Mathematical Analysis 1

Demeubayeva Zhanar Yerkinovna

The instructor profile

Description: The goal of the course is to familiarize students with key areas of calculus and its applications in computer science. During the learning process, students are expected to understand and apply mathematical methods and tools to solve various applied problems. Furthermore, they will study the fundamental methods of analyzing infinitesimal quantities through calculus, which is based on the theory of differential and integral computations.

Amount of credits: 5

Пререквизиты:

  • Математика. Школьный курс

Course Workload:

Types of classes hours
Lectures 15
Practical works 30
Laboratory works
SAWTG (Student Autonomous Work under Teacher Guidance) 30
SAW (Student autonomous work) 75
Form of final control Exam
Final assessment method Written exam

Component: University component

Cycle: Base disciplines

Goal
  • The purpose of studying the discipline: The course of mathematical analysis is the foundation of mathematical education for a specialist in mathematical modeling, and within the framework of this course, orientation is carried out on the application of mathematical methods in professional activities.
Objective
  • The tasks of studying the discipline: - mastering the main provisions of the classical sections of mathematical analysis, basic ideas and methods of mathematics, the system of basic mathematical structures and the culture of mathematical thinking, logical and algorithmic culture, understanding the general structure of mathematical knowledge, the relationship between various mathematical disciplines, the ability to implement the basic methods of mathematical reasoning based on common methods of scientific research and experience in solving educational and scientific problems
Learning outcome: knowledge and understanding
  • Knowledge and understanding: knowledge and understanding of the basic mathematical definitions, theorems and other theoretical information of the course "Mathematical Analysis 1", as well as knowledge of the types of problems solved by certain mathematical methods;
Learning outcome: applying knowledge and understanding
  • Application of knowledge and skills: application of knowledge and skills in the formulation of applied practical problems by mathematical methods, as well as the use of known methods to solve the formulated problems;
Learning outcome: formation of judgments
  • Formation of judgments: the ability, based on the existing knowledge of the discipline "Mathematical Analysis 1", to draw conclusions about possible methods of analysis and solving practical problems in a special area;
Learning outcome: communicative abilities
  • Communication skills: ability to work in a team to effectively solve the set practical problems based on knowledge of mathematical methods;
Learning outcome: learning skills or learning abilities
  • Learning skills or learning abilities: the ability of independent or on the basis of educational educational programs for advanced training in the field of mathematical knowledge in order to meet the modern requirements of the specialty.
Teaching methods

интерактивные технологии обучения;

компьютерные технологии обучения;

решение учебных задач;

самостоятельная исследовательская работа студентов во время учебного процесса.

Assessment of the student's knowledge

Teacher oversees various tasks related to ongoing assessment and determines students' current performance twice during each academic period. Ratings 1 and 2 are formulated based on the outcomes of this ongoing assessment. The student's learning achievements are assessed using a 100-point scale, and the final grades P1 and P2 are calculated as the average of their ongoing performance evaluations. The teacher evaluates the student's work throughout the academic period in alignment with the assignment submission schedule for the discipline. The assessment system may incorporate a mix of written and oral, group and individual formats.

Period Type of task Total
1  rating Colloquium 0-100
Test
Individual homework 1
Individual homework 2
Individual homework 3
2  rating Colloquium 0-100
Test
Individual homework 4
Individual homework 5
Individual homework 6
Total control Exam 0-100
The evaluating policy of learning outcomes by work type
Type of task 90-100 70-89 50-69 0-49
Excellent Good Satisfactory Unsatisfactory
Interview on control questions (colloquium) demonstrates systematic theoretical knowledge, has a command of terminology, logically and consistently explains the essence of phenomena and processes, makes reasoned conclusions and generalizations, gives examples, demonstrates fluency in monologue speech and the ability to quickly respond to clarifying questions demonstrates solid theoretical knowledge, has a command of terminology, logically and consistently explains the essence of phenomena and processes, makes reasoned conclusions and generalizations, gives examples, demonstrates fluency in monologue speech, but at the same time makes minor mistakes that he corrects independently or with minor correction from the teacher demonstrates shallow theoretical knowledge, displays poorly developed skills in analyzing phenomena and processes, insufficient ability to make reasoned conclusions and give examples, demonstrates insufficiently fluent command of monologue speech, terminology, logic and consistency of presentation, makes mistakes that can only be corrected with correction by the teacher. demonstrates systematic theoretical knowledge, has a command of terminology, logically and consistently explains the essence of phenomena and processes, makes reasoned conclusions and generalizations, gives examples, demonstrates fluency in monologue speech and the ability to quickly respond to clarifying questions
IH (individual homework) or written work/exam completed the practical work in full, observing the required sequence of actions; in the answer, correctly and accurately completes all entries, tables, drawings, diagrams, graphs, calculations; correctly performs error analysis.When answering questions, correctly understands the essence of the question, gives an accurate definition and interpretation of the main concepts; accompanies the answer with new examples, is able to apply knowledge in a new situation; can establish a connection between the material being studied and previously studied material, as well as with material learned in studying other disciplines. выполнил требования к оценке «5», но допущены 2-3 недочета. Ответ обучающегося на вопросы удовлетворяет основным требованиям к ответу на 5, но дан без применения знаний в новой ситуации, без использования связей с ранее изученным материалом и материалом, усвоенным при изучении других дисциплин; допущены одна ошибка или не более двух недочетов, обучающийся может их исправить самостоятельно или с небольшой помощью преподавателя. выполнил работу не полностью, но не менее 50% объема практической работы, что позволяет получить правильные результаты и выводы; в ходе проведения работы были допущены ошибки. При ответе на вопросы обучающийся правильно понимает сущность вопроса, но в ответе имеются отдельные проблемы в усвоении вопросов курса, не препятствующие дальнейшему усвоению программного материала; допущено не более одной грубой ошибки и двух недочетов. completed the practical work in full, observing the required sequence of actions; in the answer, correctly and accurately completes all entries, tables, drawings, diagrams, graphs, calculations; correctly performs error analysis.When answering questions, correctly understands the essence of the question, gives an accurate definition and interpretation of the main concepts; accompanies the answer with new examples, is able to apply knowledge in a new situation; can establish a connection between the material being studied and previously studied material, as well as with material learned in studying other disciplines.
Evaluation form

