How to Approach Spivak's Calculus?

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In summary, the individual is seeking advice on how to approach Spivak's challenging math text in preparation for a multivariate Calculus course. The recommendation is to try proving the theorems on their own before consulting the text and to create their own examples to better understand the material. This approach may be slow and challenging, but ultimately beneficial.
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shelovesmath
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So, I've decided I need to do some Calculus reviewing since I haven't been in a Calc class since last fall, and I'm taking multivariate Calculus this fall.

I own a copy of Spivak's calculus, and I know it's supposed to be a challenging math text, but I want to at least try my luck with it. There's nothing at stake.

Any recommendations on how to approach this book? I'm a little intimidated.
 
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shelovesmath said:
So, I've decided I need to do some Calculus reviewing since I haven't been in a Calc class since last fall, and I'm taking multivariate Calculus this fall.

I own a copy of Spivak's calculus, and I know it's supposed to be a challenging math text, but I want to at least try my luck with it. There's nothing at stake.

Any recommendations on how to approach this book? I'm a little intimidated.

Try to prove the theorems yourself without reading them first. Struggle with exercises until you know exactly what it is that you are missing. Then look up what you need in the text. Even start a chapter by going directly to the exercises.

This method is slow and can be painful but worth it.

Make up examples of your own.
 

1. What is Spivak's Calculus and why is it important?

Spivak's Calculus is a textbook written by mathematician Michael Spivak. It covers a rigorous and comprehensive approach to single-variable calculus and is often used as a supplement to traditional calculus courses. It is important because it offers a deeper understanding of the subject and prepares students for more advanced mathematics.

2. Is Spivak's Calculus suitable for beginners?

While Spivak's Calculus is not specifically designed for beginners, it can be used by motivated and dedicated students at the high school or college level. It is recommended to have a strong foundation in algebra and trigonometry before attempting to use this textbook.

3. How does Spivak's Calculus differ from other calculus textbooks?

Spivak's Calculus takes a more rigorous and theoretical approach compared to other textbooks. It places a strong emphasis on proofs and mathematical reasoning, rather than just memorizing formulas and procedures. It also covers topics in more depth and includes challenging exercises for students to practice their skills.

4. What are some tips for studying with Spivak's Calculus?

Some tips for studying with Spivak's Calculus include reading the text carefully and actively, attempting all exercises and seeking help when needed, and reviewing and practicing material frequently. It is also helpful to work through the book with a study group or tutor to discuss and clarify concepts.

5. Is Spivak's Calculus still relevant in today's mathematics?

Yes, Spivak's Calculus is still highly relevant in today's mathematics and is often used as a recommended or supplementary textbook in advanced calculus courses. Its rigorous approach and emphasis on proofs make it a valuable resource for students pursuing higher level mathematics and research in related fields.

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