 4.2 평균값 정리 ···························································223 4.3 도함수와 그래프의 모양 ······································230 4.4 곡선 그리기 ···························································239 4.5 최적화 문제 ···························································247 4.6 뉴턴의 방법 ···························································259 4.7 역도함수 ································································265 4 복습 ···········································································272 5 적분 / 276 5.1 넓이와 거리 ··························································276 5.2 정 적분 ··································································289 5.3 정 적분의 값 찾기 ···············································303 5.4 미적분학의 기본 정리 ·········································314 5.5 치환 적분법 ··························································324 5 복습 ···········································································332 |
6 적분의 기법 / 336 6.1 부분 적분법 ··························································336 6.2 삼각 적분과 삼각 치환 ·······································343 6.3 부분 분수 ······························································354 6.4 적분표와 컴퓨터 대수 체계 ·······························362 6.5 근사 적분 ······························································368 6.6 특이 적분 ······························································382 6 복습 ···········································································392 7 적분의 활용 / 396 7.1 곡선 사이의 넓이 ·················································396 7.2 부피 ·······································································402 7.3 기둥 껍질에 의한 부피 ·······································413 7.4 호의 길이 ······························································419 7.5 회전면의 넓이 ······················································427 7.6 물리학과 공학에의 활용 ·····································432 7.7 미분 방정식 ··························································447 7 복습 ···········································································458 8 급수 / 462 8.1 수열 ·······································································462 8.2 급수 ·······································································473 8.3 적분 판정법과 비교 판정법 ·······························485 8.4 다른 수렴 판정법 ················································494 8.5 거듭제곱 급수 ·····················································505 8.6 거듭제곱 급수에 의한 함수의 표현 ·················511 8.7 테일러 급수와 매클로린 급수 ··························518 8.8 테일러 다항 함수의 활용 ··································532 8 복습 ·········································································540 9 매개 방정식과 극 좌표 / 545 9.1 매개 곡선 ····························································545 9.2 매개 곡선의 미분과 적분 ·································552 9.3 극 좌표 ································································560 9.4 극 좌표에서의 넓이와 길이 ·····························570 9.5 극 좌표에서의 원뿔 곡선 ·································575 9 복습 ········································································581 부록 / A1 A 삼각법 ···································································A1 B 합의 기호 ·····························································A10 C 적분으로 정의된 로그 함수 ······························A15 D 증명 ······································································A23
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