How can I fix my understanding of Numerical Analysis?

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I am an undergraduate student taking Numerical Analysis. I’m having a hard time understanding some of the material because it feels as though my instructor is jumping all over the place. When it comes to the applied problems I understand them and can complete them. But when he does a proof in class it’s hard to follow. Now he started giving proofs in the homework and I am getting stuck because I don’t feel I have a good grasp on the theory. To give you an idea of where our class is at, we are covering Secant Method. I took an Introduction to Real Analysis course where we covered up to Uniform Continuity and I felt that I was able to understand the proofs well. This class feels different for some reason. Does anybody have any book recommendations or resources that can make understanding the proofs easier?