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.
The contents of this book
include: Integrals, Applications of Integration, Differential Equations,
Infinite Sequences and Series, Hyperbolic Functions, Various Formulas, Table of
Integrals.
This graduate-level lecture
note covers Lebesgue's integration theory with applications to analysis,
including an introduction to convolution and the Fourier transform.
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.
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.
This note covers the following topics:
Theory, Usage, Exercises, Final solutions, Standard integrals, Tips on using
solutions and Alternative notation.
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.
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.
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.