A Handbook of Real Variables

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Focusing on the foundations of calculus, this book delves into real analysis, tracing its historical roots back to Riemann, Cauchy, and Weierstrass. It emphasizes the importance of rigor in understanding sequences, series, and the completeness of the real number system. Key concepts like compact sets, uniform convergence, and classical examples such as the Weierstrass function and the Cantor set are explored. The text also covers essential topics like the derivative, the integral, and significant theorems, providing a comprehensive toolkit for advanced mathematical study.