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This is a free, online textbook that is also part of an online course.  According to the author, "Analysis is the study of limits. Anything in mathematics which has limits in it uses ideas of analysis. Some of the examples which will be important in this course are sequences, infinite series, derivatives of functions, and integrals. As you know from calculus, limits are the basis of understanding integration and differentiation, and, as you also know from calculus, these things are the basis of everything in the world you could ever need to know."

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