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출판 > 순수과학
 
 
계측응용수학
 
저      자 : 최주호,유준
출  판 사 : 충남대학교출판문화원
페이지수 : 493
ISBN      : 978-89-7599-010-6
출판연도 : 2019년
 
판매가 : 35,000원
 
 
 

본서는 저자가 수 년간 공과과목 강의를 하는 동안 학생들이 수강을 하는데 많은 어려움을 느끼는 수학적 개념이 내포된 이론이나 법칙 및 문제 해결의 도구가 될 수 있는 내용들을 정리 하였으며 그리고 연구의 결과를 도출하기 위해 활용되는 측정시스템에서 발생되는 계통오차와 측정오차를 분석하는 방법을 수록하여 측정과 성능평가 업무를 수행하는 이들과 이공계 학부과정 및 대학원에서 이 분야를 공부하는 학생들에게 좋은 지침서가 될 수 있도록 하였다. 측정불확도(uncertainty)란 측정값의 정확도와 신뢰도를 동시에 나타내는 정량적 지표이며, 측정결과는 측정값과 함께 불확도가 반드시 명기 되어야 한다는 국제표준규정으로 정하고 있다.

 

l 최주호 ·1976.2 부산대학교 전자공학과 학사 ·1999.8 충남대학교 전자공학과 박사 ·1977.2~2010.12 국방과학연구소 종합시험단 책임연구원 ·2001.3~2002.2 한서대학교 전자공학과 겸임교수 ·2001년 국가교정기관 기술 및 시스템 평가사 ·2011.1~2016.2 코리아인스트루먼트(주) 전무이사, 연구소장 ·2011.3~2014.2 한서대학교 항공전자공학과 겸임교수 ·2017.3~2018.2 한서대학교 항공전자공학과 겸임교수 ·2016.3~현재 (주)한국계측기기연구센터 전무이사, 연구소장 l 유준 ·1978.2 서울대학교 전자공학과 학사 ·1984.8 KAIST 전기 및 전자공학과 박사(제어계측) ·1984.9~ 현재 충남대학교 전자공학과 교수 ·1988.2~1989.2 미국 미시건주립대학 방문교수 ·1992.12~1993.2 독일 생산공학 및 자동화연구소(IPA) 방문교수 ·1997.2~1998.2 미국 캘리포티아주립대학, 데이비스 방문교

 

