Mathematics 1
Description: The discipline contains sections: elements of linear and vector algebra; elements of analytic geometry; introduction to mathematical analysis; differential calculus of functions of one and several variables, their applications. The sections under consideration are necessary for the development of analytical thinking, which provides theoretical training and practical skills for modeling and researching a variety of applied problems in a wide range of scientific disciplines.
Amount of credits: 5
Пререквизиты:
- Математика. Школьный курс
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 | Graded Credit |
Final assessment method |
Component: University component
Cycle: Base disciplines
Goal
- The purpose of teaching the discipline is to present the basic concepts and methods that are the main basis for mastering the disciplines that use mathematical models, the formation of students' theoretical knowledge, and the practical skills of applying mathematical methods in the formulation and solution of applied problems, as well to enable students to: • develop their mathematical knowledge and skills in a way which encourages confidence and provides satisfaction and enjoyment; • develop the ability to analyse problems logically; • recognise when and how a situation may be represented mathematically, identify and interpret relevant factors and select an appropriate mathematical method to solve the problem.
Objective
- The objectives of teaching the discipline are to enable students to: - develop their mathematical knowledge and skills in a way which encourages confidence and provides satisfaction and enjoyment;
- - develop an understanding of mathematical principles and an appreciation of mathematics as a logical and coherent subject;
- - acquire a range of mathematical skills, particularly those which will enable them to use applications of mathematics in the context of everyday situations and of other subjects they may be studying;
- - develop the ability to analyse problems logically;
- - acquire the mathematical background necessary for further study in mathematics or related subjects.
Learning outcome: knowledge and understanding
- to show understanding of relevant mathematical concepts, terminology and notation;
- to know the formulas and properties, the symbolism of the basic concepts of analysis, the theory of comparison of infinitesimal quantities;
- to know the methods of solving problems of linear algebra and analytical geometry and differential and integral calculus functions of one and several variables;
- knowledge and understanding of mathematics, at a level necessary to achieve other learning outcomes, including some awareness in their advanced areas;
- awareness in the broad interdisciplinary context of engineering;
Learning outcome: applying knowledge and understanding
- to apply the acquired knowledge to define, formulate and solve engineering problems using appropriate methods
- to be able to combine theory, practice and methods to solve engineering problems and understand the scope of their application;
Learning outcome: formation of judgments
- the ability to plan your work;
- clearly set a system of tasks, isolate the main ones among them;
- to skillfully choose the ways of the fastest and most economical solution of the tasks;
- skillful and operational control over the implementation of the task;
- the ability to quickly make adjustments to independent work;
- the ability to analyze the overall results of the work, compare these results with those planned at the beginning of it, identify the causes of deviations and outline ways to eliminate them in future work;
Learning outcome: communicative abilities
- the ability to work effectively individually and as a member of a team, demonstrating the skills of leading separate groups of performers, including on interdisciplinary projects;
- to be able to show personal responsibility, adherence to professional ethics and standards of professional activity;
- the ability to effectively share information, ideas, problems and solutions with the engineering community and society at large;
- the ability to clearly, intelligibly and patiently explain one's position;
- tolerance (as tolerance for the other), the desire and willingness to understand the position of the other and accept it if necessary;
- the ability to think ahead, predict and foresee the result;
- striving for continuous professionally oriented self-development.
