2019 학년도 수학수업(The mathematics class of 2019)

2019학년도 수학수업 원노트
      수정날짜 : 20190303
      제작날짜 : 20190303
      url : https://gnecloud-my.sharepoint.com/:o:/g/personal/min7014_sw-ms_gne_go_kr/EhOGJPAeZURChhan0DGVHDoBgrVwos-fxWKOCY1dFx_rHQ

수업이외의 내용(Others)

  한 원이 있고 두 점이 주어졌을 때, 두 점을 지나면서 이 원과 수직으로 만나는 원을 작도하여라.
        수정날짜 : 20190302
        제작날짜 : 20190302
        pdf : https://min7014.github.io/2019/2019030202.pdf

  주어진 원과 한 점이 있을 때 이 한 점을 지나면서 원과 수직으로 만나면서 두 원의 중심을 잇는 직선이 이 점을 지나도록 하는 원을 작도하여라.
        수정날짜 : 20190317
        제작날짜 : 20190317
        pdf : https://min7014.github.io/2019/2019031701.pdf

  주어진 원과 이 원의 중심을 지나는 한 직선과 한 점이 있을 때 이 한 점을 지나면서 원과 수직으로 만나면서 주어진 직선에 중심이 있는 원을 작도하여라.
        수정날짜 : 20190407
        제작날짜 : 20190407
        pdf : https://min7014.github.io/2019/2019040703.pdf
        YouTube : https://youtu.be/6IVI8mbqyhE

  $y=\frac{1}{x}$ 위에 두 점이 있을때, 두 점이 $y=x$ 에 대칭이 되도록 $x$축 방향으로 확대하여라.(When there are two points on $y=\frac{1}{x}$, zoom in to $x$ direction to make two points symmetrical to $y=x$)
        수정날짜 : 20190331
        제작날짜 : 20190331
        pdf : https://min7014.github.io/2019/2019033101.pdf
        YouTube : https://youtu.be/6n1P6D4Z_n0

함수(Function)
      수정날짜 : 20160201
      제작날짜 : 20160201
      pdf : https://min7014.github.io/2019/2016020101.pdf

접선(Tangent line)

  접선(Tangent line)
        수정날짜 : 20160309
        제작날짜 : 20160309
        pdf : https://min7014.github.io/2019/2016030901.pdf

  접선에 접근하는 할선들(Secant lines approaching the tangent line)
        수정날짜 : 20160129
        제작날짜 : 20160129
        pdf : https://min7014.github.io/2019/2016012901.pdf

극한(Limit)

  극한의 법칙들(Limit Laws)

    극한의 법칙들(Limit Laws)
          수정날짜 : 20160314
          제작날짜 : 20160314
          pdf : https://min7014.github.io/2019/2016031402.pdf

    합의 극한은 극한의 합이다.(The limit of a sum is the sum of the limits.)
          수정날짜 : 20160314
          제작날짜 : 20160314
          pdf : https://min7014.github.io/2019/2016031403.pdf

    함수의 상수배의 극한은 함수의 극한의 상수배이다.(The limit of a constant times a function is the constant times the limit of the function.)
          수정날짜 : 20160314
          제작날짜 : 20160314
          pdf : https://min7014.github.io/2019/2016031404.pdf

    차의 극한은 극한의 차이다.(The limit of a difference is the difference of the limits.)
          수정날짜 : 20160314
          제작날짜 : 20160314
          pdf : https://min7014.github.io/2019/2016031405.pdf

    곱의 극한은 극한의 곱이다.(The limit of a product is the product of the limits.)
          수정날짜 : 20160315
          제작날짜 : 20160315
          pdf : https://min7014.github.io/2019/2016031501.pdf

    나눗셈의 극한은 극한의 나눗셈이다.(The limit of a quotient is the quotient of the limits(provided that the limit of the denominator is not 0))
          수정날짜 : 20160315
          제작날짜 : 20160315
          pdf : https://min7014.github.io/2019/2016031502.pdf

  압착정리(The Squeeze Theorem)

    $[\forall \epsilon>0 , a+\epsilon >0 ]\Leftrightarrow a\ge 0$
          수정날짜 : 20160320
          제작날짜 : 20160320
          pdf : https://min7014.github.io/2019/2016032001.pdf

