# Calculus Made Easy and then Courant/Spivak?

• emtakis
In summary, if you are looking to move on to books such as Courant and Spivak, you will need to have some basic knowledge of algebra II and trigonometry.
emtakis
For the past year, I have self-study math, algebra I/II, geometry. I've just gone through a few books covering trigonometry, and now I want to move on to calculus.

If I was to learn from Calculus Made Easy, will I be able to move on to books such as Courant and Spivak? I hear from reading several threads on here that says the two author focuses more on theory - the why's? So should I pick up Calculus Made Easy by Silvanus Phillips and Calculus by Michael Spivak/Differential and Integral Calculus by Richard Courant. Or is there more I'll have to know after Trigonometry and before Calculus?

Will I know enough after Calculus Made Easy to understand Courant/Spivak's book? I also plan to find some kind of supplemental material to help me along Courant/Spivak's. Like schaum's outline of calculus or something similar.

Thank you,
Sikat

I'm self studying calc. right now as well, out of Kline's book, mainly.

The Phillips book will give you the principles, but from what I've seen in it (Going off Google Book's and Amazon's previews), it seems like a bit of a jump if you dive right into Spivak or Courant afterwards.

Make sure you've got algebra II and trig down pretty solid before moving on to calc, your efficiency in calculus will be dependent upon those two. Maybe go down to a library or something similar and look through some pre-calc texts to make sure you've got the prereqs. down.

Proofs are fairly essential as well, that's what I struggle most with.

Also, MIT has a bunch of calculus lectures available on youtube (Search for MIT OCW 18.01). They're pretty nice to have alongside a book.

Good videos:

http://press.princeton.edu/video/banner/

you can try for yourself about spivak book ,i have been reading this book ..for about 1 week ,just finish 2 chapter .. nice reading by the way ,and i love how spivak explain the topic ,its very detail ..but the problem is very HARD

I would say that if you're worried about prerequisite knowledge for Spivak, it's not calculus that you really need (Spivak introduces calculus from first principles), it should be logic and proof that you really need to work on.

Spivak blends computational problems -- ones that you're used to from grade school, problems that end in numbers for answers -- with conceptual and proof-based problems, which are the heart of the book. He mentions in his bibliography that he has borrowed problems from Baby Rudin, an analysis book.

It's perhaps a different type of textbook then you have probably seen before. If read right, you should spend just as much time reading the section and trying to prove the theorems on your own before attempting the problem section.

If you plan on taking higher math courses after calculus or majoring in math in the future, I would recommend starting with Spivak. It's a basic analysis text, which means you will be learning calculus through a bottom-up approach, starting from the axioms of the real numbers (well, most of them). It's definitely hard, since Spivak expects the text to be the reader's first encounter with rigorous mathematics in general. I would recommend learning a little set theory beforehand (look up naive set theory on wikipedia) and some proof-writing articles (do a search on this forum, here is the thread that helped me a lot: https://www.physicsforums.com/showthread.php?t=166996). Of course Spivak doesn't assume you know everything about proof-writing since you'll develop these skills as you work through the text, but you should learn the basics.

If you just want to understand the basics of calculus without worrying too much about the theory, I would recommend Lang's First Course in Calculus. The standard text is Stewart, but Lang is exceptionally clear and concise. He builds the intuition for the subject, but also proves the fundamental results in calculus. The more theoretical aspects of calculus are usually relegated to the appendix.

## 1. What is "Calculus Made Easy and then Courant/Spivak"?

"Calculus Made Easy and then Courant/Spivak" refers to two popular calculus textbooks. "Calculus Made Easy" was written by Silvanus P. Thompson and is known for its accessible and intuitive approach to teaching calculus. "Courant/Spivak" refers to the two authors of the textbook "Calculus" - Richard Courant and John Spivak. This textbook is known for its rigorous and comprehensive treatment of calculus.

## 2. Who are the target audiences for these textbooks?

"Calculus Made Easy" is aimed at students who are new to calculus, while "Courant/Spivak" is geared towards more advanced students and those who want a deeper understanding of the subject. Both textbooks are suitable for high school and college students.

## 3. What makes these textbooks stand out from other calculus textbooks?

"Calculus Made Easy" is known for its conversational and easy-to-understand writing style, making it a popular choice for students who struggle with traditional calculus textbooks. "Courant/Spivak" is known for its rigorous and comprehensive approach, with a focus on developing mathematical intuition and problem-solving skills.

## 4. Do these textbooks cover the same topics?

Both textbooks cover the core topics of calculus, such as limits, derivatives, and integrals. However, "Courant/Spivak" also covers more advanced topics, such as multivariable calculus and differential equations.

## 5. Which textbook should I choose for learning calculus?

The choice between "Calculus Made Easy" and "Courant/Spivak" ultimately depends on your learning style and level of understanding. If you prefer a more intuitive and easy-to-understand approach, "Calculus Made Easy" may be a better choice. If you want a more rigorous and comprehensive understanding of calculus, "Courant/Spivak" may be a better fit.

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