SPECIAL SECTIONS OF MATHEMATICS-2. NUMERICAL METHODS - Syllabus
Details of the discipline
| Educational level | First (bachelor) |
| Field of knowledge | 12 Information technology |
| Specialty | 126 Information systems and technologies |
| Educational program | Integrated information systems |
| Discipline status | Normative |
| Educational form | full-time / part-time / remote |
| Educational year, semester | 1 course, spring semester |
| Discipline scope | 120 hours (36 hours – Lections, 36 hours – Laboratories, 48 hours – SSW) |
| Semester control / control measures | Credit / credit work |
| Schedule | http://rozklad.kpi.ua |
| Language | Ukrainian |
| Course leader / teachers | Lecturer: Prof., Dr.Sci. Anatoliy Doroshenko, mob. +38(099)266-9311 Laboratories: As. Prof. Alyona Vityuk, mob. +38(066)482-4991 |
| Course placement | https://campus.kpi.ua |
Curriculum of the discipline
Description of the discipline, its purpose, subject of study and learning outcomes
Description of the discipline. When studying this discipline, students will get acquainted with the basic concepts of numerical methods, their types, and numerical methods of solving the main classes of applied mathematical problems. The lectures study theoretical information on numerical analysis, and at laboratory classes, students will master the algorithms of implementation of numerical methods in programming languages. The course provides for quality control of the obtained knowledge in the form of modular control works.
Subject of the discipline: basic concepts of numerical analysis, direct and iterative numerical methods, concepts of convergence, stability and accuracy of numerical methods, algorithms for solving problems of numerical analysis.
Interdisciplinary connections. Discipline "Special sections of mathematics" is based on disciplines: Higher mathematics, Theory of algorithms; Basics of Programming, Discrete Mathematics.
Purpose of the discipline. The purpose of the discipline is attainment of highly qualified specialists who have basic concepts of numerical methods in solving applied mathematical problems and know how to perform research and calculation work in the modeling of the subject area and creation of integrated information and control systems.
Main tasks of the discipline
Knowledge:
the role and place of numerical methods in the technical systems management.
general mathematical apparatus of numerical modeling.
numerical methods of solving linear and nonlinear algebraic equations.
numerical methods of function approximation.
numerical methods of solving ordinary differential equations.
methods of numerical integration.
solving edge problems for ordinary differential equations.
modern tools for programming numerical methods on computers.
Skills:
implementing numerical methods on modern computer equipment;
using numerical methods for solving engineering problems;
choose the right and use one or another numerical method according to the conditions of the task.
Prerequisites and postrequisites of the discipline (place in the structural and logical scheme of education according to the relevant educational program)
Prerequisites: to know the basic concepts of algebra and mathematical analysis, to know the basic concepts of discrete analysis and complexity of algorithms, to be able to use a computer at the user level of application packages.
Postrequisites: after studying discipline, students will be able to use the learned numerical methods for solving engineering problems, choose the right and use one or another numerical method in accordance with the conditions of the task and implement numerical methods on modern computer equipment.
Content of the discipline
Lectures
Section 1: Algorithmizing and programming tools of computational processes
Section 2: Methods of solving nonlinear algebraic and transcendental equations
Section 3: Numerical methods of function interpolation
Section 4: Numerical methods of function integration
Section 5: Numerical integration of ordinary differential equations
Section 6: Numerical solution of linear equation systems
Section 7: Numerical solution of systems of nonlinear equations
Section 8: Numerical solution of edge problems for systems of ordinary differential equations.
