I need Calculus book that suits my level. (Or at least primary book which I will follow more closely)
I don't have much formal education but have recently read Lang's Basic Mathematics (cover to cover, doing all almost all of the exercises).
In my search for books I found:
Spivak – Calculus
Apostol – Calculus 1 and 2
Courant – Introduction to Calculus and Analysis vol 1 and 2
Lang – First Course in Calculus
I found info about the other books, and it seems that Apostol's Calculus will be best suited for self learner and covers more than Spivak (also gives some applications), while Courant covers even more than Apostol but has less and harder problems.
I have read a little bit (about derivatives, limits) of Lang's book and it's quite easy to follow.
So, where Lang's book stays? Are the other books too advanced for me?
Which book I should use as primary text if time is a concern and I want to cover more things? (Sorry if that's too many questions)
Thanks.
EDIT:
There is a thing in the college I want to go called "Mathematics and Informatics" (that's in Eastern Europe).
I'm kind of in hurry because I want to get in college and I have the chance to skip the first year if I know enough. (first year is mostly C++, Calculus and little bit of Linear Algebra and I already know enough C++)
So if I'm to skip the first year I should be ready for the Mathematical Optimization, Discrete Math, Differential Equations, Information theory (IDK if I translate correctly). All of these are intro level.
I have around 6-7 months before I try to get the exams. And little bit more before I eventually start college.
BTW, Basic Mathematics was quite challenging and there have been some exercises that got me to look at the back of the book for solutions or search on the internet. Don't wanna make it sound like I've done 100% of them (someone in my situation my get discouraged after reading this), but I tried.
Best Answer
You ask an interesting question.
First: working through Lang's Basic Mathematics on your own and doing all the exercises is an impressive feat for someone with little formal education (in mathematics).
All four of the calculus texts you ask about are more difficult than the average text, but you should be able to manage any of them. Any of them will give you a good foundation for further study.
I know Courant and Spivak reasonably well, Apostol and Lang only by reputation and reviews. Courant is a classic. It will give you the best sense of the depth and usefulness of calculus, and how to think about mathematics. Spivak is probably the most thoughtfully rigorous. I think Apostol would be the most thorough, touching just about anything that might appear in any calculus curriculum. Lang will be straightforward, but not encyclopedic.
You don't say why you are in a hurry, or where you want to go next (more reading? back to school?).
I would suggest that you spend some time working through the first chapter or so of each - I think you can see that material on line. Then decide which suits your learning style best. You might want to study from two of the books, so you can compare the approaches and learn from two views.
Good luck.
Edit in response to the edit.
In six or seven months you should be able to prepare yourself for that exam.
Optimization might require some knowledge of multivariable calculus and linear algebra. That's in the second volume of Apostol, maybe a bit in Courant.
I don't usually recommend studying toward a particular exam, but if you can find old copies of the one you have to take you'll have a little more information on what to be sure to think about.
Is there someone at the school you can talk to now about optimizing your chances for admission?