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