Mathematics 2

Description: Discipline "Mathematics 2" contains the following sections: Integral calculus of functions of one variable; differential equations; series. Reasonable mathematical conclusions provide sufficient generality of methods, breadth of applications and deep mutual penetration of the main branches of mathematics in all sectors of the market economy.

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 tasks of studying the discipline are the assimilation of the basic concepts, methods and tasks of sections: the integral calculus of the function of one variable; numerical and functional series used in approximate methods for solving various applied problems; differential equations to which many problems of geometry, mechanics, physics, hydraulics are brought.

Learning outcome: knowledge and understanding

• To organize, formulate and reproduce the basic definitions, theorems, formulas for the studied sections of the discipline and give examples of applied problems

Learning outcome: applying knowledge and understanding

• The ability to apply basic and special knowledge of mathematical sciences in the field of engineering and technology in professional activities, apply methods of mathematical analysis and modeling, theoretical and experimental research.

Learning outcome: formation of judgments

• To study and apply additional literature on the discipline to solve applied problems; to form an idea of the process or phenomenon under study by mathematical methods.

Learning outcome: communicative abilities

• To be able to work in a team for assimilation, consolidation and transfer of acquired knowledge by mathematical methods in solving applied problems

Learning outcome: learning skills or learning abilities

• To acquire skills to obtain new knowledge necessary for the development of special disciplines and continuing education in the specialty; strive for professional and personal growth.

Teaching methods

interactive technologies (with active forms of learning: executive (supervised) conversation; moderation; brainstorming; motivational speech);

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

• Berman G.N. Sbornik zadach po kursu matematicheskogo analiza. – M.: Nauka, 2016
• Pis'mennyj D.T. Konspekt lekcij po vysshej matematike. – M.: Ajris-Press, 2012, CH. 2,3.
• Ryabushko A.P., Barhatov V.V. i dr. Individual'nye zadaniya po vysshej matematike. – Minsk: Vysshaya shkola, 2013. – T. 2,3,4.
• Ajdos E.ZH. ZHoғary matematika. - Almaty: «Bastau» baspasy, 2010. - II, III, IV tomdary
• SHipachev V.S. Vysshaya matematika. – M.: Vysshaya shkola, 2012.
• Bugrov YA.S., Nikol'skij S.M. Vysshaya matematika: Zadachnik. – M.: Fizmatlit, 2011.
• Fihtengol'c G.M. Kurs differencial'nogo i integral'nogo ischisleniya. – M.: Fizmatlit, 2012. – T.1,2.

Further reading

• Hisamiev N.G., Tynybekova S.ZH., Konyrhanova A.A. Matematika. 1, 2 tomdary.- Өskemen.- SHҚMTU baspasy, 2012.
• Tynybekova S.ZH., Rahmetullina ZH.T. Matematika.- Өskemen.- SHҚMTU baspasy, 2011