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Thinker301
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If I read and work through Rudin's PMA or Real Mathematical Analysis by Pugh, what in Spivak's Calculus am I missing? I have learned Calc 1-3 satisfactorily.
Thanks!
Thanks!
Spivak's Calculus is a well-known and widely used textbook for introductory calculus. It covers topics such as limits, derivatives, and integrals. Rudin & Pugh books, on the other hand, are more advanced textbooks that cover real analysis, a more rigorous and theoretical approach to calculus.
Spivak's Calculus is meant to be an introductory textbook for students who are just starting to learn calculus. As such, it does not cover the more advanced topics and theories found in Rudin & Pugh books. These books are typically used for upper-level undergraduate or graduate courses in mathematics.
No, Spivak's Calculus is not meant to be a substitute for Rudin & Pugh books. While it may cover some similar topics, the level of rigor and depth in Rudin & Pugh books is significantly higher. It is important to use the appropriate textbook for the level of mathematics being studied.
No, Rudin & Pugh books are not necessary for understanding calculus. While they may provide a more rigorous and theoretical approach, Spivak's Calculus and other introductory textbooks are sufficient for understanding the fundamental concepts and applications of calculus.
One advantage of using Rudin & Pugh books is that they provide a deeper understanding of the theoretical foundations of calculus. This can be beneficial for students pursuing advanced studies in mathematics or related fields. Additionally, these books often have a more concise and rigorous presentation, making them a good choice for those who prefer a more challenging and in-depth approach.