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For over three decades, this best-selling classic has been used by thousands of students in the United States and abroad as a must-have textbook for a transitional course from calculus to analysis. It has proven to be very useful for mathematics majors who have no previous experience with rigorous proofs. Its friendly style unlocks the mystery of writing proofs, while carefully examining the theoretical basis for calculus. Proofs are given in full, and the large number of well-chosen examples and exercises range from routine to challenging. The second edition preserves the book’s clear and concise style, illuminating discussions, and simple, well-motivated proofs. New topics include material on the irrationality of pi, the Baire category theorem, Newton's method and the secant method, and continuous nowhere-differentiable functions. Review from the first edition: "This book is intended for the student who has a good, but naïve, understanding of elementary calculus and now wishes to gain a thorough understanding of a few basic concepts in analysis.... The author has tried to write in an informal but precise style, stressing motivation and methods of proof, and ... has succeeded admirably." —MATHEMATICAL REVIEWS.

Calculus. --- Calculus --- Engineering & Applied Sciences --- Applied Mathematics --- Analysis (Mathematics) --- Fluxions (Mathematics) --- Infinitesimal calculus --- Limits (Mathematics) --- Mathematics. --- Mathematical analysis. --- Analysis (Mathematics). --- Functions of real variables. --- Analysis. --- Real Functions. --- Global analysis (Mathematics). --- Math --- Science --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Càlcul. --- Anàlisi matemàtica. --- Real variables --- 517.1 Mathematical analysis --- Mathematical analysis

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Unity of knowledge is not easily achieved in today's Africa where often there is little conscious interaction between traditional beliefs, Christian faith and modern secularity. The challenge is taken up in this book as scholars from a variety of disciplines wrestle with the relation of faith and science at the frontiers of knowledge. The results are important alike for the integrity of faith, for scientific advance and for the attainment of creative cultural unity in society. Readers with such concerns at heart will find much food for thought as they traverse the broad frontiers explored in these wide-ranging essays.

Christianity --- Religion and science --- Christianity and science --- Geology --- Geology and religion --- Science --- Science and religion --- Religions --- Church history --- Religious aspects

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This pioneering and fascinating book is the first to tell the story of the remarkably enduring bonds between Malawi and Scotland from the time of David Livingstone to the flourishing cultural, economic and religious relationships of the present day. Why should there be any significant relationship between one small nation on Europeís north-western seaboard and another in the interior of Africa? How did it reach the stage where in 2012 Fiona Hyslop, Cabinet Secretary for Culture and External Affairs in the Scottish Government, could describe Malawi as Scotlandís ìsister nationî? This book

Missions, Scottish --- Scottish missions --- Church of Scotland --- Missions --- Malawi --- Scotland --- Caledonia --- Scotia --- Schotland --- Sŭkʻotʻŭllandŭ --- Ecosse --- Škotska --- Great Britain --- Dziko la Malaŵi --- GOM (Malawi) --- Ma-la-wei --- Malaui --- Malavi --- Maraui --- Republic of Malaŵi --- República de Malawi --- Republik Malawi --- Малави --- マラウイ --- Nyasaland --- Relations --- Racism. --- Bias, Racial --- Race bias --- Race prejudice --- Racial bias --- Prejudices --- Anti-racism --- Critical race theory --- Race relations --- History.

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