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 , Dynkinís Lemma and the Uniqueness Theorem, Borel-Cantelliís First
Lemma, Independent random variables, Kolmogorovís 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.
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.
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