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This volume aims to bridge between elementary textbooks on calculus
and established books on advanced analysis. It provides elucidation
of the reversible process of differentiation and integration
through two featured principles: the chain rule and its inverse -
the change of variable - as well as the Leibniz rule and its
inverse - the integration by parts. The chain rule or
differentiation of composite functions is ubiquitous since almost
all (a.a.) functions are composite functions of (elementary)
functions and with the change of variable method as its reverse
process. The Leibniz rule or differentiation of the product of two
functions is essential since it makes differentiation nonlinear and
with the method of integration by parts as its reverse
process.Readers will find numerous worked-out examples and
exercises in this volume. Detailed solutions are provided for most
of the common exercises so that readers remain enthusiastically
motivated in solving and understanding the concepts better.The
intention of this volume is to lead the reader into the rich fields
of advanced analysis and to obtain a much better view of useful
mathematics.
The aim of the book is to give a smooth analytic continuation from
calculus to complex analysis by way of plenty of practical examples
and worked-out exercises. The scope ranges from applications in
calculus to complex analysis in two different levels.If the reader
is in a hurry, he can browse the quickest introduction to complex
analysis at the beginning of Chapter 1, which explains the very
basics of the theory in an extremely user-friendly way. Those who
want to do self-study on complex analysis can concentrate on
Chapter 1 in which the two mainstreams of the theory - the power
series method due to Weierstrass and the integration method due to
Cauchy - are presented in a very concrete way with rich examples.
Readers who want to learn more about applied calculus can refer to
Chapter 2, where numerous practical applications are provided. They
will master the art of problem solving by following the step by
step guidance given in the worked-out examples.This book helps the
reader to acquire fundamental skills of understanding complex
analysis and its applications. It also gives a smooth introduction
to Fourier analysis as well as a quick prelude to thermodynamics
and fluid mechanics, information theory, and control theory. One of
the main features of the book is that it presents different
approaches to the same topic that aids the reader to gain a deeper
understanding of the subject.
The aim of the book is to give a smooth analytic continuation from
calculus to complex analysis by way of plenty of practical examples
and worked-out exercises. The scope ranges from applications in
calculus to complex analysis in two different levels.If the reader
is in a hurry, he can browse the quickest introduction to complex
analysis at the beginning of Chapter 1, which explains the very
basics of the theory in an extremely user-friendly way. Those who
want to do self-study on complex analysis can concentrate on
Chapter 1 in which the two mainstreams of the theory - the power
series method due to Weierstrass and the integration method due to
Cauchy - are presented in a very concrete way with rich examples.
Readers who want to learn more about applied calculus can refer to
Chapter 2, where numerous practical applications are provided. They
will master the art of problem solving by following the step by
step guidance given in the worked-out examples.This book helps the
reader to acquire fundamental skills of understanding complex
analysis and its applications. It also gives a smooth introduction
to Fourier analysis as well as a quick prelude to thermodynamics
and fluid mechanics, information theory, and control theory. One of
the main features of the book is that it presents different
approaches to the same topic that aids the reader to gain a deeper
understanding of the subject.
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