How does Atticus's courage change throughout the book ?
A more appropriate question is, "How does Scout's understanding of Atticus's courage change?" Atticus is not a dynamic character; he is essentially the same person at the end of the novel as he was at the beginning. But he changes the lives of others - notably Scout and Jem. As the novel progresses, our understanding of Atticus increases through Scout's narration. She learns what a deeply principled and courageous person he is, as she learns that there are different forms of courage. Can you trace Scout's growing understanding of her father?
Honestly, strictly speaking, I don't think his courage changes at all. Look at how he faced down the rabid dog, and how calm he was. He faced the courtroom, or the pack of men in the night, the same way. However, if we look at how it manifests, we can name a major difference: his courage, and his entire character, goes from latent and private to active and public. He stands up to and in some ways for his entire community, rather than keeping his soul under wraps.