    $\left[f(x) \le g(x) (0 < |x-a| < \delta_0) \ , \ \displaystyle \lim_{x \rightarrow a} f(x) =L \ , \ \displaystyle \lim_{x \rightarrow a} g(x) =M\right]\Rightarrow L\le M$
          수정날짜 : 20160316
          제작날짜 : 20160316
          pdf : https://min7014.github.io/2019/2016031601.pdf

    압착정리(The Squeeze Theorem)
          수정날짜 : 20160320
          제작날짜 : 20160320
          pdf : https://min7014.github.io/2019/2016032002.pdf

  좌극한, 우극한( Definiton of One-Sided Limits)
        수정날짜 : 20160307
        제작날짜 : 20160307
        pdf : https://min7014.github.io/2019/2016030702.pdf

미분(Derivatives)

  고차미분(Higher Derivatives)
        수정날짜 : 20160406
        제작날짜 : 20160406
        pdf : https://min7014.github.io/2019/2016040603.pdf

  연쇄법칙(The Chain Rule)
        수정날짜 : 20160407
        제작날짜 : 20160407
        pdf : https://min7014.github.io/2019/2016040702.pdf

  $\theta < \tan \theta \ (0<\theta<\frac{\pi}{2})$
        수정날짜 : 20160404
        제작날짜 : 20160404
        pdf : https://min7014.github.io/2019/2016040401.pdf
        gif : https://min7014.github.io/2019/2016040401.gif

  $ \displaystyle \lim_{\theta \rightarrow 0} \frac{\sin \theta}{\theta}=1 $
        수정날짜 : 20160327
        제작날짜 : 20160327
        pdf : https://min7014.github.io/2019/2016032701.pdf

  $\displaystyle\frac{d}{dx}(\sin x)=\cos x$
        수정날짜 : 20160407
        제작날짜 : 20160407
        pdf : https://min7014.github.io/2019/2016040701.pdf

미분의 응용(Applications of Derivatives)

  코시의 평균값 정리(Cauchy's Mean Value Theorem)
        수정날짜 : 20160128
        제작날짜 : 20160128
        pdf : https://min7014.github.io/2019/2016012801.pdf
        gif : https://min7014.github.io/2019/2016012801.gif

  오목 검사(Concavity Test)
        수정날짜 : 20190419
        제작날짜 : 20160714
        pdf : https://min7014.github.io/2019/2016071401.pdf
        YouTube : https://youtu.be/hQKmM36XEH4
        Geogebra Tube : https://ggbm.at/bzuqgxkz

적분과 초월함수(Integral and Transcendental Function)

  $\displaystyle \int \sec x \ dx$
        수정날짜 : 20190411
        제작날짜 : 20190411
        pdf : https://min7014.github.io/2019/2019041101.pdf
        YouTube : https://youtu.be/b9ItX1Vtzwo

  $\displaystyle \int \csc x \ dx$
        수정날짜 : 20190411
        제작날짜 : 20190411
        pdf : https://min7014.github.io/2019/2019041102.pdf
        YouTube : https://youtu.be/1nkz9-c9BqA

  $y=\ln x, \ \ y=\ln^{-1} x$
        수정날짜 : 20190412
        제작날짜 : 20190412
        AlgeoMath : http://me2.do/FKitVZci
        YouTube : https://youtu.be/aeCLqztoh1A

  $y=\log_2 x, \ \ y=2^x$
        수정날짜 : 20190412
        제작날짜 : 20190412
        AlgeoMath : http://me2.do/FNERBByo
        YouTube : https://youtu.be/YfcDSfwoQoc

  $T(u)=(\cosh u,\sinh u)$
        수정날짜 : 20190415
        제작날짜 : 20190415
        AlgeoMath : http://me2.do/xYEfu5YH
        YouTube : https://youtu.be/hfijgPnskWg

적분의 기술(Techniques of Integration)

  사다리꼴 근사법(Trapezoidal Approximations)
        수정날짜 : 20190426
        제작날짜 : 20190426
        pdf : https://min7014.github.io/2019/2019042601.pdf
        YouTube : https://youtu.be/hZwCg8rpw2o
        Geogebra Tube : https://ggbm.at/qardxfgj

  사다리꼴 방법에서의 오차(Error in the Trapezoidal Rule)
        수정날짜 : 20190428
        제작날짜 : 20161011
        pdf : https://min7014.github.io/2019/2016101101.pdf
        YouTube : https://youtu.be/VtACaNJRA6E
        Geogebra Tube : https://ggbm.at/vfdbcrf7

미분방정식(Differential Equation)

