Ministry of education of azerbaijan republic

MINISTRY OF EDUCATION

OF AZERBAIJAN REPUBLIC

Azerbaijan State Oil and Industry University

SYLLABUS
Approved: Doctor of Science in Mathematics, Prof. A.R.Aliyev

(head of department)

Signature: ____________________

Date: 09.09.2019
Department: General and Applied Mathematics

Faculty: Information Technologies and Management
I. Information on the Subject

Subject: Mathematics 1

Academic load (total hours): 30 lectures 30 seminars

Academic year: 2019-2020 Semester 1 Specialty

Number of credits: 4
II. Information on the Instructor

Lecturer- Nasibova Natavan Polad, Ph.D

(surname, name, patronymic, academic title, academic degree)

Assistant- Azimova Gulshan Musa, Ph.D

(surname, name, patronymic, academic title, academic degree)

Consultation days and hours: every week on Monday at 13.00

E-mail: [e-mail]

Work phone: [phone] (urban)
III. Required Textbooks and Manuals

Basic:

1. 
   AZIMOVA G.M., LECTURES IN HIGHER MATHEMATICS FOR ENGINEERS (PART I&II) Confirmed by Azerbaijan State Oil and Industry University. Order № 01-I/33 “14” September BAKU-2017
   
2. 
   Charles Hermite, Elementary Linear Algebra Additional Chapters.
   
3. 
   JamesStewart, Calculus Early Transcendentals. Eighthedition. USA,2014.ISBN978-1-285-74155-0
   
4. 
   Hiroyuki Shima. Tsuneyoshi Nakayama. Higher Mathematics for Physics and Engineering. Berlin 2010.
   
5. 
   George B. Thomas’, Calculus 13^th edt. 2014, 536 p.
   
6. 
   Michael Corral. Vector Calculus. Schoolcraft college.2008.
   
7. 
   Sheldon Axler. Linear Algebra Done Right. New York.1997.
   
8. 
   Donald Allen.Lectures on Linear Algebra and Matrices. Texas A and M University 2003.
   
9. 
   A.D.Myshkis. Introductory Mathematics for Engineers.Moskow.1972.
   
10. 
    A.F.Bermant.I.G.Aramanovich. Mathematical Analysis. Moskow.2005.
    

IV. Objective and Description of the Subject

Brief description of the course: The main goal of teaching mathematics is to achieve high level of mathematical knowledge among students. A student must know the basic principles of mathematics and be able to apply them. The student must understand why he or she is studying mathematics. Studying mathematics requires the student to try solving problems using the knowledge they have gained. Mathematics plays a very important role in modern science and engineering. Computers, cars, airplanes, mobile phones, iPads, iPods, bridges, dams and countless other engineering or technological achievements of the modern age were designed by people who could understand and apply mathematics.
The presentation of the subject matter

For the students majoring in oil and gas engineering and also chemical engineering include the study of the following chapters of the course “MATHEMATICS 1”:

