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At the moment I am a TA for a second semester Bachelor's class and in the lecture we treat differential calculus in Banach spaces. Some of my students asked for another reference (beside the lecture notes) and I am a bit at loss. Of course there are plenty of texts treating this, however, none I know (e.g. Ambrosetti/Prodi) is suitable for second semester students (I guess Cartan's book is the closest thing I am aware of). In case you have any suggestions, I would be really happy to hear them.

I am aware that there is the following question (Reference Request) Calculus on Banach Spaces, but the references listed are not really suitable for second semester students.

Severin Schraven
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1 Answers1

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I would highly recommend Lang's book "Real and Functional Analysis". It's mentioned in the OP of the page you linked, so I'm not sure if you consider it too advanced, but the nice thing about the book is that it keeps its different topics separate, so that they can be read independently. The chapters on calculus in Banach spaces are the best I've ever seen on the topic, and assume nothing but basic knowledge of Banach spaces, which your students presumably already have.

Yly
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  • Honestly, I did not check it before (the Functional Analysis already crushed my hopes from the beginning). Indeed, it is very clear! The only issue is that there are essentially no examples. But otherwise I like it (+1). I'll keep the question open and if there is no better alternative I'll accept your answer. – Severin Schraven Apr 27 '20 at 19:54