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 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 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