- •1.1 Aims of studying the subject
- •1.2 Tasks of studying the subject
- •1.3 The place of the subject in the structure of the study programme
- •2. Requirements for preparedness (competencies) of students “at the entry” and at the end of the study of a subject (pre-requisites and post-requisites)
- •3.1 Thematic plan of modules
- •3.2 Themes of course works (projects)
- •3.3. Topics and tasks for student’s independent work
- •3.3.1 Topics and questions for student’s individual work with teacher
- •3.3.2 Themes and tasks for siw
- •4. Brief organizational and methodological description (basic forms and methods of training and control of educational achievement, teacher’s requirements, policies and procedures of the course):
- •4.1 Teaching methods - active and interactive methods of teaching;
- •4.3 Requirements of the teacher:
- •4.4 Policies and procedures of the course:
- •Estimation system of the results of student’s learning achievements
- •6. The list of recommended literature Basic literature
- •Additional literature
1.1 Aims of studying the subject
The aim of studying the subject is achieving the following learning outcomes (on the basis of Bloom’s taxonomy): (enumerate)
have a good knowledge of the mathematical concepts in real analysis
be able to use formal notation correctly and in connection with precise statements in English
be able to demonstrate the ability to solve unseen mathematical problems in real
analysis.
be able to prove statements and to formulate precise mathematical arguments.
1.2 Tasks of studying the subject
This course covers the fundamentals of mathematical analysis: convergence of sequences and series, continuity, differentiability, Riemann integral, sequences and series of functions, uniformity, and the interchange of limit operations. It shows the utility of abstract concepts and teaches an understanding and construction of proofs.
The course is designed to enable students to:
develop further their ability to think in a critical manner
formulate and develop mathematical arguments in a logical manner
improve their skills in acquiring new understanding and experience
acquire an understanding of advanced mathematical analysis.
1.3 The place of the subject in the structure of the study programme
The subject «Integral Calculus»is referred to the cycle of BD subjects of SP 5B0110900-«mathematics» to which refers the subject and included in the module «Mathematical analysis2».
2. Requirements for preparedness (competencies) of students “at the entry” and at the end of the study of a subject (pre-requisites and post-requisites)
Contents of the subject are the logical continuation of subjects: «Elementary Mathematics». This is a course in real analysis, designed for those who already know some real analysis. The emphasis is on functions, sequences and series in n-dimensional real space. The general concept of a metric space will also be studied. and serve as a basis for learning of the subject «numerical mathematics».
After studying this course, students should be equipped with a knowledge of concepts which are central not only to further mathematical courses, but toapplications of mathematics in theoretical economics and other areas. More generally, acourse of this nature, with the emphasis on abstract reasoning and proof, will help students to think in an analytical way, and be able to formulate mathematical arguments in a precise, logical manner.
To study the subject students should possess the following competencies:
Competencies |
Pre-requisites |
1) Acquire the necessary mathematical concepts and skills for everyday life, and for continuous learning in mathematics and related disciplines. 2) Develop the necessary process skills for the acquisition and application of mathematical concepts and skills. 3) Develop the mathematical thinking and problem solving skills and apply these skills to formulate and solve problems. 4) Recognise and use connections among mathematical ideas, and between mathematics and other disciplines. 5) Develop positive attitudes towards mathematics. 6) Make effective use of a variety of mathematical tools (including information and communication technology tools) in the learning and application of mathematics. 7) Produce imaginative and creative work arising from mathematical ideas. 8) Develop the abilities to reason logically, communicate mathematically, and learn cooperatively and independently. |
Elementary Mathematics |
After studying the subjects students acquire the following competencies:
Competencies |
Post-requisites |
Cultural CC1-Describe the definite integral as a limit of Riemann sums and illustrate and interpret definite integrals as areas and signed areas. CC2-Apply the fundamental theorem of calculus to evaluate integrals and to differentiate CC3-Use integration to find areas and volumes of regions and calculate physical quantities such as total distance traveled, displacement, work, and center of mass.
Professional PC1- Evaluate integrals using basic numerical integration rules. PC2- Use first order differential equations to model and solve problems of growth and decay, cooling, and mixing. |
numerical mathematics |
Cultural CC4- procedural skills for numerical calculation,algebraic manipulation, spatial visualization. CC5- data analysis, measurement, use of mathematical tools, and estimation. CC6- The development of skill proficiencies in students. Professional PC3- ability to use technology confidently, where appropriate, for exploration and problem solving. PC4- incorporate the use of thinking skills and heuristics in the process of developing skill proficiencies. |
teaching practice |
Learning outcomes (LO):
Descriptors |
Code of LO |
Learning outcomes (LO) |
Competencies |
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А |
To demonstrate knowledge and understanding in the studying field, including the elements of most advanced knowledge in this field |
А1
А2
А3 |
have a good knowledge of the mathematical concepts in real analysis
be able to use formal notation correctly and in connection with precise statements in English
be able to demonstrate the ability to solve unseen mathematical problems in real analysis. |
CC1, PC2 |
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В |
To use this knowledge and understanding at professional level
|
В1
В2
В3 |
be able to prove statements and to formulate precise mathematical arguments.
able to use an object, action, technology and / or by trial and error learning tasks Mathematical
ability to describe mathematical situations using everyday language, actions, materials and unofficial records |
CC2,СС3, PC1 PC2 |
|||
С |
To formulate the arguments and solve the problems in the field studied
|
С1
С2 С3 |
nalyze and use the right methods for solving problems
to plot functions and graphs find differential elementary functions |
CC2, PC1.PC3 |
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D |
To conduct gathering and interpretation of information in order to form opinions taking into account social, ethical and scientific considerations |
D1
D2 D3 |
problem-solving skills differentiation problem-solving skills integration ability to explain and show the course of the solution |
CC3, СС4,PC2 |
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E |
Ability of further continuation of self-learning |
Е1
Е2
Е3 |
analyze the efficiency of solving the problems of differentiation analyze the efficiency of solving the problems of integration synthesize various methods for solving problems of mathematical analysis |
CC3, СС5, PC3 PС4 |
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3. Description of each module (the list of modular units, i.e. themes with their brief content, plans of seminar and laboratory-practical classes, topics and issues of student’s independent work, including SIW with teacher