The student's final grade in the course is calculated on a 100 point grading scale, it includes:

  • 40% of the examination result;
  • 60% of current control result.

The final grade is calculated by the formula:

FG = 0,6 MT1+MT2 +0,4E
2

 

Where Midterm 1, Midterm 2are digital equivalents of the grades of Midterm 1 and 2;

E is a digital equivalent of the exam grade.

Final alphabetical grade and its equivalent in points:

The letter grading system for students' academic achievements, corresponding to the numerical equivalent on a four-point scale:

Alphabetical grade Numerical value Points (%) Traditional grade
A 4.0 95-100 Excellent
A- 3.67 90-94
B+ 3.33 85-89 Good
B 3.0 80-84
B- 2.67 75-79
C+ 2.33 70-74
C 2.0 65-69 Satisfactory
C- 1.67 60-64
D+ 1.33 55-59
D 1.0 50-54
FX 0.5 25-49 Unsatisfactory
F 0 0-24
Topics of lectures
  • Basic concepts of set theory: set, operations on sets (intersection, union, difference of sets)
  • Real numbers
  • Complex numbers and their representation on the number plane
  • Sequence and its limit
  • Function, its domains of definition and values
  • Bounded functions, exact upper and lower bounds of a function on a set
  • Limit of a function at a point
  • Infinitesimal and infinitely large functions
  • Continuity of a function at a point
  • Points of discontinuity of a function and their classification
  • The concept of a derivative
  • Derivative of a composite function
  • Derivatives and differentials of higher orders
  • Extrema of a function
  • Convex functions, conditions for function convexity
Key reading
  • Берман Г.Н. Сборник задач по курсу математического анализа. – СПб.: Лань, 2018.
  • Бугров Я.С., Никольский С.М. Дифференциальное и интегральное исчисление. – М.: Дрофа, 2016.
  • Сборник задач и упражнений по математическому анализу : учебное пособие для вузов, Б. П. Демидович, Москва: АСТ, 2014.
  • Кудрявцев Л.Д. и др. Сборник задач по математическому анализу. – М. : Физматлит, 2018. – 496 с.
  • Пискунов Н.С. Дифференциальное и интегральное исчисления для втузов. – М.: Интеграл - Пресс, 2015, Т.1.
Further reading
  • Демидович Б.П. Краткий курс высшей математики. – М.: Астрель-АСТ, 2019.
  • Китапбаев М.К., Сидоренко В.Н., Чи-Дун-Чи Ю.В. Высшая математика в вопросах и задачах. Дифференциальное и интегральное исчисление.- У-ка, ВКГТУ, 2002.
  • Кузнецов Л.А. Сборник задач по высшей математике (типовые расчеты). – СПб.: Лань, 2015.
  • Лунгу К.Н. и др. Сборник задач по высшей математике. 1 курс. – М.: Айрис-пресс, 2014. 1
  • Рябушко А.П., Бархатов В. В и др. Индивидуальные задания по высшей математике.- Алматы: Образование и наука, 2013, Ч 1.
  • Фихтенгольц Г.М. Курс дифференциального и интегрального исчисления. – М.: Лань, 2019, Т.1.