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Complex analysis --- Calculus --- -Functions of real variables --- -Real variables --- Functions of complex variables --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematical analysis --- Functions --- Geometry, Infinitesimal --- Problems, exercises, etc --- Functions of real variables --- -Problems, exercises, etc --- Real variables --- Analyse mathématique --- Fonctions d'une variable réelle --- Analyse mathématique. --- Fonctions d'une variable réelle
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Number and geometry are the foundations upon which mathematics has been built over some 3000 years. This book is concerned with the logical foundations of number systems from integers to complex numbers. The author has chosen to develop the ideas by illustrating the techniques used throughout mathematics rather than using a self-contained logical treatise. The idea of proof has been emphasised, as has the illustration of concepts from a graphical, numerical and algebraic point of view. Having laid the foundations of the number system, the author has then turned to the analysis of infinite proc
Sequences (Mathematics) --- Mathematics. --- Number theory. --- Number study --- Numbers, Theory of --- Algebra --- Math --- Science
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Understanding the techniques and applications of calculus is at the heart of mathematics, science and engineering. This book presents the key topics of introductory calculus through an extensive, well-chosen collection of worked examples, covering; algebraic techniques functions and graphs an informal discussion of limits techniques of differentiation and integration Maclaurin and Taylor expansions geometrical applications Aimed at first-year undergraduates in mathematics and the physical sciences, the only prerequisites are basic algebra, coordinate geometry and the beginnings of differentiation as covered in school. The transition from school to university mathematics is addressed by means of a systematic development of important classes of techniques, and through careful discussion of the basic definitions and some of the theorems of calculus, with proofs where appropriate, but stopping short of the rigour involved in Real Analysis. The influence of technology on the learning and teaching of mathematics is recognised through the use of the computer algebra and graphical package MAPLE to illustrate many of the ideas. Readers are also encouraged to practice the essential techniques through numerous exercises which are an important component of the book. Supplementary material, including detailed solutions to exercises and MAPLE worksheets, is available via the web.
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