Question

Can someone suggest me a rigorous Calculus textbook?

Answer 1

intro calc?
SPIVAK is in a class by itself

Answer 2

http://books.google.com/books/about/Calculus.html?id=7JKVu_9InRUC

Answer 3

Rigorous is a dangerous word... :)
Usually rigorous Calculus would mean Analysis ... :) so... be careful ...
Also rigorous may mean "not friendly" ...
My extended book list has around 500 titles ... grouped by various levels and future directions to be followed.
The most direct interpretation of rigorous would be for me "to include all proofs"
Another useful interpretation would be complete (as in proofs, exercises and solutions)

This implies more than one book - perhaps (at least) one with theory and (at least) one with exercises and solutions.
I will give you a list for each category - just some titles which I find to be of good quality - but not exhaustive... just examples ... the levels are also debatable ...
First, a text on Precalculus ...
Fred Safier: "Schaum's Outline of PreCalculus", 2nd Ed. isbn:9780071508643
Then, level 0 of Calculus ...
James Stewart "Single Variable Calculus Concepts and Context 4ed 2010" isbn:9780495559726
James Stewart "Study Guide for Single Variable Calculus Concepts and Contexts 4ed 2010" isbn:9780495560647
Level 1 ... with proofs ...
Richard Beals "Analysis: An Introduction" isbn:0511227744
Richard J. Bagby "Introductory Analysis: A Deeper View of Calculus" isbn:9780120725502
Level 2 ...
Sterling K. Berberian "A First Course in Real Analysis" isbn:9788181282361
Marian Mureşan "A Concrete Approach to Classical Analysis" isbn:9780387789323
Some classics:
Walter Rudin "Principles of Mathematical Analysis" isbn:9780070542358
Tom M. Apostol
N. Bourbaki :)
Isidor Pavlovich Natanson
Edward James McShane
Richard Ernest Bellman
Vladimir Igorevitch Arnold



Some exercise books ...

Asuman G. Aksoy & Mohamed A. Khamsi "A Problem Book in Real Analysis" isbn:9781441912954
George W. Bluman & Paul Richard Halmos "Problem Book for First Year Calculus" isbn:9780387909202
B. P. Demidovich "Problems in Mathematical Analysis" MIR
Wieslawa J. Kaczor & Maria T. Nowak "Problèmes D'analyse: vols I II III" isbn:9782759800865
Isaak Abramovich Maron "Problems in Calculus of One Variable, With Elements of Theory Translated From the Russian by Leonid Levant Revised From the 1970 Russian Ed" MIR
George Polya & Gabor Szegö "Problems and Theorems in Analysis I - Series. Integral Calculus. Theory of Functions" isbn:9783540636403
George Polya & Gabor Szegö "Problems and Theorems in Analysis II - Theory of Functions. Zeros. Polynomials. Determinants. Number Theory. Geometry" isbn:9783540636861

For more specific titles you have to be less ambiguous ... :)

Answer 4

I want something that will make me sweat .I want problems not exercises.I am in tenth grade and I want serious books on analysis not just some collection of theorems and exercises.

Answer 5

You got me and you made me curious ... so ... when you'll find the "serious books on analysis not just some collection of theorems and exercises" please let me know ... I want to read them, too