Laboratory classes
1. Preparing for the use of Python programming tools
2. Approximate solution of nonlinear and transcendental equations.
3. Lagrange and Newton methods for function interpolation
4. Methods of spline interpolating functions
5. Methods of numerical integration
6. Numerical solution of ordinary differential equations
7. Solving systems of linear algebraic equations
8. Methods of numerical solution of systems of nonlinear algebraic equations
9. Methods of solving the edge problem for systems of ordinary differential equations
Training materials and resources
Basic literature
Programming of numerical methods in Python : textbook / A.V. Anisimov, A.Y. Doroshenko, S.D. Pogorily, Ya.Yu. Dorogyi; by ed. A.V., Anisimova.—K.: Publishing and Printing Center "Kyiv University", 2015.—640 p. (in Ukrainian)
Programming of numerical methods in Python language: teaching.posib./ A.Y. Doroshenko, S.D. Poguril, Y.Yu. Dear, E.V. Glushko; by ed.. A.V., Anisimova.—K.: Publishing and Printing Center "Kyiv University", 2013.—463 p. (in Ukrainian)
Special sections of mathematics -2. Part 1. Introduction to the Python programming language. Tutorial for studs. Direction "System Engineering" [Electronic resource] / concluded:Dear Ya.Yu., Glushko E.V., Doroshenko A.Yu.-- NTUU "KPI"; 143 p.,2010. (in Ukrainian)
Special sections of mathematics - 2.Part 2. Numerical methods. Tutorial for studs. Direction "System Engineering" [Electronic resource] / concluded:Dear Ya.Yu., Glushko E.V., Doroshenko A.Yu. -- NTUU "KPI", 141 p., 2010. (in Ukrainian)
Additional literature
Zelensky K. H., Ignatenko V. M. Kots O.P. Computer methods of applied mathematics. K.; Design, 2000.-468 p. (in Ukrainian)
Korn G., Corn T. Handbook on Mathematics for Scientists and Engineers, M.: Science,1970. (in Russian)
Bakhvalov N.S., Shitkov N.P., Kobelkov G.M. Numerical methods. M.: Fismatlit. Basic Knowledge Laboratory, 2002 632 p. (in Russian)
Stephen Wolfram, The Mathematica Book, Fifth Edition. 2003.
Educational content
Methods of mastering the discipline (educational component)
Lectures
| № | The title of the lecture Subject and a list of key issues (list of teaching aids, references to literature and tasks on SSW) |
|---|---|
| 1 | Subject 1.1. Problems of numerical modeling in engineering science Subject 1.2. Elements of the theory of close calculations Lecture 1. Numerical modeling in engineering science and elements of the theory of approximate computing. Physical and mathematical models in engineering science. The concept of numerical modeling. Approximate numbers and types of errors. A significant figure and the number of correct signs of the approximate number. Rules for rounding numbers. Calculate function error from n arguments. Tasks for SSW. Issues of mathematical modeling and creation of numerical models of processes in complex technical systems Literature: [1, Chapter 1], [5, Chapter 1] |
| 2 | Subject 1.3. Application programming in Python Lecture 2. Introduction to the Python programming language Types of Python data and collections and their use for computing programming. Control structures, functions and modules and python language packs. Tools for organizing programs in Python. Modular hierarchy of applications. Work with files in Python. Tasks for SSW. Learn the tools for perfect python programming methods Literature: [1], [2, Chapter 1] |
| 3 | Subject 2.1. Horde method Subject 2.2. Newton method Lecture 3. Methods of solving nonlinear equations Half division method for solving nonlinear equations. Horde method. Newton's method. Tasks for SSW. Graphical methods of solving nonlinear equations and investigating functions. Literature: [1, Chapter 4], [5] |
| 4 | Subject 2.3. Simple iteration method Lecture 4. The method of simple iteration of solving nonlinear equations. The method of simple iteration. Theorem on compressive maps. Tasks for SSW. Methods of investigationg functions and localization of equation roots Literature: [1, Chapter 4], [5] |
| 5 | Subject 3.1. Interpolation of functions by Lagrange Lecture 5. Interpolation of functions by Lagrange. Interpolation by Lagrange. Accuracy of interpolation by Lagrange polynomiums. Tasks for SSW. Methods of aproximation and smoothing of functions. Literature: [2, Chapter 5.2], [1], [5] |
| 6 | Subject 3.2. Newton's feature interpolation Lecture 6. Interpolation of functions by Newton method. The finite differences of different orders. Divided differences. Newton's interpolation formula. Tasks for SSW. Different methods of aproximation and smoothing of functions Literature: [2, Chapter 5.2], [1] |
| 7 | Subject 3.3. Interpolation of functions by splines Lecture 7. Interpolation of functions by splines. Interpolation by cubic splines. Accuracy of interpolation splines. Tasks for SSW. Other methods of aproximation and smoothing of functions. Literature: [2, Chapter 5.3], [1], [5] |
