# Homework 0: Basics

- Page ID
- 143055

## Q1: Black Body Radiators

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:

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

## Q2: Basic Units

What units are appropriate for each variable?

- Energy
- Wavelength
- Frequency (\(\nu\))
- Mass
- Energy Density
- Momentum
- Power
- Temperature
- 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):

\[ e^{x} \]

\[ \sin{x} \]

\[ \cos{x} \]