Mathematics 2

Description: Discipline "Mathematics 2" contains the following sections: Integral calculus of functions of one variable; differential equations; series.

Amount of credits: 4

Пререквизиты:

• Mathematics 1

Course Workload:

Component: University component

Cycle: Base disciplines

Goal

• The purpose of studying the discipline is the formation of students' scientific and practical ideas about mathematical methods for describing and solving practical problems in engineering, technology, and economics.

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;
• ecognise when and how a situation may be represented mathematically, identify and interpret relevant factors and select an appropriate mathematical method to solve the problem;
• 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

• өз жұмысын жоспарлай білу;
• 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 technologies (with active forms of learning: executive (supervised) conversation; moderation; brainstorming; motivational speech);

computer learning technologies;

independent research work of students during the educational process;

solving educational problems.

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.

The evaluating policy of learning outcomes by work type

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:

 

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:

Topics of lectures

• Primitive function
• Integration methods
• Decomposition of rational fractions into simple partial fractions
• Integration of radical and trigonometric functions
• Definite integral
• Numerical series
• Sign of d'Alamber
• Leibniz's theorem
• Functional series
• Taylor and Maclaurin series
• Differential equations
• First-order differential equations
• Differential equations of higher orders
• Linear homogeneous equations of second and higher orders with constant coefficients
• Linear non-homogeneous equations of second and higher orders with constant coefficients

Key reading

• Pis'mennyi D.T. Konspekt lekcij po vysshej matematike. – M.: Ajris-Press, 2015с-Пресс, 2014, Ч. 2,3.
• Berman G.N. Sbornik zadach po kursu matematicheskogo analiza. – M.: Nauka, 2016.
• 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.
• Fikhtengolts G.M. Kurs differentsialnogo i integralnogo ischisleniya. – M.: Fizmatlit. 2015. – T.1.2.
• Bugrov Ya.S., Nikol'skij S.M. Elementy linejnoj algebry i analiticheskoj geometrii. – M.: Fizmatlit, 2013.
• Shipachev V.S. Vysshaya matematika. – M.: Vysshaya shkola. 2014.
• Baranova E., Vasil'eva N. i dr. Prakticheskoe posobie po vysshej matematike. Tipovye raschety. 2-e izdanie-SPb.: Piter,2013