Course code Mate5004
Credit points 3
Use of Mathematics Methods
Total Hours in Course81
Number of hours for lectures12
Number of hours for seminars and practical classes12
Independent study hours57
Date of course confirmation12.04.2021
Responsible UnitInstitute of Mathematics and Physics
Course developers
Natālija Sergejeva
Dr. math.
Svetlana Atslēga
Dr. math.
Course abstract
The aim of study course - differential calculus of functions of several variables, graphical solution of linear programming problems, simplex method, transportation problem, basics of mathematical game theory are considered. The study course provides an understanding of modern concepts and problems of mathematical modeling. The study course promotes mathematical thinking, looks at different applications of mathematics in engineering.
Learning outcomes and their assessment
By the successful completion of this study course, students will have
1. knowledge of the differentiation of functions of several variables and their applications, methods for solving linear programming problems, transportation problems and mathematical game problems.. Knowledge is assessed during the exam, practical and independent works.
2. skills to perform necessary calculations and operations, understanding of relevant concepts and regularities. Skills are assessed during exam, practical and independent works.
3. Competence to perform intermediate results of calculations and professional evaluation and interpretation of final results. Competences are assessed during exam and practical work.
Course Content(Calendar)
1. Functions of several variables. Partial and total increments. Partial derivatives. – 2 h
2. Extrema of functions of several variables. - 3 h
3. Optimization with constraints (elimination method). – 1 h
4. Scalar and vector field. Directional derivatives, gradients. - 2 h
5. Presentation of the first individual coursework.
6. Introduction to operations research. An introduction to mathematical modelling.
7. Graphical method for solving linear programming problems. – 2 h
8. Basic solution for linear programming problem. Gauss-Jordan elimination method. – 2 h
9. Simplex method and its implementation. – 3 h
10. Transportation problem and determination of basic feasible solution of transportation problem. – 3 h
11. Matrix game. Graphical method for solving matrix game problems. – 3 h
12. Presentation of the second individual coursework.
Requirements for awarding credit points
Exam must have passed.
Description of the organization and tasks of students’ independent work
The following independent works must be completed:
Independent work 1: Differentiation of Functions of Several Variables.
Independent work 2: Operations Research.
Criteria for Evaluating Learning Outcomes
Students take a written exam (80% practical tasks, 20% theoretical questions) at the time indicated by the lecturer if all independent works have been passed (all tasks have been completed correctly). Independent works that have not been credited in time can be defended at the times indicated by the teaching staff.
Compulsory reading
1. Hamdy A.Taxa. Operation research. An Introduction. University of Arkansas, Fayetteville, Upper Saddle River, NJ 07458, 8th ed., 2007. 838 p.
2. Kļaviņš D. Optimizācijas metodes ekonomikā I, II. Rīga: Datorzinību centrs, 2003. – 271 lpp.
3. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika II daļa. Rīga: Zvaigzne, 1988. – 527 lpp.
Further reading
1. Peļņa M., Gulbe M. Optimizācijas uzdevumi ekonomikā. Rīga: Datorzinību centrs, 2003. 159 lpp.
2. Хэмди А. Така. Введение в исследование операций. 6-е издание: Пер. с англ. Москва: Издательский дом ”Вильямс”, 2001. 912 с.
3. Hillier F.S., Lieberman G.J. Introduction to mathematical programming. New York: McGraw-Hill, 1995. 716 p.
Notes
Compulsory course for Faculty of Forest and Environmental Sciences academic Master's study programme "Environmental, Water and Land Engineering" and master’s study programme „Wood Materials and Technology”.