대학 기초 수학

제Ⅰ장 함수와 도형의 방정식
01. 함수의 종류 ······················································································11
02. 도형(함수)의 이동 ············································································13
03. 도형(함수)의 대칭·주기성 ·······························································15
04. 함수의 위로 볼록(아래로 오목) ························································17
05. 절대값 함수 ······················································································19
06. 가우스 기호 ····················································································22
07. 함수방정식 ························································································24
08. 근과 계수의 관계 ·············································································26
09. 합성함수의 그래프 ············································································27
10. 역함수 ······························································································29
11. 근의 분리 ·························································································31
12. 지수와 로그 ······················································································32
13. 원 ·····································································································42
14. 포물선 ······························································································47
15. 타원의 방정식 ···················································································49
16. 쌍곡선의 방정식 ···············································································52
17. 이차곡선 기타 내용 ········································································55
18. 삼각함수 : 고교 공통수학 삼각함수 요약 ·········································59
19. 삼각함수의 덧셈정리 ·········································································64

제Ⅱ장 수열과 수열극한
01. 등차수열 ···························································································77
02. 등비수열 ···························································································81
03. 여러가지 수열 ···················································································84
04. 점화식(수학적 귀납법) ····································································87
05. 수열의 극한 ····················································································102
06. 무한 급수 ·······················································································108

제Ⅲ장 행렬, 복소수, 벡터와 공간도형
01. 행렬의 정의 ····················································································113
02. 행렬의 연산 ····················································································114
03. 역행렬과 연립 1 차 방정식 ···························································119
04. 복소수 ····························································································124
05. 복소수의 극형식 Polar Coordinates (평면도형의 극좌표) ······127
06. 복수수와 도형 ················································································130
07. 공간도형 및 성질 ···········································································137
08. 공간좌표와 구면의 방정식 ······························································140
09. 벡터의 정의 및 성질 ······································································142
10. 위치벡터와 벡터의 성분표시 ···························································147
11. 벡터의 내적과 외적 ········································································150
12. 벡터 방정식 및 공간도형의 방정식 ·················································155
13. 일차변환 ·························································································166

제Ⅳ장 미적분학(해석학)
01. 함수 극한의 정의 ···········································································173
02. 함수 극한값의 정의 ········································································175
03. 극한값의 성질 ················································································178
04. 극한의 유형에 대한 설명 ································································179
05. 삼각함수, 지수함수 로그함수의 극한 ··············································183
06. 연속함수의 정의 및 성질 ································································187
07. 최대소의 정리 및 중간값 정리 ·······················································190
08. 변화율과 도함수 (미분) ··································································191
09. 곡선의 접선과 미분 ········································································205
10. 도함수의 성질(미적분학 전용) ························································209
11. 함수의 극대와 극소 ········································································212
12. 함수의 요철: 그래프 개형 ·······························································218
13. 함수의 최대-최소, 방부등식과 미분 ··············································223
14. 부정적분 ·······················································································225
15. 부분 적분과 치환적분 ·····································································226
16. 정적분과 면적 및 부피 ···································································232
17. 속도·가속도와 미적분학 ································································241
18. 간단한 미분 방정식에 대한 소개 ····················································246

제Ⅴ장 확률통계
01. 경우의수 ·························································································251
02. 순열 ·······························································································254
03. 조합 ·······························································································257
04. 이항정리 ·························································································261
05. 확률의 기본 정리 ···········································································267
06. 덧셈정리와 곱셈 정리 ·····································································268
07. 평균·분산·표준편차 ······································································275
08. 확률분포의 소개(이산확률분포를 중심으로) ·····································278
09. 이산확률분포 ··················································································280
10. 연속확률분포 ··················································································288
11. 정규분포(연속확률분포의 대표) ·······················································289
12. 여러 가지 연속분포 ········································································294
13. 통계적 추론 ····················································································300
14. 가설의 검정 ····················································································310
15. 통계적 추론의 실제 ········································································315