| 8 | Modular control work The control work is carried out based on previous material, including methods of solving nonlinear equations and methods of interpolation of functions Tasks include one task per each of the two specified sections Tasks for SSW. Repeat the material of lectures 1-7. |
| 9 | Subject 4.1. Formulas of rectangles and trapezoids for numerical integration Lecture 8. Formulas of rectangles and trapezoids for numerical integration Rectangle formula. Trapezoid formula for numerical integration. Evaluate the accuracy of the formulas of rectangles and trapezoids. Tasks for SSW. Approximate calculation of multiples of integrals Literature: [2, Chapter 8.1] |
| 10 | Subject 4.2. Simpson's formula for numerical integration Lecture 9. Simpson's formula for numerical integration. The problem of accuracy of formulas of rectangles and trapezoids. Simpson's method for numerical integration. Tasks for SSW. Approximate calculation of different types of integrals. Literature: [2, Chapter 8.3]. |
| 11 | Subject 5.1. Euler methods of solving ordinary differential equations Lecture 10. Euler methods of solving conventional differential equations Cauchy's problem. Euler method of solving conventional differential equations. Euler's modified method of solving ordinary differential equations. Tasks for SSW. Analytical methods of solving conventional differential equations of the first order. Literature: [1, Chapter 9],[5] |
| 12 | Subject 5.2. Runge-Kutta method of solving ordinary differential equations Lecture 11. Runge-Kutta's method of solving conventional differential equations. One-step methods of solving ordinary differential equations. Runge-Kutta methods. The Euler -Cauchy method as partial case of the Rouge-Kutta method. Tasks for SSW. Some analytical methods of solving ordinary differential equations of the second order. Literature: [1, Chapter 9],[5] |
| 13 | Subject 5.3. Adams’ method of solving conventional differential equations Lecture 12. Adams’ method of solving conventional differential equations. Adams' method of solving differential equations. The differential look of Adams' method. Methods predictor-corrector by Adams-Beshforts. Tasks for SSW. Software tools to support the system of solving conventional differential equations in the Mathematica system [8]. Literature: [1, Chapter 9],[5] |
| 14 | Modular control work The control work is given based on the material of lectures 8-12, including themes on numerical integration and solving of conventional differential equations. The tasks of control work include one task per ech of the two specified sections Tasks for SSW. Repeat material of the lectures 8-12. |
| 15 | Subject 6.1. Elements of algebra vectors and matrixes Subject 6.2. Solving systems of linear equations by Gaussian method Lecture 13. Direct methods of solving systems of linear equations. Norms of vectors and matrices. Theorem on the LU-factoring of the nondegenerate matrix. Solving systems of linear equations by Gaussian method. Gauss-Jordan method. Method of processing the solution of systems of linear equations for tridiagonal matrices. Tasks for SSW. Elements of algebra vectors and matrices. Methods of ensuring the stability of solutions of linear equation systems. Literature: [1, Chapter 3], [2, Chapter 6] |
| 16 | Subject 6.3. Iterative methods of solving systems of linear equations Lecture 14. Jacobi's simple iteration method and the Seidel method Jacobi's simple iteration method and error assessment. Sufficient condition for the convergence of the simple iteration method. A necessary and sufficient condition for the convergence of the simple iteration method. Seidel's method and error assessment. Tasks for SSW. Implementation of Seidel methods and simple iteration in Python programming language. Literature: [2, Chapter 6], [3] |
| 17 | Subject 7.1. Numerical solution of systems of nonlinear equations Lecture 15. Newton's method of solving systems of nonlinear equations. Conditions of application of the Newton method. Newton's method for solving systems of nonlinear equations. Iterative method for solving systems of nonlinear equations. Conditions of convergence of the iterative method. Tasks for SSW. Study of examples of solving systems of nonlinear equations. Literature: [1, Chapter 7.1], [2, Chapter 7.2], [5] |
| 18 | Subject 8.1. Numerical solution of edge problems for systems of ordinary differential equations Lecture 16. Firing method and finite-difference method for solving regional problems. Method of firing. Finite-difference method for solving edge problems. Tasks for SSW. Studying examples of solving edge problems of ordinary differential equations. Literature: [5, Chapter 8] |
Lectures for students by correspondence
| № з/п | The title of the lecture Subject and a list of key issues (list of teaching aids, references to literature and tasks on SSW | Hours |
|---|---|---|
