Stage 2 Calculus

Calculus (Introductory Real Analysis, Several Variables Calculus, Vector Calculus, etc):
Learn the very basic concept of real analysis, like open set, close set, boundary point, closure, limit point, bounded set, connected set, compact set, Bolzano-Weierstrass theorem. To get yourself ready for the stage 3 analysis, make sure you understand those stuff. Next, the Lagrange multiplier, inverse and implicit function theorems can also be studied. For the several variables section, gradients, double, triple and surface integrals, cylindrical coordinates, Green's theorem and divergence theorem are the key things. Also learn basic Fourier series.

• Apostol T.M. Calculus Vol. 2
• Bartle R.G. The Elements of Real Analysis
• Cain C. and Herod J. Multivariable Calculus (FREE!)
• Chen W.W.L. Fundamentals of Analysis (FREE!)
• Chen W.W.L. Multivariable and Vector Analysis (FREE!)
• Courant R. and John F. Introduction to Calculus and Analysis II/1, II/2 - If you want to get one several variables calculus text. (here and here for FREE!)
  
• Dawkins P. Calculus III (FREE!)
• Demidovich B.P. Problems in Mathematical Analysis
• Gaughan E.D. Introduction to Analysis - Expensive. Have a look in the library.
• Ikenaga B. Calculus Notes (FREE!)
• Kaplan W. Advanced Calculus
• Krantz S.G. Real Analysis and Foundations - The author is a fan of Rudin and he was trying to bridge between less rigorousX books and hard-edged classical books like baby Rudin.
• Keisler H.J. Elementary Calculus: An Approach Using Infinitesimals (FREE!) - Check it out, can you believe it's free?
• Lewin J. An Interactive Introduction to Mathematical Analysis - Come with a CD-ROM. Very friendly, aimed particularly for non-mathematicians who need to study this hardest ever course (the author means analysis) in their life.
• Protter M.H. Basic Elements of Real Analysis
• Rosenlicht M. Introduction to Analysis
• Santos D. Vector Calculus Notes [.pdf] (FREE!)
• Shilov G.E. Elementary Real and Complex Analysis - Republication of Mathematical Analysis Vol. I, MIT Press, Cambridge, Mass.
• Shapiro B.E. Multivariate Calculus in 25 Easy Lectures [.pdf] (FREE!)
• Sloughter D. The Calculus of Functions of Several Variables (FREE!)
• Tao T. Analysis 1 (FREE!) - Not only Terry is a good mathematician, but also a good educator.
• Thomson B.S., Bruckner J.B. and Bruckner A.M. Elementary Real Analysis (here for FREE!)
• Veeh J.A. Lectures Notes on Multivariate Calculus [.pdf] (FREE!)
• Wachsmuth B.G. IRA: Interactive Real Analysis (FREE!)
• Wilde I.F. Real Analysis: An Introduction (FREE!)
• Zakon E. Mathematical Analysis I (FREE!)
• 山东大学数学学院：新高数课件 [.rar] (FREE!)
• 张筑生：《数学分析新讲》第三册，北京大学出版社
• 國立交通大學：微積分(一) (FREE!)
  國立交通大學：微積分(二) (FREE!)