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This graduate-level lecture note covers Lebesgue's integration theory with applications to analysis, including an introduction to convolution and the Fourier transform.
Author(s): Prof. Jeff Viaclovsky
NA Pages
The Integration of Functions of a Single Variable
This book describes the following topics: Elementary functions and their classification, The integration of elementary functions, The integration of rational functions, The integration of algebraical functions and The integration of transcendental functions.
Author(s): G. H. Hardy
NA Pages
Integration Theory Lecture notes
This note introduces the concepts of measures, measurable functions and Lebesgue integrals. Topics covered includes: Measurable functions / random variables , Dynkin’s Lemma and the Uniqueness Theorem, Borel-Cantelli’s First Lemma, Independent random variables, Kolmogorov’s 0-1-law, Integration of nonnegative functions , Jordan-Hahn Decompositions, The Lebesgue-Radon-Nikodym Theorem, The law of large numbers.
Author(s): Johan Jonasson
71 Pages
This book covers the following topics: Fundamental integration formulae, Integration by substitution, Integration by parts, Integration by partial fractions, Definite Integration as the limit of a sum, Properties of definite Integrals, differential equations and Homogeneous differential equations.
Author(s): Deepak Bhardwaj
NA Pages
This lecture note explains the following topics: The integral: properties and construction, Function spaces, Probability, Random walk and martingales, Radon integrals.
Author(s): William G. Faris
72 Pages
This note covers the following topics: Integration as summation, Integration as the reverse of differentiation, Integration using a table of anti-derivatives, Integration by parts, Integration by substitution, Integrating algebraic fractions, Integrating algebraic fractions, Integration using trigonometric formulae, Finding areas by integration, Volumes of solids of revolution, Integration leading to log functions.
Author(s): mathtutor.ac.uk
NA Pages
Differential and integral calculus
This book consist as a first course in the calculus. 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 districting his attention by the discussion of a multitude of details.
Author(s): Clyde E Love, Earl David Rainville
369 Pages
Notes on Calculus Integral Calculus (PDF 120P)
This is useful notes for integral calculus. This notes contain Integrals, Applications of Integration, Differential Equations, Infinite sequences and series and Application of Taylor polynomials.
Author(s): Miguel A. Lerma
120 PagesAdvertisement
