Could you suggest basic mathematics textbooks (calculus, linear algebra) that are written in an intuitive manner?

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For instance, I really loved reading the book " Div, Grad, Curl, and All That" by H.M.Schey. I would like texts closely written in that particular style.

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One option for an intuitive - yet comprehensive and rigorous - textbook is Stephen Abbott's Understanding Analysis. It is great for students who would like a well-motivated introduction to real analysis that provides good intuition for what is going on. Michael Spivak's Calculus textbook is another analysis-heavy calculus textbook that I think is very intuitive.

If you have an abstract algebra background, I've enjoyed reading through Office Hours with a Geometric Group Theorist - it's a very relaxed tour through the basics of geometric group theory and some neat associated problems, along with a brief group theory refresher.

I'll also second littleO's suggestion of Visual Complex Analysis - if you prefer visual arguments this is a well-known and helpful introduction to basic complex analysis.