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Mathematics I

Course developers

Replaced course

MateB006 [GMATB006] Mathematics I

Course abstract

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.

Learning outcomes and their assessment

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.

Course Content(Calendar)

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

Requirements for awarding credit points

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

Description of the organization and tasks of students’ independent work

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

Criteria for Evaluating Learning Outcomes

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.

Compulsory reading

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.

Further reading

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.

Notes

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