Self-Study Math Books for Calculus, Linear Algebra, and Differential Equations

[clarence829]

I'm interested in teaching myself the following subjects:

- Calculus I, II, and III

- Linear Algebra

- Differential equations

The highest math courses I've taken are pre-calculus in high school and business calculus in high school.

What books would you all recommend for learning these subjects on my own?

 

[micromass]

I can recommend highly the books by Serge Lang:

For calculus I and II: https://www.amazon.com/dp/0201041499/?tag=pfamazon01-20
Afterwards, you might want to read a rigorous calculus book. Spivak's calculus is a very good second calculus book: https://www.amazon.com/dp/0914098918/?tag=pfamazon01-20

For calculus III, I think Hubbard is a very good first book: https://www.amazon.com/dp/0130414085/?tag=pfamazon01-20

For linear algebra, I like the books by Friedberg: https://www.amazon.com/dp/0130084514/?tag=pfamazon01-20
and by Lang: https://www.amazon.com/dp/1441930817/?tag=pfamazon01-20

Finally, for differential equations there are a lot of books. If you're more interested in the practicalities then I would suggest Boyce and Diprima: https://www.amazon.com/dp/047003940X/?tag=pfamazon01-20

 

[mathwonk]

to micromass's suggestions i would add martin braun's book on differentila equations and maybe also guterman and nitecki.

 

[muzak]

On a related question, are there books on optimization that you guys could recommend, specifically something related to linear algebra and more on the problem solving side? I've taken the advanced linear algebra courses where we covered most of the topics in the Friedberg book. Perhaps something related to minimizing the work involved in solving the standard Ax = b. Kindly appreciated.

 

[clarence829]

Thank you both for the responses.

Two follow up questions for micromass:

1) Do you think the trigonometry I learned in high-school precalculus will be sufficient to work my way through Lang's Calculus I?

2) Is Spivak's Calculus actually Calculus II?

 

[micromass]

Thank you both for the responses.

Two follow up questions for micromass:

1) Do you think the trigonometry I learned in high-school precalculus will be sufficient to work my way through Lang's Calculus I?

Normally yes. Calculus doesn't use heavy trig. You don't need to be able to derive trig identities and you don't need to work with finding angles in triangles and such. You will have to know some basic formula's, but you can always revise these as necessary.
I've heard that some people start in calculus without any trig knowledge and they still do fine (they will have to learn some things on their own though). This isn't what I would recommend to anybody, but it gives the idea that you should be fine.

2) Is Spivak's Calculus actually Calculus II?

No, Spivak is Calculus I and II. But Spivak is a lot harder than most other calculus books. In reality, it is more of a "intro to real analysis" book than a calculus book. I would not recommend Spivak to somebody who is completely unfamiliar to calculus. But if your goal is to really understand calculus, then Spivak is a must at some time.

Lang is significantly easier (although Lang is certainly not dumbed down), as it doesn't go into epsilon-delta stuff.

 

[clarence829]

One of my friend's has Stewart's Calculus. Should I save the money and use his textbook or is it worth the money to track down a used copy of Lang's?

 

[theorem4.5.9]

Stewart's calculus is pretty common text to use for calc I-III in university. In a lot of ways it has a high school feel to it, with most of the learning done through examples. This may be good if that's what you're use to. You can't really go wrong with any calc text, so I suggest reading a chapter or so of a few different books and stick with the one you think is the easiest to read.