Mathematical Analysis 2
Description: The course explains the fundamental concepts and properties of the definite integral; teaches the use of various mathematical methods for evaluating integrals and applying definite integrals to solve practical problems; explores numerical integration methods; defines infinite series, function approximation, and the concept of convergence; and provides instruction on using infinite series in approximate computations.
Amount of credits: 5
Пререквизиты:
- Mathematical Analysis 1
Course Workload:
Types of classes | hours |
---|---|
Lectures | 15 |
Practical works | 45 |
Laboratory works | |
SAWTG (Student Autonomous Work under Teacher Guidance) | 15 |
SAW (Student autonomous work) | 75 |
Form of final control | Exam |
Final assessment method | Written exam |
Component: University component
Cycle: Base disciplines
Goal
- 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
- mastering the main provisions of the classical sections of mathematical analysis, the basic ideas and methods of mathematics, the system of basic mathematical structures and the culture of mathematical thinking, logical and algorithmic culture, is able to understand the general structure of mathematical knowledge, the relationship between various mathematical disciplines, to implement the basic methods of mathematical reasoning based on general methods scientific research and experience in solving educational and scientific problems
Learning outcome: knowledge and understanding
- Master the methods of mathematical analysis for solving applied problems and solving problems in mathematical and computer modeling
Learning outcome: applying knowledge and understanding
- Be able to develop mathematical models of technical problems, be able to choose effective methods of mathematics for solving applied problems
- Application of the acquired knowledge in the study of the discipline "mathematical analysis 2" in solving applied problems and creating mathematical models of various problems and comparative data analysis;
Learning outcome: formation of judgments
- To form an idea of the process or phenomenon being studied by the methods of mathematical analysis, to be flexible and mobile in various conditions and situations related to professional activities
Learning outcome: communicative abilities
- Be able to work in a team, correctly defend your point of view, offer new solutions using mathematical methods of applied problems
Learning outcome: learning skills or learning abilities
- Possess the skills of acquiring new mathematical knowledge necessary for everyday professional activities and continuing education in the magistracy, strive for professional and personal growth
- own the fundamental concepts of mathematical analysis and their differences, the skills of calculating the representation of mathematical information in various ways (analytical, graphic, symbolic and logical), use it in the development of major disciplines;
Teaching methods
interactive learning technologies;
computer learning technologies;
solving educational problems;
independent research work of students during the educational process.
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 | Mathematics dictation | 0-100 |
Independent work 1 | ||
IH 1 | ||
Final test 1 | ||
2 rating | IH 2 | 0-100 |
Independent work 2 | ||
IH 3 | ||
Final test 2 | ||
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
- Indefinite integral
- Integrirovaniye ratsional'nykh funktsiy
- Integration of square irrationalities
- Integration of square irrationalities
- Integration of trigonometric expressions
- Definite integral
- Concepts of parametrically defined curves and rectifiable lines
- Improper integrals
- Function of several variables
- Partial derivatives and differentials of higher orders
- Theory of series
- Alternating numerical series
- Functional sequences and functional series
- Fourier series
- Final lecture
Key reading
- 1.Ильин В.А., Позняк Э.Г.Основы математического анализаМ.: Наука, 2014г. 2.Фихтенгольц Г.М.Основы математического анализа.М.:Наука, 2019г. 3.Бугров Я.С., Никольский С.М. Дифференциальные уравнения. Кратные интегралы. Ряды.М.: Наука, 2015г. 4 Берман Г.Н. Сборник задач по курсу математического анализа. – М.: Наука, 2016. 5.Демидович Б.П. Сборник задач и упражнений по математическому анализу: учебное пособие.-Издательство "Лань".-2019. 6.Сборник задач по математике для втузов: Линейная алгебра и основы математического анализапод редакцией Ефимова А.В. и Демидовича Б.П. М.: Наука, 2013г. 7.Сборник задач по математике. Специальные разделы математического анализа под редакциейЕфимова А.В. и Демидовича Б.П. М.: Наука, 2016г.
Further reading
- 1. Кузнецов Л.А.Сборник заданий по высшей математике (типовые расчеты). М.: Высшая школа, 2003г. 2.Демидович Б.П.Сборник задач по математике для втузов: сборник задач. М.: Наука, 2006г. 3. Сборник индивидуальных заданий по высшей математика под редакцией Рябушко А.П. ч.1,2,3. Минск.: Вышейшая школа, 2013г.