Course code Mate1003

Credit points 4.50

Total Hours in Course120

Number of hours for lectures16

Number of hours for seminars and practical classes32

Independent study hours72

Date of course confirmation19.10.2022

Responsible UnitInstitute of Mathematics and Physics

Matemātikas un fizikas institūts
## Svetlana Atslēga

Dr. math.

lect.
## Liene Strupule

Mg. math.

MateB006 [GMATB006] Mathematics I

The aim of the study course is to acquire the mathematical knowledge and practical skills for applying math techniques to study different problems related to Information technologies.

The study course deals with elements of linear algebra, analytic geometry, limits, differentiation of function of one variable.

Upon successful completion of this course:

1. Students are able to manage and demonstrate knowledge and critical understanding of linear algebra, vectors algebra, analytic geometry, limits, differentiation of function of one variable. Students manage the application of the acquired topics in practical examples related to the specialty of the Information Technologies 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 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. Determinants. Evaluation of a determinant. Solutions of systems of linear equations – 6h

2. Matrices. Operations with matrices. Applications of matrix operations – 6h

3. Equations of lines. Applications of straight line – 1h

4. **Test 1.** Linear algebra – 1h

5. Vector algebra: dot product of two vectors, cross product of two vectors, scalar triple product – 6h

6. Limits and their properties. Indeterminate forms, applications of limits – 7h

7. **Test 2.** Vector algebra. Limits – 1h

8. Differentiation – 13h

9. Applications of differentiation. Optimization problems – 6h

10. **Test 3.** Differentiation – 1h

Formal test (Pass/Fail assessment) must be passed.

The following independent works must be completed in writing form:
**Independent work 1.** Linear algebra
**Independent work 2.** Vector algebra
**Independent work 3.** Limits of functions
**Independent work 4.** Differentiation

The course is completed without additional knowledge examination if the results of the semester are summarized as all independent works are completed (all tasks are completed correctly); during the semester each test score is at least 4.

Failed tests can be repeated during the study process at the time indicated by the academic staff. The student can repeat the last test in the 1st week of period of individual studies and examinations at the time indicated by the academic staff.

In the case of unsuccessful work in the semester student answers for all the topics together in the period of the individual studies and examinations at the time indicated by the academic staff.

1. Volodko I. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 2007. – 294 lpp

2. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika I daļa. Rīga: Zvaigzne, 1988. – 534 lpp.

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

4. Stewart J. Calculus. Bellmont CA: Brooks/Cole, Cengage Learning, 2012. 146 p.

5. Bird J.O. Engineering Mathematics. London; New York:Bellmont Routledge/Taylor & Francis Group, 2017. 709 p.

1. Šteiners K. Augstākā matemātika. I, II, III daļa. Rīga: Zvaigzne ABC, 1997. - 96 lpp.,1998. - 116 lpp., 1998. - 192 lpp.

2. Stroud K.A. Engineering Mathematics. South Norwalk, CT: Industrial Press, 2013. 1155 p.

3. Uzdevumu krājums augstākajā matemātikā. / Dz.Bože, L.Biezā, B.Siliņa, A.Strence. Rīga: Zvaigzne, 2001. 332 lpp.

Compulsory course for Faculty of Information Technologies Bachelor’s study programmes “Computer Control and Computer Science” and „Information Technologies for Sustainable Development”.