Mathematical analysis (Book recommendation)

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A first-year physics student is struggling with mathematical analysis and seeks beginner-friendly book recommendations to better understand concepts like definite integrals and Cauchy sequences. They find the recommended texts from professors too advanced and express a need for clearer explanations. Suggestions include Fichtenholz, Rudin's "Principles of Mathematical Analysis," and Thomson and Bruckner's book, which is praised as an excellent introductory resource available in print and as a free PDF. Abbott's work is also recommended as a good choice for beginners. The student appreciates the suggestions and finds them potentially useful.
Motivanka
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I don't know is this good place to put this topic anyway I am on the first year of physics and I am struggling with mathematical analysis. I can't understand a lot of thngs that we are doing actually I can't even follow our lectures. I would be really grateful if someone recommend me a book that has fundamentals of math analysis and it is really good explained. All these books that were recommended by our professors are on really high level, it would be really great if there is a book that is for beginners os something like that.
 
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What exactly do you mean by mathematical analysis? Is there a specific problem to which you are trying to apply the technique?
 
To be more determined what I don't understand is theory. For example today we were doing " Definite integral of Darboux sum " and I couldn't follow, but in the last semester we were doing for example cauchy sequence and convergence,bolzano weierstrass theorem and these sequences and sums killed me :D I don't understand concept of theory, I don't know how to be more clearer.
 
I can tell you a few names. Fichtenholz and Rudin.

I am not sure if Fichtenholz's work is translated into English - I have the collection in Russian.

Not familiar with Rudin's work myself, but I hear his "Principles of mathematical analysis" is top-shelf material.
 

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