| 1 | Lecture 1. Numerical modeling in engineering science and elements of the theory of approximate computing. Methods of solving nonlinear equations. Physical and mathematical models in engineering science. The concept of numerical modeling. Approximate numbers and types of errors. A significant figure and the number of correct digits of the approximate number. Rules for rounding numbers. Calculate function error from n arguments. Half division method for solving nonlinear equations. Horde method. Newton's method. The method of simple iteration. Literature. [ 2,3,5] Tasks for SSW. Graphical methods of solving nonlinear equations and investigating functions. |
2 |
| 2 | Lecture 2. Methods of interpolating functions. Interpolation by Lagrange and Newton. Accuracy of interpolation by Lagrange polynomials. Interpolation of functions by splines. Simpson's formula for numerical integration. Evaluation of the accuracy of formulas. Euler method of solving ordinary differential equations. Euler's modified method of solving ordinary differential equations. Literature [2-5] Tasks for SSW. Methods of aproximation and smoothing of functions. Approximate calculation of multiple integrals. Analytical methods of solving ordinary differential equations. |
2 |
| 3 | Lecture 3. Methods of solving systems of linear equations Runge-Kutta's one-step methods and Adams' multi-step methods for ordinary differential equations. Solving systems of linear equations by Gauss method. Gauss-Jordan method. Method of processing the solution of systems of linear equations for tridiagonal matrices. Jacobi's simple iteration method and Seidel method. Literature [2-4] Tasks for SSW. Methods of ensuring the stability of solutions of linear equation systems. Newton's method for solving systems of nonlinear equations. Iterative method for solving systems of nonlinear equations. Method of firing. End-to-difference method for solving regional problems. |
2 |
| Total | 6 |
**
**
Laboratory classes
| № | Name of laboratory work | Number of hours |
|---|---|---|
| 1 | Laboratory work 1. Preparing for Python programming tools It is necessary to find the appropriate material for a given topic and get acquainted with the installation procedure of the Python programming system. The result of the work should be the deployment of the Python software package on the Microsoft Windows platform and training with its basic programming tools. Literature: [3, Chapter 1] |
4 |
| 2 | Laboratory work 2. Approximate solution of nonlinear and transcendental equations. It is necessary to implement Python methods of solving nonlinear and transcendental equations: half division, horde, Newton and simple iteration. The result of this laboratory is the solution a nonlineary or transcendental equation (on the choose of the teacher) by these methods. Literature: [2, Part 2, Chapter 4] |
4 |
| 3 | Laboratory work 3. Lagrange and Newton methods for interpolating functions. Python methods of interpolation of Lagrange and Newton functions must be implemented. The result of laboratory work is the interpolation of a function (on the choose of the teacher) by these methods. Literature: [2, Part 2, Chapter 5] |
4 |
| 4 | Laboratory work 4. Method of spline interpolation of functions. It is necessary to implement the method of spline interpolation of functions in Python. The result of laboratory work is the implementation of spline-interpolation of the function on the task of the teacher. Literature: [2, Part 2, Chapter 5] |
4 |
| 5 | Laboratory work 5. Methods of numerical integration. It is required to realize in Python some numerical integration methods: rectangle formulas, trapezoid formulas, and Simpson formulas. The result of laboratory work is the calculation an integral numerically (according to the teacher's task) by these methods. Literature: [3, Part 2, Chapter 8] |
4 |
| 6 | Laboratory work 6. Numerical solution of ordinary differential equations Implement Python methods of solving conventional differential equations: Euler method, Euler-Cauchy method and Runge-Kutta method. The result of laboratory work is the solution of the ordinary differential equation (on the choose of the teacher) by these methods. Literature: [3, Part 2, Chapter 9] |
4 |
| 7 | Laboratory work 7. Solving systems of linear algebraic equations Implement Python methods of solving systems of linear algebraic equations: the direct method of Hauss-Jordan and the iterative method of Seidel. The result of laboratory work is the solution of systems of linear algebraic equations (on the choose of the teacher) by these methods. Literature: [3, Part 2, Chapter 6] |
4 |
| 8 | Laboratory work 8. Methods of numerical solution of systems of nonlinear algebraic equations Implement Python methods of solving systems of nonlinear algebraic equations: Newton method and Jacobi method. The result of laboratory work is the solution of systems of nonlinear algebraic equations (on the task of the teacher) by these methods. Literature: [3, Part 2, Chapter 7] |
