Higher mathematics for engineering and technology : problems and solutions

273 Pages·2018·3.166 MB·English

by  Sabzaliev, Mahir M., Sabzalieva, Ilhama M

HIGHER MATHEMATICS
FOR ENGINEERING
AND TECHNOLOGY
Problems and Solutions

HIGHER MATHEMATICS
FOR ENGINEERING
AND TECHNOLOGY
Problems and Solutions
Mahir M. Sabzaliev, PhD
Ilhama M. Sabzalieva, PhD
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Library and Archives Canada Cataloguing in Publication
Sabzaliev, Mahir M., author
Higher mathematics for engineering and technology : problems and solutions / Mahir M.
Sabzaliev, PhD, Ilhama M. Sabzalieva, PhD.
Includes bibliographical references and index.
Issued in print and electronic formats.
ISBN 978-1-77188-642-0 (hardcover).--ISBN 978-0-203-73013-3 (PDF)
1. Engineering mathematics. I. Sabzaliev, Ilhama M., author II. Title.
TA330.S23 2018 620.001’51 C2018-900583-1 C2018-900584-X
CIP data on file with US Library of C ongress
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ABOUT THE AUTHORS
Mahir M. Sabzaliev
Mahir M. Sabzaliev is head of Higher Mathematics and Technical Sciences
chair at Baku Business University. He is also a professor of general and
applied mathematics at Azerbaijan University of Oil and Industry, Baku,
Azerbaijan, where he was a head of the higher mathematics chair in 2011–
2015. He is a member of the International Teachers Training Academy of
Science. He has authored over 100 published scientific works, including 30
educational works and scientific-methodical aids. He has given many talks
at international conferences. His papers were published in several well-
known journals, including Doklady Academy of Sciences of SSSR, Doklady
of Russian Academy of Sciences, Differential Equations (Differentsial’nye
Uravneniya), and Uspekhi Matematicheskikh Nauk, among others.
Dr. Sabzaliev graduated from Azerbaijan State Pedagogical University
with an honors diploma in mathematics. He worked as a teacher of math-
ematics in a secondary school and subsequently enrolled as a full-time
post graduate student and earned the candidate of physical-mathematical
sciences degree. In 2013, he earned a PhD in mathematics.
Ilhama M. Sabzalieva
Ilhama M. Sabzalieva, PhD, is an associate professor of general and
applied mathematics and also department chair at Azerbaijan University
of Oil and Industry, Baku, Azerbaijan. She has authored over 40 scientific
works, including 10 educational works and scientific-methodical aids. She
has authored more than 40 scientific works and has prepared educational
supplies and scientific-methodical aids. She has attended several interna-
tional conferences and given talks. She has also published papers in jour-
nals such as Doklady of Russian Academy of Sciences and Differentsial’nye
Uravneniya. Dr. Sabzalieva graduated from Azerbaijan State University of
Oil and Industry with an honors diploma and also earned the candidate of
physical-mathematical sciences degree.

CONTENTS
Preface .........................................................................................................ix
1. Elements of Linear Algebra and Analytic Geometry ...............................1
2. Introduction to Mathematical Analysis.................................................115
3. Differential Calculus of a Function of One Variable ...........................183
4. Studying Functions of Differential Calculus and Their
Application to Construction of Graphs.................................................221
5. Higher Algebra Elements .......................................................................243
Index .................................................................................................................257

PREFACE
This book was prepared and written based on the long-term pedagog-
ical experience of the authors at Azerbaijan State University of Oil and
Industry.
The problems that cover all themes of mathematics on engineering-
technical specialties of higher technical schools have been gathered in this
volume, which consists of three parts. The volume contains sections on
“elements of linear algebra and analytic geometry,” “differential calculus
of a function of one variable,” and “higher algebra elements.”
In this book, on every theme we present short theoretical materials and
then give problems to be solved in class or independently at home, along
with their answers. On each theme we give the solution of some typical,
relatively difficult problems and guidelines for solving them.
In the case of when students will be working out the problems to be
solved independently, we have taken into account the problems’ similarity
with the problems to be solved in class, and we stress the development of
the self-dependent thinking ability of students.
The problems marked by “*” are relatively difficult and are intended
for students who want to work independently.
This book is intended for bachelor students of engineering-technical
specialties of schools of higher education and will also be a good resource
for those beginning in various engineering and technical fields. The book
will also be valuable to mathematics faculty, holders of master’s degrees,
engineering staff, and others.