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.
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.
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.
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