HIGHER MATHEMATICS 1

Abstract of the academic discipline

The purpose of studying the discipline: To provide theoretical and practical training of applicants for the formation of the development of logical and algorithmic thinking, studying the basics of mathematical apparatus, which is necessary for solving theoretical and practical problems of technology, raising the general level of mathematical culture. To teach students to independently work on mathematical literature and its application, to acquire skills in mathematical research of applied problems and to be able to build mathematical models of technical tasks.

Practical significance and use of acquired knowledge. To know the theoretical foundations of higher mathematics and practical methods of solving relevant problems. To choose methods of reducing a real problem to a mathematical model and apply them for the purpose of research and analysis. To use the mathematical apparatus for questions related to the specialty and literature on applied mathematics, reference books, tables. To understand cause-and-effect relationships, to have basic mathematical apparatus, knowledge of modern information technologies and fundamental sciences to the extent necessary for mastering general professional disciplines. To have the ability to write and speak in your native language and computer skills, etc. To be able to solve typical mathematical problems, to use in practice the algorithm for solving typical problems, to be able to systematize typical problems, to find criteria for reducing problems to typical problems, to be able to recognize a typical problem or to reduce it to a typical problem; be able to use various information sources to find procedures for solving typical problems (textbook, reference book, Internet resources).
Possess the deductive method of proving and refuting statements and use in practice the conceptual apparatus of deductive theories, reproduce deductive proofs of theorems and prove the correctness of procedures for solving typical problems. Conduct deductive justifications of the correctness of solving problems and look for logical errors in incorrect deductive reasoning; use mathematical and logical symbols in practice. Be able to see and apply mathematics in real life, understand the content and method of mathematical modeling, be able to build a mathematical model, investigate it using mathematical methods, interpret the results obtained, estimate the calculation error.Understand the need to be persistent in achieving the goal and quality performance of work in the professional field.

Main learning outcomes
PRN#1. Apply knowledge of the basic forms and laws of abstract and logical thinking, the basics of the methodology of scientific knowledge, the forms and methods of extracting, analyzing, processing and synthesizing information in the subject area of computer science.
PRN#2. To use the modern mathematical apparatus of continuous and discrete analysis, linear algebra, analytical geometry, in professional activities to solve problems of a theoretical and applied nature in the process of designing and implementing informatization objects.

