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Differential geometry. Global analysis --- Bifurcation theory. --- Dynamics.

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This book provides a rigorous introduction to the techniques and results of real analysis, metric spaces and multivariate differentiation, suitable for undergraduate courses. Starting from the very foundations of analysis, it offers a complete first course in real analysis, including topics rarely found in such detail in an undergraduate textbook such as the construction of non-analytic smooth functions, applications of the Euler-Maclaurin formula to estimates, and fractal geometry. Drawing on the author’s extensive teaching and research experience, the exposition is guided by carefully chosen examples and counter-examples, with the emphasis placed on the key ideas underlying the theory. Much of the content is informed by its applicability: Fourier analysis is developed to the point where it can be rigorously applied to partial differential equations or computation, and the theory of metric spaces includes applications to ordinary differential equations and fractals. Essential Real Analysis will appeal to students in pure and applied mathematics, as well as scientists looking to acquire a firm footing in mathematical analysis. Numerous exercises of varying difficulty, including some suitable for group work or class discussion, make this book suitable for self-study as well as lecture courses.

Mathematics. --- Fourier analysis. --- Functions of real variables. --- Sequences (Mathematics). --- Topology. --- Real Functions. --- Sequences, Series, Summability. --- Fourier Analysis. --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Mathematical sequences --- Numerical sequences --- Algebra --- Mathematics --- Analysis, Fourier --- Mathematical analysis --- Math --- Science --- Sequences (Mathematics) --- Real variables --- Functions of complex variables

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The keystones for provision in the new era of Further Education will be flexibility of response, open access, equality of opportunity, and valuing and accrediting alternative ways of learning - all linked together within the concepts of providing life-long learning opportunities. The provision of APL, along with the support services needed to ensure its success, can be used as the `acid test' of whether a college is truly open and accessible to a variety of learners. Written by an experienced manager, this book offers invaluable advice for other managers and senior staff engaged in transformin

Experiential learning --- Universities and colleges --- College credits --- School credits --- Experience-based learning --- Learning, Experiential --- Experience --- Learning --- Active learning --- Administration.

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