Course code Mate1035

Credit points 3

Total Hours in Course81

Number of hours for lectures16

Number of hours for seminars and practical classes16

Number of hours for laboratory classes8

Independent study hours41

Date of course confirmation12.04.2021

Responsible UnitInstitute of Mathematics and Physics

Matemātikas un fizikas institūts
## Svetlana Atslēga

Dr. math.

reserch
## Aivars Āboltiņš

Dr. sc. ing.

Mate4016, Mathematics I

The study course deals with function of one and two variables and it’s applications, indefinite integration and numerical integration, linear programming. The study course is intended to acquire the mathematical knowledge and practical skills needed to study future special subjects, as well as to acquire skills for applying math techniques to study different problems related to wood processing and related fields. During the course, students acquire skills in working with appropriate application software, such as “Matlab”.

Upon successful completion of this course:

1. Students are able to manage and demonstrate knowledge and critical understanding of function of two variables and it’s applications, indefinite integration and numerical integration, linear programming. Students manage the application of the acquired topics in practical examples related to the specialty of the forest engineering science and related fields. – **tests**.

2. Students are able to show understanding of the corresponding concept and regularities, to perform necessary calculations and operations. Students are able to use appropriate software for calculations. – **practical and laboratory works**.

3. Working in a group or doing work independently, student is able to apply the mathematical calculations corresponding to the specialty problem situation, to make a professional assessment and interpretation of the intermediate result of the calculations and the final results – **independent works**.

1. Applications of derivatives of function of one variable (2h)

2. Extrema of functions of one variables. Practical application (3h)

3. Numerical methods for solving nonlinear equations (2h)

4. Partial derivatives of function of two variables (2h)

5. Extrema of functions of two variables (3h)

6. Practical applications (2h)

7. **Test 1:** Extrema of functions of one and two variables (1h)

8. Indefinite integration. Basic integration rules. Integration by substitution. Integration by parts (5h)

9. Definite integrals. Integration by substitution in the definite integrals. Integration by parts (4h)

10. Application of the definite integrals (3h)

11. **Test 2:** Indefinite and definite integrals (1h)

12. Linear programming problems (LPP) and interpretation (2h)

13. Feasible solution and optimal solutions. Two-variable linear programming (2h)

14. Graphical method for solving LPP (2h)

15. Simplex method.(5h)

16. **Test 3:** Linear programming (1h)

Assessment: Exam.

In writing form and by using the appropriate software, the following independent work must be completed (all tasks are executed correctly) at times specified by the teaching staff:
**Independent work 1.** Applications of derivatives
**Independent work 2.** Functions of two variables
**Independent work 3.** Indefinite integration
**Independent work 4.** Definite integrals
**Independent work 5.** Linear programming

The student can receive the **accumulative exam** if:

1. all independent works are completed at times specified by the teaching staff;

2. during the semester each test score is at least 4.

Failed tests can be repeated.

The student may overwrite unsuccessfully written test work during the study process, at times specified by the teaching staff. The student can rewrite the last test in the 1st week of the individual study and examination period at the time indicated by the teaching staff.

The accumulative exam mark is

- 90% of the average mark of all tests

- 10% for completed independent works.

The **written exam** can be arranged at the time indicated by the teaching staff, if all the independent works are defended (all tasks are performed correctly).

1. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika I un II daļa. Rīga: Zvaigzne, 1988. 534 lpp.; 1988. 527 lpp.

2. Volodko I. Augstākā matemātika. I un II daļa. Rīga: Zvaigzne ABC, 2007. 294 lpp.; 2003. 271 lpp.

3. Kļaviņš D. Optimizācijas metodes ekonomikā. I, II daļa. Rīga: Datorzinību centrs, 2003. 271 lpp.

1. Peļņa M., Gulbe M. Optimizācijas uzdevumi ekonomikā Mācību līdzeklis, Rīga Datorzinību centrs 2003.—180 lpp.

2. Āboltiņa B., Liepiņa K. Rokasgrāmata matemātikā vecāko klašu skolēniem un studentiem Rīga, Zvaigzne ABC 2018.- 320 lpp.

3. Lewin J. An Interactive Introduction to Mathematical Analysis. Cambridge University Press.2003.- 492 P

The study course is included in the compulsory part of the professional higher education bachelor study program “Wood Processing”.