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Integral Calculus Books

Measure and Integration

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): NAPages

Guide to Integration

This note covers the following topics: Elementary Integrals, Substitution, Trigonometric integrals, Integration by parts, Trigonometric substitutions, Partial Fractions.

Author(s): 96Pages

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): NAPages

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): 71Pages

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): NAPages

Course Material for Analysis III Integration

In these lectures we define a simple integral and study its properties; prove the Mean Value Theorem for Integrals and the Fundamental Theorem of Calculus. This gives us the tools to justify term-by-term differentiation of power series and deduce the elementary properties of the trigonometric functions.

Author(s): NAPages

Lecture Notes for Integration

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.

Author(s): NAPages

Lectures on Integration

This lecture note explains the following topics: The integral: properties and construction, Function spaces, Probability, Random walk and martingales, Radon integrals.

Author(s): 72Pages

Integration by Mathtutor

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): NAPages

Integration By Parts

This note covers the following topics: Theory, Usage, Exercises, Final solutions, Standard integrals, Tips on using solutions and Alternative notation.

Author(s): 39Pages

A treatise on the integral calculus; with applications, examples and problems

This book describes the following topics: Standard Forms, Change Of The Independent Variable,Integration by parts and powers of Sines and cosines, Rational Algebraic Fractional Forms, Reduction Formulae, General Theorems, Differentiation Of a definite Integral with regard to a parameter, Rectification Of Twisted Curves, Moving Curves, Surfaces and volumes in general.

Author(s): 946Pages

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): 369Pages

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): 120Pages

Lecture Notes on Integral Calculus (PDF 49P)

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

Author(s): 49Pages