audio
audioduration (s)
0.83
21
transcription
stringlengths
3
127
LaTeX
stringlengths
7
142
Source
stringclasses
89 values
R sub y minus Q sub z times i plus P sub z minus R sub x times j
$(R_{y}-Q_{z})i+(P_{z}-R_{x})j$
https://www.youtube.com/watch?v=seO7-TwXH_I
partial over partial y of r minus partial partial z of q
$\displaystyle \frac{\partial}{\partial y}(R)-\frac{\partial}{\partial z}(Q)$
https://www.youtube.com/watch?v=seO7-TwXH_I
two to the n
$2^{\mathcal{n}}$
https://www.youtube.com/watch?v=oI9fMUqgfxY
6 times 1 plus 4 plus 9 plus 16 plus 25 plus 36
$6\times(1+4+9+16+25+36)$
https://www.youtube.com/watch?v=oI9fMUqgfxY
r over t times t
$\frac{r}{t}t$
https://www.youtube.com/watch?v=oI9fMUqgfxY
two plus a half divided by two is one and a quarter.
$(2+\frac{1}{2})\div2=1+\frac{1}{4}$
https://www.youtube.com/watch?v=oI9fMUqgfxY
x is c times the expected value of r
$x =c\cdot\operatorname*{\mathbb{E}}[r]$
https://www.youtube.com/watch?v=q4mwO2qS2z4
u minus expected value of r over u minus x
$\displaystyle u - \operatorname*{\mathbb{E}}\left[r\right]\over{u-x}$
https://www.youtube.com/watch?v=q4mwO2qS2z4
1 over C squared plus 1
$\frac{1}{C^{2}+1}$
https://www.youtube.com/watch?v=q4mwO2qS2z4
1 over 2c squared
$\frac{1}{2c^{2}}$
https://www.youtube.com/watch?v=q4mwO2qS2z4
z is c natural log of c plus 1
$z=c\ln(c)+1$
https://www.youtube.com/watch?v=q4mwO2qS2z4
c minus 1 times the sum j equals 1 to n expected value of tj
$(c-1)\cdot\sum_{j=1}^{n}\mathbb{E}[t_j]$
https://www.youtube.com/watch?v=q4mwO2qS2z4
e to the minus c log of c plus c minus 1
$e^{-(c\log(c)+c-1)}$
https://www.youtube.com/watch?v=q4mwO2qS2z4
negative c minus one
$\displaystyle -(c-1)$
https://www.youtube.com/watch?v=q4mwO2qS2z4
dy dx equal y squared
$\frac{dy}{dx}=y^{2}$
https://www.youtube.com/watch?v=76WdBlGpxVw
y of x equals minus 1 over x plus c
$y(x)=-\frac{1}{x+c}$
https://www.youtube.com/watch?v=76WdBlGpxVw
y of x equals 1 over 1 minus x
$y(x)=\frac{1}{1-x}$
https://www.youtube.com/watch?v=76WdBlGpxVw
y dot plus ty equals to t
$y\dot{+}ty=t$
https://www.youtube.com/watch?v=4gJLEYc3p5w
y of 0 equals to 3
$y(0)=3$
https://www.youtube.com/watch?v=4gJLEYc3p5w
u equals exponential of t squared over 2
$u=\exp(t^{2}/2)$
https://www.youtube.com/watch?v=4gJLEYc3p5w
exponential of minus t squared over 2
$\exp(-t^{2}/2)$
https://www.youtube.com/watch?v=4gJLEYc3p5w
3 equals to 1 plus c
$3=1+c,$
https://www.youtube.com/watch?v=4gJLEYc3p5w
exponential of t squared over 2 minus 1
$\exp(t^{2}/2)-1$
https://www.youtube.com/watch?v=4gJLEYc3p5w
b modulus r
$b\mod r$
https://www.youtube.com/watch?v=sn3orkHWqUQ
pi over 2
$\frac{\pi}{2}$
https://www.youtube.com/watch?v=sn3orkHWqUQ
3i pi over 6
$3i(\pi/6)$
https://www.youtube.com/watch?v=sn3orkHWqUQ
3 sine pi over 6
$3\sin(\pi/6)$
https://www.youtube.com/watch?v=sn3orkHWqUQ
3 root of 3 over 2
$3\sqrt{\frac{3}{2}}$
https://www.youtube.com/watch?v=sn3orkHWqUQ
a plus ib
$a+\mathrm{i}b$
https://www.youtube.com/watch?v=sn3orkHWqUQ
1 over minus 2 plus 3i
$\frac{1}{-2+3i}$
https://www.youtube.com/watch?v=sn3orkHWqUQ
reverse tan of minus 3 over 2
$\tan^{-1}(-\frac{3}{2})$
https://www.youtube.com/watch?v=sn3orkHWqUQ
exponential 2n pi
$\exp(2n\pi)$
https://www.youtube.com/watch?v=sn3orkHWqUQ
0 modulus 2 pi
$0\mod2\pi$
https://www.youtube.com/watch?v=sn3orkHWqUQ
n equals to 2
$(n\!=\!2)$
https://www.youtube.com/watch?v=sn3orkHWqUQ
i dot i minus one
$i(i-1)$
https://www.youtube.com/watch?v=fkGAF5jHjdY
