Looking for textbook/online resourse

[ducmod]

Homework Statement

Hello!

I would be grateful for recommendations on a truly brilliant, fully explanatory textbook or online resource to learn calculus (with problems sets, etc), including explanations and problems on derivatives, integrals, etc.

Thank you very much!

Homework Equations

The Attempt at a Solution

 

[micromass]

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.

 

[ducmod]

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.

Thank you very much! I absolutely agree that seeing and learning different approaches is very helpful.

 

[ducmod]

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.

Indeed, all books I have encountered previously (not yet helpful, although I have almost read through one of them, to no avail) use the notion of limit; same is used in statistics.

 

[micromass]

Limits are a very important concept. But Keisler certainly covers it and he covers the classical definition of a limit too. So you won't miss out!