1.Elements of linear algebra and analytical geometry

2.Differential calculus of functions of one variable and its applications

3. Differential calculus of functions of several variable and its applications

V. List of Lecture Topics

Week	Topics	Lecture	Seminar	Total
1.	Matrices and operations on matrices. Determinants.Basic properties,rules for calculation. Chapter 8(Textbook 2), ex1-8, ex9-12	2	2	4
2.	Rank of matrix.Metods for finding the rank.Inverse matrix. Chapter 8(Textbook 2), ex29-34, ex39-43	2	2	4
3.	Basic notions of a system of linear equtions. Basic methods for solving a system of linear equtions.Cramer`method. Gauss`method(the method of elimination. Chapter 8 (Textbook 2)	2	2	4
4.	Vectors.Linear operations on vectors.Dot product(Scalar product).Cross product(Vector product).Mixed product(Scalar triple product) Chapter 12 (Textbook 3)	2	2	4
5.	Equation of a straight line in plane and in space. Equation of a plane. Chapter 12 (Textbook 3)	2	2	4
6.	Second –order curves. Ellipse, hyperbola, parabola. Chapter 12 (Textbook 3)	2	2	4
7.	Numerical sequences. Limit of a sequence. Properties of convergent sequences. Limit of monotone sequence. Number . Chapter 11 (Textbook 3)	2	2	4
8.	Limit of a function. Basic theorems on limits. Remarkable limits. Chapter 2 (Textbook 3)	2	2	4
9.	Continuity of a function. Points of discontinuity of a function. Properties of continuous functions Chapter 2 (Textbook 3)	2	2	4
10.	Derivative. Geometrical meaning of the derivative. Differential. Differentiating functions. Table of derivatives. Basic differentiation rules. Chapter 2 (Textbook 3)	2	2	4
11.	Basic theorems of differential calculus. Theorems of Rolle, Lagrange, Cauchy.L`Hospital`s rule.Indeterminate forms of the type.Taylor`s formula. Chapter 2 (Textbook 3)	2	2	4
12.	Application of differential calculus to investigation of behavior of functions. Testing functions for monotonicity. Extrema of functions. Chapter 2 (Textbook 3)	2	2	4
13.	Convexity and concavity of a curve. Point of inflection. Asymptotes of a curve. Chapter 2 (Textbook 3)	2	2	4
14.	Functions of two variables. Limit of a function of two variables. Continuity. Partial derivatives. Differentials. Total differential. Chapter 2 (Textbook 3)	2	2	4
15.	Derivatives and differentials of higher orders. Extrema of function of two variables. Chapter 2 (Textbook 3)	2	2	4

VI. Form of the Exam – in writing, orally, in the form of a dialogue or text

The examination will be conducted in orally

VII. Evaluation during the semester and points layout Maximum number of points: 100 points
A) Maximum number of points earned during the semester: 50 points

Individual work (essay, presentation, research, etc.)	20 points
Midterm exams are held 2 times only in writing.
First midterm exam – in one of these days «21-25» october 2019 (The first midterm exam will cover materials, during the period 16.09.2019-18.10.2019)	5 points
Second midterm exam – in one of these days «25-29» november 2019 (The second midterm exam will cover materials, during the period 16.09.2019-22.11.2019)	25 points

B) Tasks for independent work of students

In the process of learning is important the independent work of sdudents.During of the semester it is planned to perfom (write) 10 independent works.Topic for independent work of sdudents are prepared by lecture.Students perfom the work applying knowledge gained in the classroom and using the given literature (bibliography).The students reseive advice from the lecture. The lecture assesses the work out of working time.

№	Tasks for independent work	Time of delivery of work(dates)
1	Finding the inverse matrix.	11.10.2019
2	Solving a system of linear equtions.	18.10.2019
3	Dot product.Cross product.Mixed product.	01.11.2019
4	Equation of a straight line Equation of a plane.	08.11.2019
5	Limit of a sequence. Limit of a function.	15.11.2019
6	Finding the derivatives.	22.11.2019
7	Indeterminate forms of the type.	06.12.2019
8	Testing functions for monotonicity. Extrema of functions.	13.12.2019
9	Asymptotes of a curve.	20.12.2019
10	Partial derivatives of a function of two variables.	26.12.2019

C) According to the results of the semester exam: maximum 50 points

Each examination card has 5 questions; for each question a maximum of 10 points are given

Remark: The number of points earned by the student at the examination shall not be less than 17.
D) Evaluation on the results of the semester (based on the points earned at and before the examination):

91 – 100 points	Excellent	A
81 – 90 points	Very good	B
71 – 80 points	Good	C
61 – 70 points	Satisfactorily	D
51 – 60 points	Passed	E
less than 51 points	Unsatisfactorily	F

Instructor: Nasibova Natavan Polad Signature: __________

(surname, name, patronymic)

Date: __________