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.
these lectures we define a simple integral and study its properties; prove the
Mean Value Theorem for Integrals and the Fundamental Theorem of Calculus. This
gives us the tools to justify term-by-term differentiation of power series and
deduce the elementary properties of the trigonometric functions.
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 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
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.