Subjects and types of educational classes
1 week
Lecture #1. 
"Matrix. Definition, operations on matrices. Inverse matrix. Theorem on the existence of an inverse matrix. The method of elementary transformations for calculating the inverse matrix. Solving systems of linear inhomogeneous algebraic equations by the matrix method".
Practical lesson #1. 
"Operations on matrices. Product of matrices. Elementary matrix transformations. The method of elementary transformations for calculating the inverse matrix.
Solving the system of linear algebraic equations by the matrix method".
Obtaining a task for calculation and graphic work
2 week
Lecture #2. 
"Determinants. Properties of determinants. Calculation methods. Kramer's rule for solving systems of linear inhomogeneous algebraic equations".
Practical lesson #2. 
"Determinants of the 2nd and 3rd orders. Calculation. Kramer's rule".
Performing calculation and graphic work. Part 1. Elements of linear algebra.
3 week
Lecture #3. 
"Solution of systems of linear algebraic equations. Matrix rank. Methods of finding the rank of a matrix. Basic minor theorem. The Kronecker-Capelli theorem. Solving systems of linear inhomogeneous equations by the Gaussian method. Solving systems of linear homogeneous algebraic equations".
Practical lesson #3. 
"The rank of the matrix, two methods of finding the rank. Application of the Kronecker-Capelli theorem. Gauss method for solving systems of linear inhomogeneous equations. Solving systems of linear homogeneous equations".
Performing calculation and graphic work. Part 1. Elements of linear algebra.
4 week
Lecture #4. 
"Vectors. Definition of a vector as a directed segment. Linear operations on vectors. Scalar product of vectors. Properties of the scalar product. The cosine of the angle between the vectors. Guide cosines".
Practical lesson #4. 
"Linear operations on vectors. The scalar product of vectors, its properties and applications".
Performing calculation and graphic work. Part 2. Elements of vector algebra.
5 week
Lecture #5. 
"Vector and mixed product. Definition Properties. Application of vector and mixed products".
Practical lesson #5. 
"Properties of the vector product. Properties of the mixed product of three vectors. The geometric content of the mixed product".
Performing calculation and graphic work. Part 2. Elements of vector algebra.
6 week
Lecture #6. 
"A line on a plane: a general equation, normal, with an angle coefficient, through two points, in segments, a canonical equation, through a point perpendicular to a vector. Angle between lines. The distance from a point to a straight line. Plane: general equation, normal, equation in segments, equation through a point perpendicular to a vector, through three points. The distance from the point to the plane. Conditions of parallelism and perpendicularity of planes".
Practical lesson #6. 
"Different types of straight lines on a plane. The equation of the plane. The distance from a point to a straight line and to a plane. Angle between lines. Conditions of parallelism and perpendicularity of planes".
Performing calculation and graphic work. Part 2. Elements of vector algebra.
7 week
Lecture #7. 
"Equation of a straight line in space: through two points, general, canonical. The angle between a plane and a straight line in space. Determining the coordinates of the point of intersection of a straight line and a plane".
Practical lesson #7. 
"Different types of equations of a straight line in space. The angle between a straight line and a plane. The point of intersection of a straight line in space and a plane".
8 week
Lecture #8. 
"Transformation of coordinates on the plane. Canonical equations of a circle, ellipse, hyperbola, parabola".
Practical exercise #8. 
"Canonical equations of the simplest lines of the second order."
Modular test (control work) #1.
9 week
Lecture #9. 
"Numerical sequence. The limit of a numerical sequence. Weierstrass theorem".
Practical lesson #9. 
"Numerical sequence. Finding the limit of a numerical sequence".
Performing calculation and graphic work. Part 3. Elements of analytical geometry. Numerical sequence.
10 week
Lecture #10. 
"Boundary of a monotone bounded sequence. Number e. Natural logarithm.
Practical lesson #10. "Infinitely small and infinitely large sequences. The number is ".
Performing calculation and graphic work. Part 3. Elements of analytical geometry. Numerical sequence.
11 week
Lecture #11. 
"Boundary of a function. Infinitesimal and infinitely large functions. Definitions and basic theorems. The connection between the function, its limit and the infinitesimal".
Practical lesson #11. 
"Finding the limit of a function."
Performing calculation and graphic work. Part 3. Elements of analytical geometry. The limit of a function
12 week
Lecture #12. 
"Basic theorems about limits. Signs of the existence of borders. The first important border. The second important border".
Practical lesson #12. 
"The first and second important boundaries."
Performing calculation and graphic work. Consequences of the first and second limits. Part 4.
13 week

Lecture #13. 
"Equivalent infinitesimal functions. Comparison of infinitesimals. Basic theorems about infinitesimal functions. Application of infinitesimal functions".
Practical lesson #13. 
"Application of equivalent infinitesimal functions to find the limit."
Performing calculation and graphic work. Asymptotes. Part 4.
14 week
Lecture #14. 
"Continuity of a function at a point, on an interval, on a segment. Breakpoints and their classification".
Practical lesson #14. 
"Research of the function for continuity. Determination of the nature of the break point of the function". Performing calculation and graphic work. Local and global properties of a continuous function. Part 4.
15 week
Lecture #15. 
"Basic theorems about continuous functions. Properties of functions continuous on a segment. Bolzano-Cauchy theorem. Weierstrass theorem".
Practical lesson #15. 
"Application of properties of continuous functions on a line segment."
Modular test (control work) #2.

Individual work of the applicant takes place during the semester and consists of preparation for classroom classes, control measures, individual tasks.
Consultations: are carried out by the teacher during the semester according to the schedule

Assessment of learning outcomes
The evaluation of the results of studies in the discipline is carried out according to the cumulative system, which allows the student to receive a maximum of 100 points during the semester.
Module #1
Completion of the first part of the Calculation-Graphic Work –  10 points
Completion of the second part of the Calculation-Graphic Work – 10 points
Modular test # 1 – perfect execution of 30 points (in each task of the modular test, the maximum number of points for each task is given).
Module #2
Completion of the third part of the Calculation-Graphic Work – 10 points
Completion of the fourth part of the Calculation-Graphic Work – 10 points
Modular test # 2 – perfect execution of 30 points (in each task of the modular test, the maximum number of points for each task is given).

