I'm a professional programmer by day, and audio tinkerer by night. My main job is writing high-performance computer graphics software for the feature film industry, specializing in high-end rendering technology, but I've written a LOT of DSP code as of the last few years, including quite a few "good" VST plug-in implementations that simulate analog devices.
I can direct you to my list of audio-related DSP resources, but you'll need a lot of practice to get it right.
To start at the very basics, there is a great treatment of deriving a 6dB low pass filter from an analog base circuit here:
http://en.wikipedia.org/wiki/Low_pass_filter - however it's a rubbish filter with a quite poor high-frequency response and it will alias quite badly depending on the situation of it's use and want you want out of it, but it's fast, simple and sometimes that's more important.
To build REALLY good audio code is incredibly hard, and, outside the scope of a huge number of people. Without assuming your background ( on this forum it's generally safe to assume you are replying to a crazy genius ) the math is not exactly simple, and you need to really have a good understanding of FFT's, FIR and IIR filters, oversampling/undersampling, resampling filters etc. etc. to even have a vague change of being able to write a DAW of any particular level. If you don't know what any of that means, get on that Google and search!
For a DAW, the most important thing is the performance of the GUI and the audio engine together and the threading techniques you will use to get accurate synchronization and priority to the sound, which is more important than the GUI.
There are some open source audio plug-in databases out there, but I haven't found one that I REALLY like - you could start with something like synth-edit
http://www.synthedit.com ( although I wouldn't, I prefer learning everything from first principles ), or
http://www.portaudio.com/,
http://clam-project.org/,
http://code.google.com/p/dspfilterscpp/, etc. etc. etc.
However it's really not a plug and play exercise. For instance I got a 35 times speed up by hand writing my core code directly in SSE2 assembler on PC. I also have a 3-line implementation of an accurate sine-wave generator that's unconditionally stable along with a few band-limited saw and square-wave implementations, but they are REALLY hard to do well.
GOOD digital audio is a science that few, if any, current producers of audio plug-ins have got "right" imo, cause doing it "right" costs a lot in CPU, smears in the time-domain, and, quite simply, doesn't sound as good as analog can given the same input data.
However, I wish you luck with it, cause it'll be ONE HELL of an undertaking.
However long you estimate, multiply that by 10 times at least and quote that.
However if you are determined you'll do it I'm sure - but keep us updated!