제1장 기초 수리 ···································································· 6 1. 기본용어 ···································································· 8 2. 수의 체계 ·································································· 12 3. 연산의 기본법칙 ························································· 16 4. 다항식의 전개와 인수분해 ············································ 17 5. 분수식과 비례식 ························································· 20 6. 절대값 ······································································ 25 7. 부등식 ······································································ 27 8. 지수와 로그 ······························································· 29 9. 삼각함수 ··································································· 37 10. 기초 정수론 ····························································· 44 11. 이항정리 ·································································· 50 12. 방정식 ····································································· 52 13. 수열과 급수 ····························································· 58 〉〉〉 참고자료 ································································ 67 1. 글자와 기호 ························································· 68 2. 진법 ··································································· 70 〉〉〉 연습문제 ································································ 73 제2장 확률과 통계 ······························································ 80 제1절 확률 ···································································· 82 1. 용어의 정의 ····················································· 82 2. 확률 ································································ 84 3. 경우의 수 ························································ 90 4. 조건부 확률과 베이즈 정리 ································ 94 제2절 확률변수와 확률분포 ············································ 101 1. 확률변수 ························································ 101 2. 이산형 확률분포 ············································· 110 3. 연속형 확률분포 ············································· 119 제3절 기초 통계학 ························································ 128 1. 용어의 정의 ··················································· 128 2. 기술통계학 ····················································· 130 3. 측도 ······························································ 134 〉〉〉 연습문제 ······················································ 143 수리과학 제3장 미분 ······································································· 150 제1절 함수의 극한과 도함수 ············································ 152 1. 함수의 극한과 연속 ········································· 152 2. 도함수와 미분 ················································ 159 〉〉〉 연습문제 ····················································· 167 제2절 미분법 ······························································· 172 1. 미분(도함수)의 기본공식 ·································· 172 2. 합성함수 미분 ················································ 174 3. 음함수 미분 ··················································· 178 4. 역함수 미분 ··················································· 180 5. 매개변수 미분 ················································ 182 6. 삼각함수, 지수함수, 로그함수 미분 ···················· 185 7. 고계도함수 ····················································· 191 〉〉〉 연습문제 ····················································· 193 제3절 미분의 응용 ························································ 200 1. 미분의 응용 ··················································· 200 2. L'Hospital의 정리 ··········································· 207 3. 함수의 증감, 극대·극소, 최대·최소 ················· 211 〉〉〉 연습문제 ······················································ 219 제4절 편미분 ······························································· 224 1. 편도함수 ························································ 224 〉〉〉 연습문제 ······················································ 229 제4장 적분법 ···································································· 232 제1절 부정적분 ···························································· 234 1. 적분의 기본공식 ············································· 235 〉〉〉 연습문제 ······················································ 247 제2절 정적분 ······························································· 254 1. 정적분의 정의 ················································ 254 2. 정적분의 기본성질 ·········································· 258 3. 미분·적분의 기본정리 ···································· 260 〉〉〉 연습문제 ······················································ 269 제3절 정적분의 응용 ····················································· 272 1. 곡선사이의 면적 ············································· 272 〉〉〉 연습문제 ······················································ 277 부록 : 통계분포표 · 찾아보기 ··················································· 282