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 :
제작날짜 :
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 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
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 $C : \begin{cases} \displaystyle r=\frac{2}{\sqrt{\cos^2 t -\sin^2 t}} \\ \displaystyle \theta= t \end{cases} , \ \displaystyle -\frac{\pi}{4} < t < \frac{\pi}{4}$
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