chapter 1 통계이론의 기초 1.1 용어 설명 ························································································· 14 1.2 모집단과 표본 ·················································································· 15 1.3 분산 평가 ························································································· 27 1.4 통계적 추정(statistical estimation) ····················································· 30 1.5 측정불확도 포함 ·············································································· 32 연습문제 ································································································ 34 chapter 2 확률변수와 확률분포함수 2.1 연속확률분포 ··················································································· 36 2.2 Q function의 정의 ············································································· 37 2.3 이항분포(binominal distribution) ····················································· 41 2.4 표준정규분포 ··················································································· 43 2.5 student's 분포 ··················································································· 47 2.6 균등분포(uniform distribution) 및 삼각형 분포 ·································· 55 2.7 F-분포 ······························································································ 57 2.8 중심극한 정리(central limit theorem) ················································· 59 연습문제 ································································································ 62 chapter 3 자유도 해석 3.1 개 요 ································································································ 66 3.2 표본의 크기에 대한 자유도 ······························································· 68 3.3 표본 변수의 자유도 ········································································ 70 3.4 회귀와 영(null) 모델 자유도 ···························································· 72 3.5 정규 모집단의 통계량 분포와 자유도 ················································ 72 3.6 수학에서의 자유도 ·········································································· 74 3.7 역학계의 자유도 ·············································································· 76 3.8 화학계 및 물리계의 자유도 ······························································ 78 연습문제 ································································································ 80 chapter 4 신호 해석을 위한 함수론 응용 4.1 센서의 직선성과 감도 ······································································ 82 4.2 테일러급수(Taylor series) ······························································· 86 4.3 오일러(Euler's) 공식 ········································································ 89 4.4 직교 함수 (orthogonal function) ······················································ 92 4.5 계단 함수와 임펄스 함수 ································································· 96 4.6 sinc 함수와 샘플(Sa) 함수 ····························································· 100 4.7 푸리에 급수(fourier series) ····························································· 102 4.8 푸리에 변환(fourier transform) ······················································· 110 4.9 중첩 적분 ······················································································ 118 4.10 라플라스 변환 ·············································································· 123 4.11 퍼스발의 정리(parseval's theorem) ··············································· 126 4.12 전달함수(transfer function) ··························································· 129 4.13 힐버트 변환(Hilbert transform) ····················································· 136 4.14 베셀 함수 (Bessel function) ·························································· 138 4.15 확률(probability) ·········································································· 143 4.16 표본화(Sampling)와 보간법(interpolation) ···································· 146 4.17 랜덤 펄스열의 자기상관 함수 ······················································ 152 4.18 정합 필터 (matched filter) ···························································· 156 4.19 상관 함수 (correlation function) ···················································· 161 4.20 2차 시스템 해석(Analysis of 2nd order system) ···························· 166 4.21 백색 잡음 (additive white gaussian noise) ····································· 169 연습문제 ······························································································ 172 chapter 5 미분 방정식과 해석함수 5.1 개요 ······························································································ 176 5.2 상미분 방정식 ··············································································· 176 5.3 벡터의 미분 ·················································································· 184 5.4 선 적분 과 면 적분 ········································································ 187 5.5 편미분 방정식 ··············································································· 190 5.6 복소함수 ······················································································· 193 5.7 유수 정리(Residue Theorem) ·························································· 197 연습문제 ······························································································ 203 chapter 6 이산신호 처리 6.1 개 요 ···························································································· 208 6.2 이산신호 ························································································ 210 6.3 이산시간 푸리에 분석 ···································································· 214 6.4 이산 푸리에 변환 ··········································································· 220 6.5 이산시스템의 응답 ········································································ 227 6.6 z변환 ····························································································· 235 6.7 이산시스템 표현과 분석 ································································ 246 6.8 디지털 필터 구조 ··········································································· 251 연습문제 ······························································································ 259 chapter 7 선형 연산자와 동적 시스템의 수학적 표현 7.1 개 요 ···························································································· 262 7.2 선형 연산자 ··················································································· 262 7.3 시스템의 수학적 표현 ···································································· 273 7.4 선형 동적방정식과 임펄스 행렬 ··················································· 276 7.5 비선형 수학적 모델의 선형화 ························································ 281 연습문제 ······························································································ 283 chapter 8 측정불확도의 표현 및 평가 8.1 개 요 ····························································································· 286 8.2 측정불확도의 기초 개념 ······························································· 287 8.3 측정불확도 요소 ············································································ 288 8.4 측정불확도 전파법칙 ····································································· 289 8.5 측정불확도 평가방법 ···································································· 292 8.6 불확도 평가절차 ··········································································· 293 8.7 A형 표준불확도 평가 ····································································· 294 8.8 B형 표준불확도 평가 ····································································· 298 8.9 합성표준불확도 ·············································································· 303 8.10 확장불확도 ·················································································· 305 8.11 유효자유도 ··················································································· 306 8.12 포함인자의 결정 ··········································································· 307 8.13 불확도 보고 ················································································· 310 연습문제 ······························································································ 311 chapter 9 측정시스템의 불확도 평가 방법 9.1 측정시스템의 구성 ········································································ 314 9.2 측정시스템의 주요 오차 요소 ························································· 315 9.3 측정오차 분류 ················································································ 315 9.4 RSS 방식에 의한 불확도 평가 ·························································· 317 9.5 힘 측정시스템의 불확도 평가 ························································ 318 9.6 도플러 레이더 측정시스템의 불확도 평가 ······································ 320 9.7 솔레노이드 코일을 이용한 속도 측정시스템의 불확도 평가 ··········· 322 9.8 동구게이지 측정불확도 평가 ························································ 325 9.9 압전형 압력센서를 이용한 포구(砲腔) 내부 압력 측정불확도 평가 · 329 9.10 열전대 센서를 이용한 온도 측정시스템의 불확도 평가 ················· 331 9.11 모발 습도계의 측정불확도 평가 ··················································· 336 연습문제 ······························································································ 339 chapter 10 교정 불확도 평가 10.1 최고 측정능력(BMC : Best Measurement Capability) ····················· 358 10.2 최고 측정능력의 표현방법 ···························································· 358 10.3 최고 측정능력의 도시적 이해 ························································ 359 10.4 교정시스템의 불확도 요소 ···························································· 359 10.5 교정 대상기기의 불확도 종류 ························································ 359 10.6. 스텝 동압력 교정기기의 불확도 평가 ·········································· 362 10.7 멀티미터 교정 불확도 평가 ·························································· 368 연습문제 ······························································································ 381 chapter 11 측정불확도 평가 사례 11.1 측정불확도 평가 논문 작성 예 ······················································ 388 11.2 변형률 측정시스템의 불확도 평가 ················································ 393 11.3 압력 측정시스템의 불확도 평가 ··················································· 398 11.4 RTD 저항 및 열전대 센서를 이용한 교정시스템의 불확도 평가 ····· 401 11.5 포구속도 측정용 도플러레이더 측정불확도 평가 ······················· 405 11.6 포구속도 측정용 광 스크린시스템의 측정불확도 평가 ·················· 408 연습문제 ······························································································ 420 chapter 12 회귀분석의 결정계수 적합도 평가 12.1 개 요 ····························································································· 422 12.2. 회귀모형과 회귀방정식의 결정 ··················································· 423 12.3 최소자승법의 회귀계수 추정 ························································· 424 12.4. 회귀선의 적합도 ·········································································· 430 12.5. 회귀계수와 결정계수 계산 ··························································· 435 12.6 검토 ······························································································ 440 연습문제 ······························································································ 441 chapter 13 신호 검출용 회로 해석 13.1 브리지 회로 ·················································································· 444 13.2 원형 코일센서 ·············································································· 447 13.3 압전기 센서 ·················································································· 450 13.4 LVDT 센서 ··················································································· 452 13.5 도플러 신호 발생기 ······································································· 455 13.6 필터 회로 ······················································································ 457 연습문제 ······························································································ 462 chapter 14 오일러상수 감마 14.1 조화급수 ······················································································· 464 14.2 제타함수 ······················································································· 465 14.3 감마함수 ······················································································· 465 14.4 오일러-매클로린 합 ······································································ 467 14.5 리만의 소수 세기 ········································································· 468 14.6 테일러 전개 ················································································· 469 14.7 복소미분과 적분 ·········································································· 473 연습문제 ······························································································ 479 부 록 ···································································································· 481 참고문헌 ·································································································489 찾아보기 ·································································································491

 

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