Thank you very much! I absolutely agree that seeing and learning different approaches is very helpful.micromass said:In my opinion, the most brilliant textbook in calculus is Keisler: https://www.math.wisc.edu/~keisler/calc.html
First of all, it is completely free! It contains about everything one should know about calculus including multivariable calculus, vector calculus and a bit of differential equations.
But a word of warning. This book is truly nonconventional. It deals with calculus the historic way, that is the way that calculus was first done, namely with infinitesimals. In my opinion, this is a superior technique, and it is very useful in physics and math too. But it is not the way that most calculus books deal with things. Now Keisler does treat the standard formalism too, but just be aware that you will see things done quite differently than in other books. In my opinion, seeing things from multiple points of view is beneficial, but some might consider it to be confusing.
micromass said:In my opinion, the most brilliant textbook in calculus is Keisler: https://www.math.wisc.edu/~keisler/calc.html
First of all, it is completely free! It contains about everything one should know about calculus including multivariable calculus, vector calculus and a bit of differential equations.
But a word of warning. This book is truly nonconventional. It deals with calculus the historic way, that is the way that calculus was first done, namely with infinitesimals. In my opinion, this is a superior technique, and it is very useful in physics and math too. But it is not the way that most calculus books deal with things. Now Keisler does treat the standard formalism too, but just be aware that you will see things done quite differently than in other books. In my opinion, seeing things from multiple points of view is beneficial, but some might consider it to be confusing.
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