1 over k squared plus omega squared
$\frac{1}{k^{2}+\omega^{2}}$
https://www.youtube.com/watch?v=fkGAF5jHjdY
k sine omega t
$k\sin\omega t$
https://www.youtube.com/watch?v=fkGAF5jHjdY
cosine omega t plus three sine omega t
$\cos\omega t+3\sin\omega t$
https://www.youtube.com/watch?v=fkGAF5jHjdY
plus minus three omega cosine omega t
$\pm3\omega\cos\omega t$
https://www.youtube.com/watch?v=fkGAF5jHjdY
exponential of minus three t
$\exp(-3t)$
https://www.youtube.com/watch?v=XbiEUwVQqVM
8 root 4 minus 5i
$8\sqrt{4}-5{i}$
https://www.youtube.com/watch?v=XbiEUwVQqVM
root 4 plus or minus 5i
$\mathrm{\sqrt{4}}\pm5i$
https://www.youtube.com/watch?v=XbiEUwVQqVM
e 4t cosine 5t
$\displaystyle e^{4t}\cos(5t)$
https://www.youtube.com/watch?v=XbiEUwVQqVM
C1 exponential lambda 1 plus C2 exponential lambda 2
$\displaystyle C_{1}\exp(\lambda_{1})+C_{2}\exp(\lambda_{2})$
https://www.youtube.com/watch?v=2-5oq-igwtU
x dot of 0 equals to 0
$\dot{x}(0)={0}$
https://www.youtube.com/watch?v=2-5oq-igwtU
lambda1 c1 plus lambda2 c2 equals to 0
$\lambda_{1}C_{1}+\lambda_{2}C_{2}=0$
https://www.youtube.com/watch?v=2-5oq-igwtU
log of minus c2 over c1
$\log{((-c_{2})/{c_{1}})}$
https://www.youtube.com/watch?v=2-5oq-igwtU
minus c2 over c1 is less than 1
$-\frac{c2}{c1}<1$
https://www.youtube.com/watch?v=2-5oq-igwtU
P D equals D squared plus 4i
$P(D)=D^{2}+4i$
https://www.youtube.com/watch?v=RzaB0t9dx0A
x dot dot plus 4x equal f0
$x\ddot{x}+4x=f0$
https://www.youtube.com/watch?v=RzaB0t9dx0A
s squared plus 4
$(s^{2}+4)$
https://www.youtube.com/watch?v=RzaB0t9dx0A
s squared equal minus 4
$s^{2}=-4$
https://www.youtube.com/watch?v=RzaB0t9dx0A
4 minus omega squared
$4-\omega^{2}$
https://www.youtube.com/watch?v=RzaB0t9dx0A
exponential i omega t
$\exp(i\omega t)$
https://www.youtube.com/watch?v=RzaB0t9dx0A
omega equals to 2t
$\omega\mathrm{=}2\mathrm{t}$
https://www.youtube.com/watch?v=RzaB0t9dx0A
delta t minus 2 exponential of t squared sine t cos 2t
$\delta(t-2)\exp(t^{2})\sin t\cos 2t$
https://www.youtube.com/watch?v=q0PxCQWG3ic
delta t exponential of t squared dt
$\delta(t)\exp(t^{2})dt$
https://www.youtube.com/watch?v=q0PxCQWG3ic
3u t minus 2u t minus 1
$3u(t)-2u(t-1)$
https://www.youtube.com/watch?v=q0PxCQWG3ic
exponential t squared dt
$\exp(t^{2})dt$
https://www.youtube.com/watch?v=q0PxCQWG3ic
4 sine 2 cos 4
$4\sin2\cos4$
https://www.youtube.com/watch?v=q0PxCQWG3ic
f of t equals three u t
$f(t)=3u(t)$
https://www.youtube.com/watch?v=q0PxCQWG3ic
minus two u of t minus one
$-2u(t-1)$
https://www.youtube.com/watch?v=q0PxCQWG3ic
seven x dots plus three x equals f of t
$7x\dot{+}3x=f(t)$
https://www.youtube.com/watch?v=LjqUV6vqwkg
minus 3C1 minus 1 half C2 equals to 0
$-3C_{1}-\frac{1}{2}C_{2}=0$
https://www.youtube.com/watch?v=LjqUV6vqwkg
C2 exponential minus one half t minus exponential minus three t
$\displaystyle {C_2}(\exp(-\frac{1}{2}t)-\exp(-3t))$
https://www.youtube.com/watch?v=LjqUV6vqwkg
c1 equals minus 2
$\mathrm{c_1}=-2$
https://www.youtube.com/watch?v=LjqUV6vqwkg
one minus exponential of minus two t
$1-\exp(-2t)$
https://www.youtube.com/watch?v=LjqUV6vqwkg
i squared equals negative one
$i^{2}=-1$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
a squared plus b squared
$a^{2}+b^{2}$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
two plus i divided by one minus 3i
$\frac{2+i}{1-3i}$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
one squared plus three squared