4 |
| 9 | Laboratory work 9. Methods of solving the edge problem for systems of ordinary differential equations. Implement shooting method in Python to solve the edge problem for systems of ordinary differential equations. The result of laboratory work is the solution of the edge problem for the systems of ordinary differential equations (according to the teacher's task) by firing method. Literature: [2, Part 2, Chapter 8] |
4 |
| Total | 36 |
Laboratory classes
| № | Name of laboratory work | Hours |
|---|---|---|
| 1 | Approximate solution of nonlinear and transcendental equations. To implement methods of solving nonlinear and transcendental equations in Python: half division, horde, Newton, and simple iteration methods. The result of this laboratory is the solution of the same nonlinear or transcendental equation (on the task of the teacher) by these methods. Literature: [2, Part 2, Chapter 4] |
2 |
| 2 | Method of spline interpolation of functions. You must implement the method of spline interpolation functions in Python. The result of laboratory work is the implementation of spline-interpolation of the function chosen by the teacher. Literature: [2, Part 2, Chapter 5] |
2 |
| 3 | Methods of numerical solution of systems of nonlinear algebraic equations. Implement Python methods of solving systems of nonlinear algebraic equations: Newton method and Jacobi method. The result of laboratory work is the solution of systems of nonlinear algebraic equations (chosen by the teacher) by these methods. Literature: [3, Part 2, Chapter 7] |
2 |
| Total | 6 |
Student’s self work
| № | The name of the Subject submitted for self-study | Number of SSW hours |
|---|---|---|
| 1 | Issues of mathematical modeling and creation of numerous models of processes in complex technical systems | 2 |
| 2 | Learn the tools for perfect Python programming methods | 2 |
| 3 | Graphical methods of solving nonlinear equations and investigating functions | 4 |
| 4 | Methods of investigating functions and localization of equation roots | 4 |
| 5 | Methods of approximation and smoothing of functions | 2 |
| 6 | Difference methods of approximation and smoothing of functions | 2 |
| 7 | Other methods of approximation and smoothing of functions | 4 |
| 8 | Repeating the material of lectures 1-7 | 2 |
| 9 | Approximate calculation of multiples integrals | 2 |
| 10 | Approximate calculation of different types of integrals | 2 |
| 11 | Analytical methods of solving ordinary differential equations of the first order | 2 |
| 12 | Some analytical methods of solving ordinary differential equations of the second order | 2 |
| 13 | Software tools to support solving the system of ordinary differential equations in the MATHEMATICA system | 4 |
| 14 | Repeating the material of lectures 8-12 | 4 |
| 15 | Elements of algebra vectors and matricies. Methods of ensuring the stability of solutions of linear equation systems | 2 |
| 16 | Implementing methods of Seidel and simple iteration in Python programming language | 4 |
| 17 | Study of examples of solving systems of nonlinear equations | 2 |
| 18 | Studying examples of solving edge problems | 2 |
| Total | 48 |
SSW (correspondence form of education)
| № | The name of the Subject submitted for self-study | Number of SSW hours |
|---|---|---|
| 1 | Graphical methods of solving nonlinear equations and investigating functions | 10 |
| 2 | Methods of approximation and smoothing of functions | 10 |
| 3 | Approximate calculation of multiples integrals | 10 |
| 4 | Analytical methods of solving ordinary differential equations | 10 |
| 5 | Methods of ensuring the stability of solutions of linear equation systems | 10 |
| 6 | Newton method for numerical solution of systems of nonlinear equations | 10 |
| 7 | Jacobi method for numerical solution of systems of nonlinear equations | 10 |
| 8 | Shooting method | 10 |
| 9 | Finite difference method for solving systems of edge problems | 10 |
| 10 | Preparing to module control work | 8 |
| 11 | Preparing to examination | 10 |
| Total | 108 |
Policy and control
Policy of academic discipline (educational component)
The system of requirements for students:
attending lectures and laboratory classes is a mandatory component of studying the material.
at the lecture the teacher uses his own presentation material, uses Google Drive to teach the material of the current lecture, additional resources, laboratory work, etc.; the teacher opens access to a certain directory of the Google disk for downloading electronic laboratory reports and responses to modular control work (MCW).
it is forbidden to distract the teacher from teaching the material, all questions, clarifications, etc. at the lecture; students ask at the end of the lecture in the allotted time.
