I’m taking an introductory real analysis course now (though I’m much more advanced than any previous courses I took in calculus) and I’ve already finished about half the course. I’ve found my studies make it easier to understand but I’m still having trouble with understanding through all those exercises and such. I do understand the basics of variables, arithmetic and geometry, but I have no idea what it means to have a derivative in terms of a limit of a function. I’m basically afraid I won’t understand at all when I get to the tricky parts. Almost all of the textbooks I’m finding are extremely dense and I just need something that’s understandable but includes exercises.
I really just want to learn this material! In my previous courses I spent not only a semester, but also many hours, doing homework and studying for the final. It is very frustrating to find the time to do homework, and not have the material to back up those hours. At the start of the year I was a complete burnout, but I am nearing the end of the year, still not really confident in my knowledge of calculus. I have withdrawn from a few courses because I knew I would be at a complete loss when I faced a problem, and now I am really worried there is absolutely no chance I can pass this course (my tutor has even pointed it out).
A website that I use a lot is Complex Analysis by Katkov . He is an extremely knowledgeable mathematician who wrote a very complete and in-depth introduction to complex analysis. His approach to the subject is perhaps more complex than Rudin, but in a much more intuitive fashion. 7211a4ac4a