Course code Mate1032

Credit points 2

Total Hours in Course80

Number of hours for lectures16

Number of hours for seminars and practical classes16

Number of hours for laboratory classes8

Independent study hours40

Date of course confirmation12.04.2021

Responsible UnitDepartment of Mathematics

prof.
## Natālija Sergejeva

Dr. math.

Matemātikas katedra
## Svetlana Atslēga

Dr. math.

reserch
## Aivars Āboltiņš

Dr. sc. ing.

Mate4014, Mathematics I

The study course deals with function of two variables and it’s applications, indefinite integration and numerical integration, linear programming, ordinary differential equations. 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 forest science 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 and differential equations. 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. Partial derivatives of function of two variables (2h)

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

3. Practical applications (3h)

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

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

6. Graphical method for solving LPP (2h)

7. Simplex method (5h)

8. **Test 1:** Linear programming and functions of two variables (1h)

9. Indefinite integration. Basic integration rules (2h)

10. Integration by substitution. Integration by parts (3h)

11. Definite integrals. Integration by substitution in the definite integrals (2h)

12. Integration by parts (3h)

13. Application of the definite integrals (4h)

14. First-order ordinary differential equations (5h)

15. **Test 2:** Indefinite and definite integrals. Differential equations (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.** Functions of two variables
**Independent work 2.** Linear programming
**Independent work 3.** Indefinite integration
**Independent work 4.** Definite integrals
**Independent work 5.** Differential equations

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).

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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. Siliņa B., Šteiners K. Rokasgrāmata matemātikā: elementārā matemātika: augstākā matemātika.. Rīga: Zvaigzne ABC, 2006. 367 lpp.

4. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem I daļa Zvaigzne ABC Rīga, 2003 – 256 lpp.

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

https://www.macmillanihe.com/companion/Singh-Engineering-Mathematics-Through-Applications/fully-worked-solutions/