laboratory works are defended in two stages: the first stage – students perform tasks for admission to the defense of laboratory work; the second stage – defending of the laboratory work. Points for laboratory work are considered only in the presence of an electronic report.
modular tests can be written in lectures with the help of calculating devices (mobile phones, calculators, tablets, etc.); the result is sent in a file to the appropriate directory of Google Drive.
incentive points are awarded for: active participation in lectures; participation in faculty and institute Olympiads in academic disciplines, participation in competitions of works, preparation of reviews of scientific works; presentations on one of the Subjects of the SSW disciplines, etc. Number of encouraged points no more than 10.
penalty points are set for: late delivery of laboratory work. Number of penalty points for no more than 10.
Types of control and rating evaluation system for assessing learning outcomes (RES)
The student's rating in the discipline consists of points that he receives for:
performance of 9 laboratory works.
performance of 2 modular control works (MCW);
incentive and penalty points.
answers to the questions of the examination ticket
The student's rating of the correspondence form in the discipline consists of points that he receives for:
performance of laboratory works.
performance of a modular control works (MCW);
incentive and penalty points.
answers to the questions of the examination ticket.
Rating points system and evaluation criteria
Answers to the questions of the examination ticket (maximum 44 points):
«Excellent» – complete answer (not less than 90% of the required information).
«Good» – a fairly complete answer (at least 75% of the required information) or a complete answer with minor flaws.
«Satisfactory» – incomplete answer (not less than 60% of the required information) and minor errors.
«Unsatisfactory» – the answer does not meet the requirements for «satisfactory».
Laboratory works (maximum 36 points):
«Excellent», a complete answer to the question during the defense (not less than 90% of the required information) and a properly executed electronic protocol for laboratory work - 4 points;
«Good», a sufficiently complete answer to the question during the defense (not less than 75% of the required information) and a properly executed electronic protocol for laboratory work - 3 points;
«Satisfactory», incomplete answer to the question during the defense (not less than 60% of the required information), minor errors and properly executed electronic protocol for laboratory work - 2 points;
«Unsatisfactory», unsatisfactory answer and/or not properly executed electronic protocol for laboratory work - 0 points.
For each lesson late with the submission of laboratory work to defend against the deadline, the score is reduced by 1 point.
Modular control works (maximum 20 points, 10 points for each one):
«Excellent», complete answer (not less than 90% of the required information) – 9-10 points;
«Good», a sufficiently complete answer (not less than 75% of the required information), or a complete answer with minor errors - 6-8 points;
«Satisfactory», incomplete answer (but not less than 60% of the required information) and minor errors – 3-5 points;
«Unsatisfactory», unsatisfactory answer (incorrect solution of the problem), requires mandatory rewriting at the end of the semester – 0 points.
Correspondence form of education:
Laboratory works (maximum 36 points):
«Excellent», a complete answer to the question during the defense (not less than 90% of the required information) and a properly executed electronic protocol for laboratory work - 8 points;
«Good», a sufficiently complete answer to the question during the defense (not less than 75% of the required information) and a properly executed electronic protocol for laboratory work – 6-7 points;
«Satisfactory», incomplete answer to the question during the defense (not less than 60% of the required information), minor errors and properly executed electronic protocol for laboratory work - 5 points;
«Unsatisfactory», unsatisfactory answer and/or not properly executed electronic protocol for laboratory work - 0 points.
Modular control work:
«Excellent», complete answer (not less than 90% of the required information) – 28-32 points;
«Good», a sufficiently complete answer (not less than 75% of the required information), or a complete answer with minor errors - 24-27 points;
«Satisfactory», incomplete answer (but not less than 60% of the required information) and minor errors – 19-23 points;
«Unsatisfactory», unsatisfactory answer (incorrect solution of the problem), requires mandatory rewriting at the end of the semester – 0 points.
Incentive points
- for performing creative work on the credit module (for example, participation in faculty and institute competitions in academic disciplines, participation in competitions, preparation of reviews of scientific papers, etc.); for active work on lectures (questions, additions, remarks on the Subject of the lecture, when the lecturer asks students to ask their questions) 1-2 points, but in the amount of not more than 10.
- SSW presentations - from 1 to 5 points.