$1^{2}+3^{2}$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
r cosine theta plus i times r sine theta
$r\cos\theta+i\times r\sin\theta$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
a to the x times a to the y equals a to the x plus y
$a^{x}\times a^{y}=a^{x+y}$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
dy dt equals a times y
$\frac{dy}{dt}=ay$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
e to the i theta two
$e^{i\theta_{2}}$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
sine of theta one plus theta two
$\sin(\theta_{1}+\theta_{2})$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
e to the i theta times r2 e to the i theta two
$e^{i\theta}\times r_{2}e^{i\theta_{2}}$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
e to the i theta one plus theta two
$e^{i(\theta_{1}+\theta_{2})}$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
e to the negative x cosine x
$e^{-x}\cos x$
https://www.youtube.com/watch?v=EQJBp6Ym-6A
e to the i omega t divided by two plus three i
$e^{i\omega t}/(2+3i)$
https://www.youtube.com/watch?v=2IBWxERRjvM
e to the i omega t divided by root 13 e to the i phi
$\frac{e^{i\omega t}}{\sqrt{13}e^{i\phi}}$
https://www.youtube.com/watch?v=2IBWxERRjvM
1 over root 13 cosine omega t minus phi
$\displaystyle \frac{1}{\sqrt{13}}\cos(\omega t-\phi)$
https://www.youtube.com/watch?v=2IBWxERRjvM
1 over 13 2 times cosine omega t plus 3 sine omega t
$\displaystyle \frac{1}{13}(2\cos\omega t+3\sin\omega t)$
https://www.youtube.com/watch?v=2IBWxERRjvM
tan inverse 3 over 2
$\tan^{-1}(3/2)$
https://www.youtube.com/watch?v=2IBWxERRjvM
3 pi over 2 omega
$(3\pi/2\omega)$
https://www.youtube.com/watch?v=2IBWxERRjvM
y i minus y hat i
$\mathcal{y}_{i}-\hat{\mathcal{y}}_{i}$
https://www.youtube.com/watch?v=l1kLCrxL9Hk
y prime equals negative y divided by x squared plus y squared
$y^{\prime}=-\frac{y}{x^{2}+y^{2}}$
https://www.youtube.com/watch?v=X5-ucBtneVM
y is equal to negative one over two m
$y=-\frac{1}{2m}$
https://www.youtube.com/watch?v=X5-ucBtneVM
r squared is equal to one over four m squared
$r^{2}=\frac{1}{4m^{2}}$
https://www.youtube.com/watch?v=X5-ucBtneVM
d1 plus d2
$\mathcal{d}_{1}+\mathcal{d}_{2}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
z minus y over n
$\frac{z-y}{n}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
y over n times a half is y over two n
$\frac{y}{n}\times\frac{1}{2}=\frac{y}{2n}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
z minus y over 2n
$z-\frac{y}{2n}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
y over 2n plus z minus y over 2n
$\frac{y}{2n}+z-\frac{y}{2n}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
one half plus one over two n
$\frac{1}{2}+\frac{1}{2n}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
p to the k times 1 minus p to the n minus k power
$p^{k}(1-p)^{n-k}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
2 to the minus n minus k
$2^{-(n-k)}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
2 to the alpha log p over alpha plus 1 minus alpha log 1 minus p over 1 minus alpha times n
$2^{(\alpha \log (\frac{p}{\alpha}) + (1-\alpha) \log (\frac{1-p}{1-\alpha})) \cdot n}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
hundred over square root two pi alpha one minus alpha n
$100/\sqrt{2\pi\alpha(1-\alpha)n}$
https://www.youtube.com/watch?v=MOfhhFaQdjw
1 over square root 2 pi P1 minus Pn
$1/\sqrt{2\pi p(1-p)n}$
https://www.youtube.com/watch?v=MOfhhFaQdjw