**Introductory Calculus:**

As you may have seen, calculus is crucial. It is not only important in advanced mathematics but also can be applied to many other fields. If you learn first year calculus in a college, your suggested text is probably J. Stewart's

*Calculus*. This is a standard modern text, it is colorful and quite detailed. If you prefer it, that's fine. This book is thick, you would like to leave a few section, say vector calculus, double, triple, line and surface integrals, to the next stage. I would suggest a few non-standard texts and notes.

The first thing we need to fix up is the definition of limit, learn the epsilon and delta proof. Other key concepts are the mean value theorem, fundamental theorem of calculus, logarithm and exponential functions, inverse trigonometric functions, hyperbolic functions, basic differential equations, limit of sequences, indeterminate form, infinite series, basic idea of several variables.

- Apostol T.M.
*Calculus Vol. 1* - Burn R.P.
*Numbers and Functions: Steps into Analysis* - Chen W.W.L. First Year Calculus (FREE!)
- Courant R. and John F.
*Introduction to Calculus and Analysis I*- One of the better calculus text in print. - Crowell B.
*Calculus*(FREE!) - Dawkins, P Calculus I and Calculus II (FREE!)
- Garrett P. Calculus (FREE!)
- Ghorpade S.R. and Limaye B.V.
*A Course in Calculus and Real Analysis*- See their web for errata. - Gill G.S.
*Calculus Bible*(FREE!) - Guichard D.
*Whitman Calculus*(FREE!) - You may leave the multivariable part to next stage. - Hardy G.H.
*A Course of Pure Mathematics*- Contains Cambridge Mathematical Tripos' exam paper, have fun! - Hwang A.D. Calculus for Mathematicians, Computer Scientists, and Physicists: An Introduction to Abstract Mathematics [.pdf] (FREE!)
- Ikenaga B. Notes on Calculus (FREE!)
- Santos D. Differential Calculus [.pdf] (FREE!)
- Shapiro B.E. Calculus and Analysis 2 (FREE!)
- Spivak M.
*Calculus*- To paraphrase J.R. Giles, Spivak presents a first course in real analysis or a course in calculus that has been carefully developed with attention given to the real analysis foundations with an eye on rigour. - Strang G.
*Calculus*(FREE!) - Thomas G.B. and Finney R.L.
*Calculus and Analytic Geometry* - Tranter C.J.
*Advanced Level Pure Mathematics* - Tranter C.J.
*Techniques of Mathematical Analysis* - Veeh J.A. Lectures Notes on Calculus [.pdf] (FREE!)
- 张筑生：《数学分析新讲》第一、二册，北京大学出版社

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