Intersessional certification
According to the results of educational work for the first 7 weeks the maximum possible number of points – 22,5 points (2 laboratory, MCW-1). At the first certification (8th week) the student receives "enrolled" if his current rating is not less than 8 points.
According to the results of 13 weeks of training, the maximum possible number of points is 45 points (4 laboratory, MCW-2). At the second attestation (14th week) the student receives "credited" if his current rating is not less than 16 points.
The maximum amount of weight points of control measures during the semester is:
RD = 7*rlab+2*rmcr+ (ri - rp) = 7*5+2*5+2*2,5+ (ri - rp) = 50
- (ri - rp),
where rlab – points for laboratory work (0…4);
rmcr – points for MCW (0…10);
ri – incentive points for active participation in lectures, presentations, participation in competitions, competitions, research papers on the subject of the discipline (0…10);
rp – penalty points.
Examination:
The condition for admission to the exam is enrollment in all laboratory work, writing both modular tests and a starting rating of at least 20 points.
At the exam, students perform a written test. Each ticket contains two theoretical questions (tasks). The list of theoretical questions is given in appendices 1 and 2. Each question (task) is evaluated in 20 points.
Question evaluation system (maximum 44 points for 2 questions):
«Excellent», complete answer (not less than 90% of the required information) - 18-22 points;
«Good», a fairly complete answer (at least 75% of the required information, or minor inaccuracies) – 14-16 points;
«Satisfactory», incomplete answer (not less than 60% of the required information and some errors) - 10-12 points;
«Unsatisfactory», unsatisfactory answer - 0-7 points.
The sum of starting points and points for the examination test is transferred to the examination score according to the table:
Table 1. Translation of rating points to grades on a university scale
| Points | Mark |
| 100-95 | Excellent |
| 94-85 | Very good |
| 84-75 | Good |
| 74-65 | Satisfactory |
| 64-60 | Enough |
| Less, then 60 | Unsatisfactory |
There are no credited labs or modular control work is not included |
Not allowed |
Additional information on the discipline (educational component)
the list of theoretical questions submitted for semester control is given in Appendix 1;
At the beginning of the semester, the teacher analyzes the existing courses on the subject of the discipline and offers students to take the appropriate free distance courses. After the student receives a certificate of distance or online courses on the subject, the teacher closes the relevant part of the course (laboratory or lectures) by prior arrangement with the group.
Syllabus:
Written by Prof., Dr.Sci, Anatoliy Doroshenko and senior teacher Yulia Timofeeva.
Approved by department ACTS (protocol № 1 dated 30.08.2021 р.)
Agreed with Methodical commission of the faculty [1] (protocol № 1 dated 30.08.2021 р.)
Appendix 1
List of theoretical questions for examenation
1. 1. The concept of numerical method.
2. Approximate numbers and types of errors.
3. A significant number and number of correct digits of the approximate number.
4. Rules for rounding numbers
5. Calculation of function error from n arguments
6. Method of half division for solving nonlinear equations.
7. Horde method for solving nonlinean equations.
8. Newton's method for solving nonlinear equations.
9. Method of simple iteration. Compressive maps Theorem
10. Interpolation by Lagrange.
11. Accuracy of interpolation by Lagrange polynomials.
12. The finite differences of different orders
13. Split differences
14. Newton's interpolation formula
15. Interpolation with cubic splines
16. Formula of rectangles for numerical integration
17. Trapezoid formula for numerical integration
18. Simpson's formula for numerical integration
19. Euler method of solving differential equations
20. Modified Euler method for solving differential equations
21. Runge-Kutta method for solving differential equations
22. Adams method of solving differential equations
23. The differential appearance of the Adams method
24. Adams-Beshforts predictor method
25. Norms of vectors and mages
26. Theorem about the own numbers of matrices
27. Theorem about the LU-factorization of matrices
28. Gaussian algorithm for solving systems of linear equations
29. Method of racing the solution of systems of linear equations
30. Jacobi's simple iteration method and error assessment
31. Sufficient condition for the convergence of the simple iteration method
32. A sufficient and necessary conditions for the convergence of the simple iteration method
33. Seidel method and error assessment
34. Shooting method for solving edge problems
35. Finite-difference method for solving regional problems
36. Newton's method for solving systems of nonlinear equations
37. Jacobi method for solving systems of nonlinear equations
[1] Methodical council of the university - for general university disciplines.
