A Radical Approach to Real Analysis
In the second edition of this MAA classic, exploration continues to be an essential component. More than 60 new exercises have been added, and the chapters on infinite summations, differentiability and continuity, and convergence of infinite series have been reorganized to make it easier to identify the key ideas. A Radical Approach to Real Analysis is an introduction to real analysis, rooted in and informed by the historical issues that shaped its development. It can be used as a textbook, or as a resource for the instructor who prefers to teach a traditional course, or as a resource for the student who has been through a traditional course yet still does not understand what real analysis is about and why it was created.
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absolute value approximating sum Archimedean understanding Archimedes binomial series Calculate Cauchy's choose close coefficients continuous function converges absolutely definition derivative differentiable Dirichlet Dirichlet's test endpoints equal equation error bound Euler Evaluate example Exercises The symbol exist Figure Fn(x Fourier series greatest lower bound harmonic series implies indicates that Maple infinite series integral intermediate value property Justify your answer Lagrange larger least upper bound Lemma limit Maple and Mathematica Mathematica codes mathematicians mathematics mean value theorem nested interval nested interval principle open interval partial sums partition polynomial positive integer power series problem are available proof prove radius of convergence ratio test rational number real numbers rearrangement Resources at www.macalester.edu/aratra Riemann root test sequence series diverges series expansion Show Sn(x Stirling's formula subintervals target value trigonometric series uniform convergence Weierstrass