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Sequences (Mathematics) --- Algorithms. --- Suites (mathématiques) --- Algorithmes. --- Suites (mathématiques) --- Algorithmes

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Digital communications --- Sequences (Mathematics) --- Digital communications --- Sequences (Mathematics) --- Transmission numérique --- Suites (Mathématiques) --- Mathematics --- Mathematics. --- Mathématiques

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Mathematical statistics --- Spectral theory (Mathematics) --- Sequences (Mathematics) --- Correlation (Statistics) --- Stochastic processes. --- Spectre (Mathématiques) --- Suites (Mathématiques) --- Corrélation (Statistique) --- Processus stochastiques --- Spectre (Mathématiques) --- Suites (Mathématiques) --- Corrélation (Statistique)

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Mathematical analysis --- Stochastic processes --- Combinatorial analysis --- Polynomials --- Convolutions (Mathematics) --- Banach algebras --- Sequences (Mathematics) --- Central limit theorem --- Analyse combinatoire --- Polynômes --- Banach, Algèbres de --- Suites (Mathématiques) --- Combinatorial analysis. --- Banach algebras. --- Polynômes --- Banach, Algèbres de --- Suites (Mathématiques)

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This text gives a rigorous treatment of the foundations of calculus. In contrast to more traditional approaches, infinite sequences and series are placed at the forefront. The approach taken has not only the merit of simplicity, but students are well placed to understand and appreciate more sophisticated concepts in advanced mathematics. The authors mitigate potential difficulties in mastering the material by motivating  definitions, results, and proofs. Simple examples  are provided to  illustrate new material and exercises are included at the end of most sections. Noteworthy topics include: an extensive discussion of convergence tests for infinite series, Wallis’s formula and Stirling’s formula, proofs of the irrationality of π and e, and a treatment of Newton’s method as a special instance of finding fixed points of iterated functions.

Mathematics. --- Real Functions. --- Sequences, Series, Summability. --- Sequences (Mathematics). --- Mathématiques --- Suites (Mathématiques) --- Mathematics --- Physical Sciences & Mathematics --- Calculus --- Functions of real variables. --- Mathematical sequences --- Numerical sequences --- Algebra --- Math --- Science --- Mathematical analysis. --- Real variables --- Functions of complex variables