  $\displaystyle\frac{dy}{dx}=y-x$

    Slope Field of $\displaystyle\frac{dy}{dx}=y-x$
          수정날짜 : 20190428
          제작날짜 : 20190428
          Geogebra Tube : https://ggbm.at/ypsetajf

    Slope Field of $\displaystyle\frac{dy}{dx}=y-x$ 제작방법 (by Geogebra)
          수정날짜 : 20190502
          제작날짜 : 20190502
          YouTube : https://youtu.be/m9kEZbiMAAo

    Slope Field of $\displaystyle\frac{dy}{dx}=y-x$ by AlgeoMath
          수정날짜 : 20190504
          제작날짜 : 20190504
          AlgeoMath : http://me2.do/FfGxem0U
          YouTube : https://youtu.be/DIZnaM9thJ8

    Slope Field of $\displaystyle\frac{dy}{dx}=y-x$ and Solutions
          수정날짜 : 20190507
          제작날짜 : 20190507
          AlgeoMath : http://me2.do/5d1md2pf
          YouTube : https://youtu.be/TZrchW7NHfU

    Slope Field of $\displaystyle\frac{dy}{dx}=y-x$ and Solutions and Approximation by Euler's Mathod
          수정날짜 : 20190509
          제작날짜 : 20190509
          AlgeoMath : http://me2.do/5Ixqx7YC
          YouTube : https://youtu.be/Rb0VIfblqfs

  $\displaystyle\frac{dy}{dx}=y-x^2$

    Slope Field of $\displaystyle\frac{dy}{dx}=y-x^2$ by AlgeoMath
          수정날짜 : 20190506
          제작날짜 : 20190506
          AlgeoMath : http://me2.do/x9Ke4cPE
          YouTube : https://youtu.be/l5qTugcniOM

    Slope Field of $\displaystyle\frac{dy}{dx}=y-x^2$ and Solutions
          수정날짜 : 20190507
          제작날짜 : 20190507
          AlgeoMath : http://me2.do/Fdj8aLtq
          YouTube : https://youtu.be/fPc2ET9rC-Q

  $\displaystyle\frac{dy}{dx}-\frac{2xy}{1+x^2}$

    Slope Field of $\displaystyle\frac{dy}{dx}-\frac{2xy}{1+x^2}$ by AlgeoMath
          수정날짜 : 20190506
          제작날짜 : 20190506
          AlgeoMath : http://me2.do/G9EISpgj
          YouTube : https://youtu.be/0F9zxkKn_5Y

    Slope Field of $\displaystyle\frac{dy}{dx}-\frac{2xy}{1+x^2}$) and Solutions
          수정날짜 : 20190507
          제작날짜 : 20190507
          AlgeoMath : http://me2.do/GG03Xhui
          YouTube : https://youtu.be/_3r9wW4W5y4

  $\displaystyle\frac{dy}{dx}=(1-x)y+\frac{x}{2}$

    Slope Field of $\displaystyle\frac{dy}{dx}=(1-x)y+\frac{x}{2}$ by AlgeoMath
          수정날짜 : 20190506
          제작날짜 : 20190506
          AlgeoMath : http://me2.do/x4n8mOA9
          YouTube : https://youtu.be/qDWiNxFzlLk

    Slope Field of $\displaystyle\frac{dy}{dx}=(1-x)y+\frac{x}{2}$ and Approximation by Euler's Method
          수정날짜 : 20190510
          제작날짜 : 20190510
          AlgeoMath : http://me2.do/FNEykjp7
          YouTube : https://youtu.be/7_M7Men6j-o

  $\displaystyle\frac{dy}{dx}=(y+1)(y-2)$

    Slope Field of $\displaystyle\frac{dy}{dx}=(y+1)(y-2)$
          수정날짜 : 20190506
          제작날짜 : 20190506
          AlgeoMath : http://me2.do/GaYmBhu4
          YouTube : https://youtu.be/2AE7oEn3dM4

    Slope Field of $\displaystyle\frac{dy}{dx}=(y+1)(y-2)$ and Solutions
          수정날짜 : 20190517
          제작날짜 : 20190517
          AlgeoMath : http://me2.do/FZ4RZwYe
          YouTube : https://youtu.be/I_uHAbUeFls

  Slope Field of $\displaystyle\frac{dy}{dx}=-\frac{y}{x}$ and Solutions and Orthogonal Trajectories
        수정날짜 : 20190518
        제작날짜 : 20190518
        AlgeoMath : http://me2.do/5Cx0gYBT
        YouTube : https://youtu.be/voTSwD4BkZU

