# Homework 0: Basics


When buying a light bulb at Home Depot, the colors of the bulb are described in Kelvin as a temperature according to an ideal Black-body Radiator.

(Photo by Suriya Kankliang. Published on 22 March 2016)

What is the peak wavelength associated with the spectral distribution correspond to for the following light bulbs with indicated "temperatures:

1. 1,850 K (Candelight)
2. 2,400 K (Standard US Bulb)
3. 2,700 K (Soft White; CFL)
4. 3,000K (Warm White; CFL)
5. 5,000 K (Tube fluorescent)
6. 6,500K (Daylight)

## Q2: Basic Units

What units are appropriate for each variable?

1. Energy
2. Wavelength
3. Frequency ($$\nu$$)
4. Mass
5. Energy Density
6. Momentum
7. Power
8. Temperature
9. Density

## Q3. Basic Math Review Perform these integrals:

$\int ax^{n}dx$

$\int \dfrac{a}{x}dx$

$\int \sin(ax)dx$

$\int \cos(ax)dx$

$\int e^{ax}dx$

## Q4: Derivatives

Perform these derivatives

$\dfrac{du^{n}}{dx}$

$\dfrac{de^{u}}{dx}$

$\dfrac{d \ln x}{dx}$

$\dfrac{d \sin x}{dx}$

$\dfrac{d \cos x}{dx}$

## Q5: Expansions and Approximations

Expand these for all $$x$$ (e.g. using a Taylor Expansion):

$e^{x}$

$\sin{x}$

$\cos{x}$

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