Courant's Introduction to Calculus place on roadmap

[renox]

Recently, knowing that I don't understand a lot of geometry and trigonometry stuff finally pissed me off, so I started re-learning math from scratch. Surprisingly, I found myself interested in discovering how all those things work and what they actually mean. Now I got a reading plan, but still have some questions about calculus. I studied it in high school and had a course in university, but was only good at calculating derivatives.

From what I've read here, it seems like starting with these books:

• "Calculus: The Elements" by Comenetz
• "Calculus and Analytic Geometry (9th Edition)" by Thomas, Finney

and continuing with:

• "Calculus" by Spivak

would be a good choice.

But I'm having a hard time working out Courant's "Introduction to Calculus" place here. Should it be in the beginner's part of list or right after it? Is it worthwhile reading just 1st vol. (or a whole series) considering I'm definitely going to read those three books I mentioned above?

Also, do you think Comenetz and Thomas will provide enough background for such linear algebra books as:

• "Linear algebra" by Friedberg, Insel, Spence
• "Linear algebra" by Serge Lang
• "Linear algebra" by Hoffman, Kunze

or should I wait until I master Spivak?

 

[verty]

Recently, knowing that I don't understand a lot of geometry and trigonometry stuff finally pissed me off, so I started re-learning math from scratch. Surprisingly, I found myself interested in discovering how all those things work and what they actually mean. Now I got a reading plan, but still have some questions about calculus. I studied it in high school and had a course in university, but was only good at calculating derivatives.

From what I've read here, it seems like starting with these books:

• "Calculus: The Elements" by Comenetz
• "Calculus and Analytic Geometry (9th Edition)" by Thomas, Finney

and continuing with:

• "Calculus" by Spivak

would be a good choice.

But I'm having a hard time working out Courant's "Introduction to Calculus" place here. Should it be in the beginner's part of list or right after it? Is it worthwhile reading just 1st vol. (or a whole series) considering I'm definitely going to read those three books I mentioned above?

Also, do you think Comenetz and Thomas will provide enough background for such linear algebra books as:

• "Linear algebra" by Friedberg, Insel, Spence
• "Linear algebra" by Serge Lang
• "Linear algebra" by Hoffman, Kunze

or should I wait until I master Spivak?

Will you be getting that Thomas & Finney book? If so, you need no other book to learn calculus. It'll certainly cover everything you need to know for those books you list. That said, you could get an even more thorough book, this one:

https://www.amazon.com/dp/0130937002/?tag=pfamazon01-20

This would include linear algebra and some differential equation content as well. So either of these would be sufficient.

Calculus by Spivak you should choose if you know calculus pretty well and want to see it developed in the pure math style, or if you want to be challenged. So that should come after one of the two books I mentioned.

Courant's usual calculus book, which you can find https://archive.org/details/DifferentialIntegralCalculusVolI (volume 2 is also available), is similar in style to Spivak, you can look at that as well. Possibly, Spivak is slightly easier if you ignore the harder questions in it.

I think, however, that you are asking about the book "Introduction to Calculus and Analysis (vol 1)" by Courant and Fritz John. From the little I can see of it, it seems to be written for younger readers, it is more wordy in the beginning. That said, Fritz John writes a PDE book that is rather terse, and of course Courant is a highly terse writer as well, so although the book starts out being wordy, I have no doubt that it'll become terse later. So without knowing much about it, I would have to place it at the level of Spivak in your schema.

 

[micromass]

Recently, knowing that I don't understand a lot of geometry and trigonometry stuff finally pissed me off, so I started re-learning math from scratch. Surprisingly, I found myself interested in discovering how all those things work and what they actually mean. Now I got a reading plan, but still have some questions about calculus. I studied it in high school and had a course in university, but was only good at calculating derivatives.

From what I've read here, it seems like starting with these books:

• "Calculus: The Elements" by Comenetz
• "Calculus and Analytic Geometry (9th Edition)" by Thomas, Finney

and continuing with:

• "Calculus" by Spivak

would be a good choice.

But I'm having a hard time working out Courant's "Introduction to Calculus" place here. Should it be in the beginner's part of list or right after it? Is it worthwhile reading just 1st vol. (or a whole series) considering I'm definitely going to read those three books I mentioned above?

If you've read those three books, then Courant is unnecessary.

Also, do you think Comenetz and Thomas will provide enough background for such linear algebra books as:

• "Linear algebra" by Friedberg, Insel, Spence
• "Linear algebra" by Serge Lang
• "Linear algebra" by Hoffman, Kunze

or should I wait until I master Spivak?

No, you don't need Spivak for those three books. You don't really need any calculus to read those books. If you're comfortable with solving linear systems and multiplication of matrices, then you can read those books immediately. Some exercises will make use of calculus, but those will not be essential, so you can skip those.

 

[verty]

It would be so nice to be able to learn like the characters in the movie The Matrix, they just download knowledge into their brains somehow. Then one could read many, many books for each subject. But as it is, one or two should be enough.

Choose a book that has a style that you like, and possibly choose a supplementary book that uses a different, complementary format. Perhaps it is more rigorous, perhaps it goes further. But more than two is overkill, I think.

 

[rezeew]

I would say that your approach to re-learning math from scratch is commendable. It is important to have a solid understanding of the fundamentals before moving on to more advanced topics like calculus.

As for your question about Courant's "Introduction to Calculus," it is a highly regarded and comprehensive book on the subject. It covers both single and multivariable calculus, making it a good choice for someone who wants a more thorough understanding of the subject. However, it may be more beneficial to read it after you have completed the other books you mentioned, as it may be more challenging for a beginner.

In terms of linear algebra, Comenetz and Thomas will likely provide enough background for the books you mentioned. However, it may be helpful to have a strong understanding of calculus before delving into linear algebra, as many concepts in linear algebra are built upon calculus.

Overall, it is important to have a well-rounded understanding of math, and the books you have chosen seem like a good starting point. As you continue to learn and progress, you may find that certain topics or books are more beneficial for your understanding than others. Keep an open mind and don't be afraid to explore different resources to find what works best for you.