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.
The contents of this book
include: Integrals, Applications of Integration, Differential Equations,
Infinite Sequences and Series, Hyperbolic Functions, Various Formulas, Table of
Integrals.
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.
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 lecture note explains the following topics: The integral:
properties and construction, Function spaces, Probability, Random walk and
martingales, Radon integrals.
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.
This note covers the following topics:
Theory, Usage, Exercises, Final solutions, Standard integrals, Tips on using
solutions and Alternative notation.
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.