수리과학

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

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