Easy proof of Black-Scholes option pricing formula

Question

I use this Book to read the option pricing in Black-Scholes model in pages 93-99, The proof of the formula given by $$c(s,t)= N(d_1(s,t)- Ke^{-rT}N(d_2(s,t)))$$ where $$d_{1,2}=\frac{\ln(s/K)+(r\pm \frac{1}{2}\sigma^2)t}{\sigma \sqrt{t}},$$ seem for me more long to read. Where do I find a short demonstration with adequate assumptions?