Links to recommended sources of information
Basic literature
1. Лінійна алгебра та аналітична геометрія / Усов А.В., Кліх Ю.О., Плотнікова Л.І., Комлева Т.О. – Одеса „Астропринт”, 2019. −280 с.(200 прим.)
2.Усов А.В. Диференціальне числення функції однієї змінної/ А.В. Усов, Ю.О. Кліх, Л.І. Плотнікова, О.М. Дубров. Навчальний посібник. −Одеса: Астропринт, 2002.− 224с. (300 прим.)
3.Усов А.В Математичні методи моделювання. / А.В. Усов, О.С. Савельєва, І.І. Становська, А.О. Перпері// Підручник / За ред. Становського О.Л. – Одеса Пальміра, 2018. – 500 с.
4. Моделювання та оптимізація систем. – Підручник /В.М. Дубовой, Р.Н. Квєтний, О.І. Михадьов, А.В. Усов/ − Вінниця: ПП «Едельвейс», 2017. – 804 с.
Additional literature
1.Вища математика: Збірник задач: У 2ч. Ч.1: Лінійна і векторна алгебра. Аналітична геометрія. Вступ до математичного аналізу. Диференціальне та інтегральне числення.: Навчальний посібник для студентів вищих технічних навчальних закладів.(Гаврильченко Х.І., Полушкін С.П., Кропив'янський П.С. та ін.; За заг. ред. д-ра техн. наук, проф. Овчинникова П.П.). К.: Техніка, 2014. 279 с. (Вміщено задачі і вправи з вищої математики для самостійної роботи студентів, наведено приклади розв'язання типових задач).
2.«Індивідуальні домашні завдання з вищої математики і методичні вказівки до їхнього виконання для студентів 1 курсу всіх спеціальностей денної форми навчання 1-го семестру»/ Укл.: Усов А.В., Кузьміна В.М,   Одеса: ОНПУ, 2020. 47 с. Рег. номер в журналі обліку МВО 3328 №00011-РС   2020.
3. Векторна алгебра. Електронний курс з дисципліни «Вища математика» (презентація). Для студентів технічних спеціальностей дистанційної й заочної форми навчання/Укл.: Колмакова Л.М.,-Одеса: ОНПУ,2017 р.-54 с. Відділ технологій дистанційного навчання, рег.№13/17 від 03.05.2017, розміщ. На ресурсі edu.op.ua
4. Матриці. Визначники та системи лінійних алгебраїчних рівнянь. Електронний курс з дисципліни  «Вища математика» (презентація). Для студентів технічних спеціальностей дистанційної й заочної форми навчання/Укл.: Колмакова Л.М., Кузьміна В.М.-Одеса: ОНПУ,2017 р.-44 с. Відділ технологій дистанційного навчання, рег.№12/17 від 03.05.2017, розміщ. На ресурсі edu.op.ua
5. Довідник з математики. Частина І.Навчальний посібник з дисципліни «Вища математика». Для студентів технічних спеціальностей за напрямом підготовки 122, 144, 141, 104./Укл. Колмакова Л.М., Комарницький О.Л.-Одеса: ОНПУ, 2017.-80с. Лаб. інф. технологій, рег. № НП08668 від 11.07.2017
6 .Індивідуальні домашні завдання з дисципліни «Вища математика», розділ «Лінійна алгебра» та методичні вказівкми до їх виконання. Для здобувачів вищої освіти усіх форм навчання за спеціальністю 122-Комп’ютерні науки та інформаційні технології./ Укл.: Л.М.Колмакова, Ю.Є.Сікіраш.-Одеса: НУОП, 2021.-40 с. Рег. Номер в журналі обліку 8316-РС-2022.