Learning outcome: learning skills or learning abilities
- the ability to recognize the need and engage in independent learning throughout life;
- the ability to follow developments in the field of science and technology;
- the ability to integrate knowledge and cope with complex tasks in the field of activity, make decisions based on incomplete or limited information that reflect the relevant social and ethical responsibilities associated with the application of their knowledge and judgment;
- the ability to manage complex technical or professional issues or projects that require new strategic approaches, taking responsibility for decision making;
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 | IH-1.1 | 0-100 |
IH-1.2 | ||
IH 2-2.1-2.2 | ||
Colloquium | ||
Final test 1 | ||
2 rating | IH 3.1-3.2 | 0-100 |
IH 5.1-5.2 | ||
IH 6.1-6.3 | ||
Colloquium | ||
Final test 2 | ||
Total control | Graded Credit | 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 issues (colloquium) | Demonstrates systemic theoretical knowledge, knows terminology, logically and consistently explains the essence of phenomena and processes, makes reasoned conclusions and generalizations, gives examples, shows fluency in monologue speech and the ability to quickly respond to clarifying questions | 1. Demonstrates good theoretical knowledge, knows terminology, logically and consistently explains the essence, phenomena and processes, makes reasoned conclusions and generalizations. 2. gives examples, shows fluency in monologue speech, but makes minor mistakes that are corrected independently or with a slight correction by the teacher. | 1. Demonstrates poor theoretical knowledge, demonstrates poorly formed skills in analyzing phenomena and processes, inability to draw reasoned conclusions and give examples. 2. does not know enough monologue, terminology, logic and sequence of presentation, makes mistakes that the teacher can correct only when correcting. | Demonstrates systemic theoretical knowledge, knows terminology, logically and consistently explains the essence of phenomena and processes, makes reasoned conclusions and generalizations, gives examples, shows fluency in monologue speech and the ability to quickly respond to clarifying questions |
IH (Individual homework) or written work/exam | 1. Performs practical work in full, observing the necessary sequence of actions. 2. Correctly and accurately performs all records, tables, drawings, drawings, graphs, calculations in the response. 3. Performs error analysis correctly. 4. Answering questions, he correctly understands the essence of the question, accurately defines and explains the basic concepts. 5. Accompanies the answer with new examples, knows how to apply knowledge in a new situation. 6. It can establish links between the studied and previously studied material, as well as material obtained in the study of other disciplines. | 1. Fulfilled the requirements for the price of " 5", but 2-3 shortcomings were allowed. 2. The student's answer to the questions satisfies the basic requirements for answer 5, but in a new situation without the use of knowledge, without using connection with previously studied material and material learned in the study of other disciplines. 3. No more than one mistake or no more than two shortcomings have been made, which the student can correct independently or with a little help from the teacher. | 1. Работа выполнена не полностью, но не менее чем на 50% от объема практической работы, что позволяет получить правильные результаты и выводы. 2. В работе были допущены ошибки. 3. При ответе на вопросы студент правильно понимает суть вопроса, но в ответе есть отдельные проблемы с усвоением вопросов курса, которые не препятствуют дальнейшему усвоению программного материала. 4. Было допущено не более одной грубой ошибки и двух недочетов. | 1. Performs practical work in full, observing the necessary sequence of actions. 2. Correctly and accurately performs all records, tables, drawings, drawings, graphs, calculations in the response. 3. Performs error analysis correctly. 4. Answering questions, he correctly understands the essence of the question, accurately defines and explains the basic concepts. 5. Accompanies the answer with new examples, knows how to apply knowledge in a new situation. 6. It can establish links between the studied and previously studied material, as well as material obtained in the study of 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
- Matrices
- Systems of linear equations
- Vectors
- Vector and mixed products of vectors, their algebraic and geometric properties
- A Line in the Plane
- Plane
- Function limit
- Remarkable limits
- Problems of mechanics leading to the concept of a derivative
- Derivatives of inverse, implicit, parametrically defined functions
- Conditions for increasing and decreasing functions
- Functions of several variables
- Partial derivatives of the first order
- Production by direction
- Derivatives and differentials of higher orders of functions of several variables; Extremum of functions of several variables
Key reading
- Karchevskij E.M., Karchevskij M.M. Lekcii po linejnoj algebre i analiticheskoj geometrii M.: Ajris-Press, 2018
- Pis'mennyj D.T. Konspekt lekcij po vysshej matematike. – M.: Ajris-Press, 2015
- Berman G.N. Sbornik zadach po kursu matematicheskogo analiza. – M.: Nauka, 2016.
- Bogomolova E.P., Baranenkov A.I., Petrushko I.M.Sbornik zadach i tipovyh raschetov po obshchemu i special'nym kursam vysshej matematiki– M.: Ajris-Press, 2015
- Osipov A.V Lekcii po vysshej matematike– M.: Ajris-Press, 2014
- Ryabushko A.P., Barhatov V.V. i dr. Individual'nye zadaniya po vysshej matematike.- Minsk: Vysshaya shkola, 2015, T.1,2,3.
- Bugrov Ya.S., Nikol'skij S.M. Elementy linejnoj algebry i analiticheskoj geometrii. – M.: Fizmatlit, 2013.
- Kletenik D.V. Sbornik zadach po analiticheskoj geometrii. – M.: Professiya, 2013, ch.1.
- Baranova E., Vasil'eva N. i dr. Prakticheskoe posobie po vysshej matematike. Tipovye raschety. 2-e izdanie-SPb.: Piter,2013