I'd like to know which are the best undergraduate calculus books for mathematicians. I'm looking for a complete and rigorous book that allows a Mathematics student to fully understand the undergraduate calculus courses. Is there a better book than Spivak or Apostol ? Which one do you think is the best ?
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1Several honors level (elementary) calculus texts are given in the first answer to Joseph Kitchen's Calculus (reference). – Dave L. Renfro Oct 17 '18 at 19:30
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Thank you very much Dave L. Renfro. – Ludwig Varg Oct 17 '18 at 20:06
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Spivak is aimed at mathematicians, but most others are intended for a broad scientific audience. If you have already taken undergraduate calculus, then it might be time to graduate to an Advanced Calculus/Analysis text. Rosenlicht’s Introduction to Analysis is an approachable textbook.
Joel
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1I should emphasize that Advanced Calculus courses are precisely those courses that aim to put undergraduate calculus in a rigorous framework. – Joel Oct 17 '18 at 19:00
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If you’re going for a standard calculus book, it does not matter. If you’re looking to truly understand the material (at least as much as you can at this level), go for Spivak. It’s a classic, filled with good exercises, and is very challenging. If you work through Spivak at this stage, you’ll be miles ahead of most people. It’ll prepare you well for analysis too.
JDivision
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Calculus, 7th Edition by James Stewart the "one and only" classics
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2I disagree. Stewart is overrated. It’s as good as any other basic calculus book. – JDivision Oct 17 '18 at 19:02
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@JDivision But it's so popular and wildly used that it has become a "standard", plus it has useful topics for most students' needs, range from mechanics to biology, computer science, and finance. etc. – ShoutOutAndCalculate Oct 17 '18 at 19:25
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Thank you for your answer @user9976437 but for now I'm just interested in mathematical applications and a book specifically aimed at mathematicians. – Ludwig Varg Oct 17 '18 at 20:18