Introduction to Calculus and Classical Analysis

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Involving rigorous analysis, computational dexterity, and a breadth of applications, this text is ideal for an undergraduate honors calculus course or an introduction to analysis. The fourth edition features corrections and additional material. Key aspects include: a self-contained approach starting with real number axioms; the integral defined as the area under the graph, applicable to every subset of the plane; a strong focus on computational problems, ranging from the quadratic formula to the derivative of the zeta function at zero; diverse applications from analysis, such as convexity, the Cantor set, continued fractions, the AGM, theta and zeta functions, transcendental numbers, and Bessel and gamma functions; traditional topics like infinite products, the Bernoulli series, and the zeta functional equation presented over the reals; and a self-contained treatment of fundamental theorems of calculus using the Sunrise Lemma. The text contains 450 problems with solutions provided at the back. Previous reviews highlight its intriguing and unique treatment of calculus and analysis, with one noting the astonishing quality of Chapter 5, while others commend its elementary approach to topics closely aligned with Euler’s work.