I hope this question hasn't been asked 1000 times before:

Can someone recommend a good book on calculus such that:

1) It covers linear algebra (or maybe how to connect lin.algebra with calculus - the only connection in my head is Jacobian - but i can only use it as a monkey - by applying)

2) It covers the topics of calculus used in statistics (esp. bayesian analysis)

3) Covers stuff like Laplace transform (need to understand wiki references to MGFs) and maybe Fourier - used in machine learning for vision, hearing, etc.

4) Can be gradually increasing difficulty - i dont write many proofs (never did sigma-proofs) and generally prefer intuitive approach, but am looking for formal explanations too, so both approaches in the text are valued.

5) Has some instruction set on which exercises to do after each chapter (i have limited time and would like to do the exercises that reinforce the topic, and are not puzzles for advanced minds)

6) My particular intention is understanding advanced proofs in probability and statistics, and as a bonus it is always good to understand calculus per se (but not too much - i dont really need such advanced things as topology, analysis or sth like that - even though im not sure what those subjects are - except they are continuation of calculus, though maths rigor is good and welcomed), because it is literally the cornerstone of all mathematics and improves brain function =)

My background:

1) Calculus 1-2 at the uni. Had multivariable calculus (gradients, double-triple integrals, stokes, green - last topics) with Adams textbook (that from my points of view jumps too much without leaving 1 picture in my mind - but it might be only me). I think i understand well differentiation but my integration skills are not that good and i dont really know well what all transforms are, i'm bad with sequences and series, and i don't need vector integration - i intend to use my skills to understand stats and machine learning so everything until vector calculus will do fine. I know nothing (except basics) about complex numbers (like i^2 = -1).

2) self taught Gilbert Strang and Philip N. Klein linear algebra up to SVD both of which i liked very much.

3) Reading on intro to probability by Blitzstein that I like very much myself

4) Also watched MIT lectures on multivariable calculus myself and liked them too.

I have browsed questions in here and 3 books that appear everywhere are - Apostol, Spivak, Courant. But Everyone says they are too difficult. Im not sure im ready for those, though I took a glimpse at Apostol - i like him starting from integration because that's my weak spot. Though these books are huge and they require a lot of time - and id like to be able to do 1 book per 6 months possibly in not a very fast tempo. Also, id like to know which exercises to do in those to enforce knowledge. The particular reason im asking this quest is that if I start with the wrong book i might have to start over with another one so id like to hear more recommendations.

So, in the light of above facts - can someone suggest maybe some book? Or just give some recommendation. I guess this question might pop up for many stats students or cs students that would like to improve their knowledge of calculus, but are not aimed at becoming mathematicians.


James Stewart's Calculus: Early Transcendentals is nice. It covers all of calc 1, 2, and 3. And contains a basic review of linear algebra as well.


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