I recently finished courses that covered op amps, capacitors, and inductors.

I learned how to calculate the gain of an ideal op amp using nodal equations.
I learned how to write transfer functions in circuits with capacitors and inductors by writing nodal equations in S-domain.
I learned how to determine what type of filter the circuit is from the transfer function.

I want to create an audio amplifier for mp3 player that will power a small speaker.

I started simple and created a simple op amp. The circuit is attached. The circuit gets louder as R2 > R1 but there is a lot of distortion. The course I took at my university so far taught how to analyze a circuit and write equations, but I have no experience the other way around (i.e to design one).

What would I need to do to make the output sound less distorted. I know I would probably need a capacitor or inductor somewhere but how do I know where to put it? And I'm guessing the next step would be to write a transfer function and solve for the component value?

 

What would I need to do to make the output sound less distorted

The understanding that an op amp can't drive a speaker. An op amp's output impedance is probably 100 Ohms and you are trying to drive a load which is probably 8 Ohms or 4 Ohms. Can't work.

Power amps that drive speakers have an output impedance om maybe a tenth of an Ohm.

 

As bounty said , a normal OP amp can't provide enough current to drive an 8 ohm speaker. Try putting a 30--80 ohm resistor in series with the speaker depending on your voltage. It will be playing at a much lower volume but undistorted

 

Use an LM386 or TDA2040 amp

 

Unfortunately, they don't seem to teach how to read a data sheet in school. If you look at that for the 741 you will see that it can typically deliver only a few mA into a load. You need an audio amp, such as Dodgydave suggested.

 

Here is a simple little amplifier that I built some time ago, and I am still using in my truck. See post number 4 for the schematic and photo.

http://forum.allaboutcircuits.com/showthread.php?t=62896