  Slope Field of $\displaystyle\frac{dx}{dt}=y+x-x(x^2+y^2), \frac{dy}{dt}=y-x-y(x^2+y^2)$ and Approximation by Euler's Method
        수정날짜 : 20190518
        제작날짜 : 20190518
        AlgeoMath : http://me2.do/xe2bzF9t
        YouTube : https://youtu.be/C6alxDgvetM

Parametric Equations and Polar Coordinates

  Parametric Equations

    Parametric Curve of $C : \begin{cases} x=t^2\\ y=t+1 \end{cases} , \ t\in \mathbb{R}$
          수정날짜 : 20190520
          제작날짜 : 20190520
          AlgeoMath : http://me2.do/xlQsn63v
          YouTube : https://youtu.be/kWeOBAGSzdQ

    Parametric Curve of $C : \begin{cases} x=\cos t \\ y=\sin t \end{cases} , \ 0\le t \le 2\pi$
          수정날짜 : 20190520
          제작날짜 : 20190520
          AlgeoMath : http://me2.do/xEBuBNfe
          YouTube : https://youtu.be/s21fz9Pyj50

    Parametric Curve of $C : \begin{cases} x=\sqrt{t} \\ y=t \end{cases} , t\ge 0$
          수정날짜 : 20190520
          제작날짜 : 20190520
          AlgeoMath : http://me2.do/Igq3q1e0
          YouTube : https://youtu.be/rVc_OJ7U4tA

    Parametric Curve of $C : \begin{cases} \displaystyle x=t+ \frac{1}{t} \\ \displaystyle y=t- \frac{1}{t} \end{cases} , t> 0$
          수정날짜 : 20190520
          제작날짜 : 20190520
          AlgeoMath : http://me2.do/FnLPLCeT
          YouTube : https://youtu.be/mRVm081fg3c

    Parametric Curve of $C : \begin{cases} \displaystyle x=2 \sec t \\ \displaystyle y=2 \tan t \end{cases} , \displaystyle -\frac{\pi}{2} < t < \frac{\pi}{2}$
          수정날짜 : 20190520
          제작날짜 : 20190520
          AlgeoMath : http://me2.do/FtgzgU5S
          YouTube : https://youtu.be/J3_JVp9CrP0

    Parametric Curve of $C : \begin{cases} \displaystyle x=t-\sin t \\ \displaystyle y=1-\cos t \end{cases} , t\in \mathbb{R}$
          수정날짜 : 20190520
          제작날짜 : 20190520
          AlgeoMath : http://me2.do/FONeNp3k
          YouTube : https://youtu.be/JeiMuVd5lxQ

    Parametric Curve of $C : \begin{cases} x=t-t^2 \\ y=t-t^3 \end{cases} , \ t\in \mathbb{R}$
          수정날짜 : 20190520
          제작날짜 : 20190520
          AlgeoMath : http://me2.do/xnEDiXdR
          YouTube : https://youtu.be/rRSM_7yKvvI

    Parametric Curve of $C : \begin{cases} x=\cos^3 t \\ y=\sin^3 t \end{cases} , \ 0\le t \le 2\pi$
          수정날짜 : 20190520
          제작날짜 : 20190520
          AlgeoMath : http://me2.do/GaYfjQX8
          YouTube : https://youtu.be/7pU6B24jH6s

  Polar Coordinates

    Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{2}{\cos t} \\ \displaystyle \theta= t \end{cases} , \displaystyle - \frac{\pi}{2} < t < \frac{\pi}{2}$
          수정날짜 : 20190521
          제작날짜 : 20190521
          AlgeoMath : http://me2.do/xbBaAULz
          YouTube : https://youtu.be/VGNTdlAzcLo

    Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{2}{\sqrt{\cos t \sin t}} \\ \displaystyle \theta= t \end{cases} , \ 0 < t < \displaystyle \frac{\pi}{2}$
          수정날짜 : 20190521
          제작날짜 : 20190521
          AlgeoMath : http://me2.do/GzXeimCU
          YouTube : https://youtu.be/iE5olnLnD_c

    Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{1}{\sqrt{\cos^2 t -\sin^2 t}} \\ \displaystyle \theta= t \end{cases} , \ \displaystyle -\frac{\pi}{4} < t < \frac{\pi}{4}$
          수정날짜 : 20190521
          제작날짜 : 20190521
          AlgeoMath : http://me2.do/xy9rdRF8
          YouTube : https://youtu.be/nXouTPyLRwA

    Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{1}{1-2\cos t } \\ \displaystyle \theta= t \end{cases} , \ \displaystyle \frac{\pi}{3} < t < \frac{5\pi}{3}$
          수정날짜 : 20190521
          제작날짜 : 20190521
          AlgeoMath : http://me2.do/GYyH3bIU
          YouTube : https://youtu.be/bXOrIGKELQE

    Parametric Curve of $C : \begin{cases} \displaystyle r=1-\cos t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$
          수정날짜 : 20190521
          제작날짜 : 20190521
          AlgeoMath : http://me2.do/xpqCwpbH
          YouTube : https://youtu.be/VxtOlVA4OWE

    Parametric Curve of $C : \begin{cases} \displaystyle r=6\sin t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$
          수정날짜 : 20190521
          제작날짜 : 20190521
          AlgeoMath : http://me2.do/xDbrmhjH
          YouTube : https://youtu.be/r4jxs_DTY2s

    Parametric Curve of $C : \begin{cases} \displaystyle r=-\frac{4}{\cos t} \\ \displaystyle \theta= t \end{cases} , \ \displaystyle -\frac{\pi}{2} < t < \frac{\pi}{2}$
          수정날짜 : 20190522
          제작날짜 : 20190522
          AlgeoMath : http://me2.do/GVYBHNs4
          YouTube : https://youtu.be/GAPHyXpO56s

    Parametric Curve of $C : \begin{cases} \displaystyle r=4\cos t \\ \displaystyle \theta= t \end{cases} , \ 0 < t < 2\pi$
          수정날짜 : 20190522
          제작날짜 : 20190522
          AlgeoMath : http://me2.do/5rCam9tQ
          YouTube : https://youtu.be/vXIfiwNb0P8

    Parametric Curve of $C : \begin{cases} \displaystyle r=\frac{4}{2\cos t -\sin t} \\ \displaystyle \theta= t \end{cases} , -\pi+\arctan 2 < t < \arctan 2$
          수정날짜 : 20190522
          제작날짜 : 20190522
          AlgeoMath : http://me2.do/x2a0TY3y
          YouTube : https://youtu.be/CB9HOfNfb4Q

  The Standard Polar Equation

    직선에 대한 표준 극좌표 방정식(The Standard Polar Equation for Lines)
          수정날짜 : 20190528
          제작날짜 : 20190528
          AlgeoMath : http://me2.do/xfGmQDmy
          제작영상 YouTube : https://youtu.be/pbgqqAar1I4

    Polar equation for the cricle of radius a centered at $\mathrm{P_0}(r_0,\theta_0)$
          수정날짜 : 20190527
          제작날짜 : 20190527
          AlgeoMath : http://me2.do/Guiy6bfa
          제작영상 YouTube : https://youtu.be/e8AZgSiDfQE

  이심률에 의한 원뿔곡선(Conics by eccentricity)

    이심률에 의한 원뿔곡선(Conics by eccentricity)
          수정날짜 : 20190612
          제작날짜 : 20190612
          AlgeoMath : http://me2.do/xuPNlyD0
          YouTube : https://youtu.be/4XCYShsm_vE

    이심률에 의한 타원(Ellipse by eccentricity)
          수정날짜 : 20190611
          제작날짜 : 20190611
          AlgeoMath : http://me2.do/G1dEXl1Y

    이심률에 의한 포물선(Parabola by eccentricity)
          수정날짜 : 20190611
          제작날짜 : 20190611
          AlgeoMath : http://me2.do/5YPU6EVL

    이심률에 의한 쌍곡선(Hyperbola by eccentricity)
          수정날짜 : 20190611
          제작날짜 : 20190611
          AlgeoMath : http://me2.do/xcHYL3Dm

  Rose ( $r=\cos\left(\displaystyle\frac{n}{m} \theta\right)$ )
        수정날짜 : 20190527
        제작날짜 : 20190527
        AlgeoMath : http://me2.do/GPwcUOYd
        참고 : https://en.wikipedia.org/wiki/Rose_(mathematics)

  Butterfly curve
        수정날짜 : 20190524
        제작날짜 : 20190524
        AlgeoMath : http://me2.do/F7wEGPVk
        pdf : https://min7014.github.io/2019/2019061702.pdf
        YouTube : https://youtu.be/IMpHUvQmtDY