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mathematical analysis (in English)
Giaquinta,Modica (Author)
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mathematical analysis (in English) - giaquinta,modica
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Synopsis "mathematical analysis (in English)"
this self-contained work in mathematical analysis introduces the main ideas and fundamental methods of the subject, focusing on a simple and direct exposition of differential and integral calculus for functions of one variable with some of its applications. key features: * interesting and valuable historical account of ideas and methods in analysis with beautiful illustrations * topics: functions of one variable, differential and integral calculus, asymptotic expansion and inequalities, basic ordinary differential equations (including 1-dimensional motions, central motions, keplers laws and free and forced vibrations), and a discussion of elementary minimum principles in physics and geometry (such as refraction laws, steiners problem, isoperimetric problems, dijkstras algorithm for minimal connections in graphs); the preliminaries treat the real numbers, trigonometric functions and some elementary cartesian geometry * rigorous exposition with full proofs motivated by numerous examples * exercises, comprehensive bibliography and index this work is a first step toward developing connections between analysis and other mathematical disciplines (e.g., topology and geometry) as well as physics and engineering. an excellent resource for self-study or for classroom use at the advanced undergraduate or graduate level.
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The book is written in English.
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