수학, 과학에서 사용되는 기호 및 영어 공식 표현 : 문서

2. Mathematical Symbols and Equations: 수학 기호 및 공식
• ab “a multiplied by b” or “ab”
• a2 “a squared”
• b3 “b cubed”
• (a+b) 2 = a 2+2ab+b 2
“The sum of a plus b squared equals a squared plus two ab plus b squared”
• + =
“a over b plus c over d equals open parenthesis ad plus bc close parenthesis over bd”
“a over b plus c over d equals the sum of ad plus bc over bd”
• “Ten to the minus nth power equals one over ten to the nth power”
• “Ten to the fifth power over ten to the seventh power equals ten to the minus
second power”
• x a x b = x (a + b) “x to the a multiplied by x to the b equals x to the a plus b”
• x a y a = (xy) a “x to the a multiplied by y to the a equals open parenthesis xy close
parenthesis to the a”
• (x a) b = x (ab) “open parenthesis x to the a close parenthesis to the b equals x to the ab”
the
• logb(1) = 0 “log b of one equals 0”
• logb(b) = 1 “log b of b equals 1”
• log39=2 “log 3 of 9 equals 2”
• log255=0.5 “log 25 of 5 equals zero point five”
• logb(xy) = logb(x) + logb(y) “log b of xy equals log b of x plus log b of y”
• sin(x + y) = sin(x)cos(y) + cos(x)sin(y) “sine of x plus y equals sine of x cosine of y plus
cosine of x sine of y”

3. Scientific Symbols and Equations: 과학 기호 및 공식
• Density = _____Mass (g)___
Volume (cm3)
D=m/v
“Density equals mass in grams over volume in centimeters cubed
Density cubed”
“D equals m over v”
• Speed = ____Distance_(m)___
Time (s)
S=d/t
“Speed equals distance in meters over time in seconds
seconds”
“S equals d over t”
• Force = Mass(kg) x Acceleration(m/ 2)
Acceleration(m/sec
F=ma
“Force equals mass in kilograms times acceleration in meters over second squared
Force squared”
“F equals ma”
• Ohm’s Law
Amperes(current) = ____Volts____
Ohms(resistance)
Ohms(resistance
I=V/R
“Ohm’s Law states that amperes equals volts over ohms
s ohms”
“I equals V over R”
• Kinetic Energy
Ek= kinetic energy of object
m = mass of object
v= speed of object
“Kinetic Energy equation states that Ek equals one half m v-squared,
Kinetic
where Ek equals kinetic energy of the object; m, mass of the object; and v, speed of the
object”
• This is a calculus-based class and I expect everyone to know at least the rudiments of
based
differential calculus. What's a function, what's a derivative, what's a second derivative how
. derivative,
to take derivatives of elementary functions, how to do elementary integrals
integrals.

4. • Newtonian mechanics is our first topic. Newtonian mechanics has two parts. The plan is to
predict the future given the present. That's what we always do. So the question is, "What do
you mean by the future? What do you mean by the present?
• Now what is the kinetic energy that you're summing up over each particle? It's ½mv2. Has
everybody seen this before? Okay, so that's the sum of classical kinetic energy over all the
particles of interest in the problem.
• How does sin(ax) look different from sin(x)? Suppose it's sin(2x). Here's sin(x). How does
sin(2x) look? It has a shorter wavelength.
• Typically the atoms are vibrating by about 0.05 angstroms in the crystal. When they're in
their lowest possible energy state they vibrate by that much, right?
• We have here the (Z/a0)3/2; √2/2; and e(-ρ/2). When you square it, what are you going to get,
for e (-ρ/2)? What is e(-ρ/2) squared?

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