이 책의 특징

① 가능한 고교수학의 기초적인 내용을 활용하였다.

학생들이 미분적분학을 처음 접한다는 생각보다는 고교수학의 연장이라는 친숙함을 느낄 수 있도록 고교수학의 내용을 도입하였다.

② 수학적 개념을 이해하고 쉽게 문제를 해결할 수 있도록 유형에 따라 구분하였다.

수학적 개념을 쉽게 이해할 수 있도록 집필하였으며 다양한 형태의 문제를 해결할 수 있도록 유형에 따라 분류하였다.

③ 가능한 그림이나 그래프를 이용하여 수학적 내용을 이해할 수 있도록 했다.

매우 간단한 수학적 개념이라 하더라도 수식만으로 이해하는데 많은 어려움이 있다. 따라서 수학적인 개념에 대해 가능한 많은 그림과 그래프를 이용하여 학생들의 이해력을 높이기 위해 노력했다.

④ 문제해결을 위해 간략하면서 친절한 풀이를 제시하였다.

많은 학생들이 수학적 개념은 이해하더라도 문제풀이 방법을 모르는 것이 수학을 포기하는 가장 근본적인 이유이다. 이에 저자들은 문제풀이를 간결하면서도 친절하게 제시하였으며, 선별적으로 연습문제의 풀이를 제공했다.

CHAPTER 01 함수

1.1 직교좌표계 ·································································································3

1.2 함수 ············································································································6

1.3 함수의 종류 ·····························································································11

1.4 함수의 대칭성과 주기성 ·········································································15

CHAPTER 02 초월함수

2.1 삼각함수 ··································································································23

2.2 역삼각함수 ·······························································································41

2.3 지수함수 ··································································································48

2.4 로그함수 ··································································································51

2.5 쌍곡선함수와 역쌍곡선함수 ····································································55

CHAPTER 03 도함수

3.1 함수의 극한과 연속성 ·············································································69

3.2 도함수와 미분법 ······················································································88

3.3 도함수의 응용 ·······················································································109

3.4 최적화 문제에의 응용 ···········································································119

CHAPTER 04 적분

4.1 부정적분과 정적분 ················································································141

4.2 적분법 ····································································································152

4.3 이상적분 ································································································168

4.4 적분의 응용 ···························································································173

CHAPTER 05 매개변수방정식과 극좌표

5.1 매개변수방정식 ······················································································199

5.2 매개곡선에 대한 미적분 ·······································································201

5.3 극좌표계와 극곡선 ················································································206

5.4 극곡선에 대한 미적분 ···········································································216

CHAPTER 06 무한급수

6.1 수열 ·······································································································229

6.2 무한급수 ································································································238

6.3 급수의 수렴 판정법 ··············································································242

6.4 거듭제곱급수 ·························································································255

6.5 테일러급수 ·····························································································262

CHAPTER 07 편미분

7.1 다변수함수 ·····························································································277

7.2 이변수함수의 극한과 연속성 ································································282

7.3 편도함수 ································································································288

7.4 편미분법 ································································································295

7.5 편도함수의 응용 ····················································································301

CHAPTER 08 중적분

8.1 이중적분 ································································································315

8.2 극좌표계에서의 이중적분 ······································································326

8.3 삼중적분 ································································································332

8.4 원기둥좌표와 구면좌표에서의 삼중적분 ···············································338

CHAPTER 09 공간벡터와 벡터함수

9.1 좌표공간과 벡터 ····················································································353

9.2 벡터의 내적과 외적 ··············································································357

9.3 직선과 평면의 방정식 ···········································································366

9.4 벡터함수의 극한 ····················································································371

9.5 벡터함수의 미분과 적분 ·······································································375

CHAPTER 10 행렬과 행렬식

10.1 행렬과 기본연산 ··················································································387

10.2 연립방정식과 가우스 소거법 ······························································398

10.3 역행렬 ··································································································406

10.4 행렬식 ··································································································412

CHAPTER 11 미분방정식의 기초

11.1 1계 미분방정식 ···················································································429

11.2 2계 미분방정식 ···················································································439

연습문제 풀이 ·································································································445

찾아보기 ··········································································································475