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Aim of this lecture note is to develop an understanding of the statements of the theorems and how to apply them carefully. Major topics covered are: Measure spaces, Outer measure, null set, measurable set, The Cantor set, Lebesgue measure on the real line, Counting measure, Probability measures, Construction of a non-measurable set, Measurable function, simple function, integrable function, Reconciliation with the integral introduced in Prelims, Simple comparison theorem, Theorems of Fubini and Tonelli. This lecture notes is really good for studying integral calculus, this note contains the following subcategories Sigma Sum, The De nite Integrals and the Fundamental Theorem, Applications of Definite Integrals, Differentials, The Chain Rule in Terms of Differentials, The Product Rule in Terms of Differentials, Integration by Substitution, Integration by Partial Fractions, Applications of Integrals, Elementary integrals and Hyperbolic Functions Sponsored links download books on: Free Integral Calculus ebooks online © Copyright 2015-2016.

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>> » » Differential and Integral Calculus by C. Rainville Publisher: The MacMillan Company 1916 ISBN/ASIN: Number of pages: 369 Description: This book presents a first course in the calculus substantially as the author has taught it at the University of Michigan for a number of years.

In the treatment of each topic, the text is intended to contain a precise statement of the fundamental principle involved, and to insure the student's clear understanding of this principle, without distracting his attention by the discussion of a multitude of details. Download or read it online for free here: (multiple formats).