Mathematics

Higher Mathematics for Engineering and Technology
Problems and Solutions

Mahir M. Sabzaliev, PhD
Ilhama M. Sabzalieva, PhD

Higher Mathematics for Engineering and Technology

In production
Pub Date: Nov, 2017
Hardback Price: $159.95 US
Hard ISBN: 9781771886420
Pages: Approx 350p w/Index
Binding Type: hardback

Based on and enriched by the long-term teaching experience of the authors, Higher Mathematics for Engineering and Technology: Problems and Solutions covers the major themes of mathematics in engineering and technical specialties. The book covers the elements of linear algebra and analytic geometry, differential calculus of a function of one variable, and elements of higher algebra. On each theme the authors first present short theoretical overviews and then go on to give problems to be solved. The authors provide the solution of some typical, relatively difficult problems and guidelines for solving them.

The authors consider the development of the self-dependent thinking ability of students in the construction of problems and indicate which problems are relatively difficult. The book is geared so that some of the problems presented can be solved in class, and others are meant to solved independently. An extensive, explanatory solution of at least one typical problem is included, with emphasis on applications, formulas, and rules.

This volume is primarily addressed to advanced students of engineering and technical specialties as well as to engineers/technicians and instructors of mathematics. It will be useful for the study of automatization of instrument-building processes, electronics, telecommunication and radiotechnics, mechanics and robototechnics, computer engineering, information technologies and systems, metrology, standardization and certification, biomedical technology, chemical engineering, ecological engineering, geology, hydrology, geophysics, oil and gas engineering, materials science, energy machine building, technological machines and equipment, electroenergetics, heat energetics, world economics, organization and management of economics, marketing, management, management of business, etc.

Key features:

  • Presents the theoretical background necessary for solving problems, including definitions, rules, formulas, and theorems on the particular theme
  • Provides an extended solution of at least one problem on every theme and guidelines for solving some difficult problems
  • Selects problems for independent study as well as those during classroom time, taking into account the similarity of both sets of problems
  • Differentiates relatively difficult problems from others for those who want to study mathematics more deeply
  • Provides answers to the problems within the text rather than at the back of the book, enabling more direct verification of problem solutions
  • Presents a selection of problems and solutions that are very interesting not only for the students but also for professor-teacher staff

CONTENTS:
Introduction

CHAPTER 1. ELEMENTS OF LINEAR ALGEBRA AND ANALYTIC GEOMETRY
1.1. Matrices and operations on them
1.2. Determinants and calculation of their features
1.3. Rank of matrices and its calculation rules
1.4. Inverse matrix and methods for its finding
1.5. System of linear equations
1.6. Linear operations on vectors basis vectors in plane and space
1.7. Scalar product of vectors
1.8. Vectorial product of vectors
1.9. Mixed product of vectors
1.10. Straight line equations on a plane
1.11. Plane and straight line equations in space
1. 12. Second order curves

CHAPTER 2. INTRODUCTION TO MATHEMATICAL ANALYSIS
2.1. A function of one variable. Domain of definition of a functions, set of values. Even and odd functions. Periodic functions
2.2. Numerical sequences. Limit of sequences
2.3. Limit of function. Infinitely decreasing functions
2.4. Continuity of functions. Discontinuity points and their classification

CHAPTER 3. DIFFERENTIAL CALCULUS OF
A FUNCTION OF ONE VARIABLE

3.1. Derivative and its calculating rules
3.2. Some applications of derivative and differential
3.3. Main theorems of differential calculus. Teylor’s formula
3.4. Opening of uncertainties Bernoulli-de L’Hospital rule

CHAPTER 4. STUDYING FUNCTIONS OF DIFFEREN-TIAL CALCULUS AND THEIR APPLICATION TO CONSTRUCTION OF GRAPHS
4.1. Finding the monotonicity intervals, extremum the lagest and least values of function
4.2. Direction and turing points of the convexity of the graph of a function. Asymptotes of the graph of a function
4.3. Graphing of a function

CHAPTER 5. HIGHER ALGEBRA ELEMENTS
5.1. Complex numbers and operations on them
5.2. Polynomials dependent on one variable


About the Authors / Editors:
Mahir M. Sabzaliev, PhD
Professor of General and Applied Mathematics, Azerbaijan University of Oil and Industry, Baku, Azerbaijan

Mahir M. Sabzaliev, PhD, is 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.

Ilhama M. Sabzalieva, PhD
Associate Professor of General and Applied Mathematics, Azerbaijan University of Oil and Industry, Baku, Azerbaijan

Ilhama M. Sabzalieva, PhD, is an associate professor of general and applied mathematics at Azerbaijan University of Oil and Industry, Baku, Azerbaijan. She has authored over 40 scientific works, including ten educational works and scientific-methodical aids.




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