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Mathematics I

Course developers

Replaced course

Mate1003 [GMAT1003] 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, vector algebra, calculus, differentiation of function of one variable and two variables, integral calculus.

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, integral calculus. 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– 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 (5 h)
2. Matrices. Operations with matrices. Applications of matrix operations (5 h)
3. Test 1: Linear algebra (1 h)
4. Vector algebra: dot product of two vectors, cross product of two vectors, triple scalar product (6 h)
5. Conic sections: ellipse, hyperbola, parabola (2 h)
6. Evaluating limits. Indeterminate forms. Continuity of a function. Applications of limits (7 h)
7. Test 2: Vector algebra. Limits (1 h)
8. Differentiation of function of one variable (10 h)
9. Applications of differentiation. Optimization problems (2 h)
10. Partial derivatives of functions of two variables. Applications (7 h)
11. Test 3: Differentiation of function of one variable and two variables (2 h )
12. Integration. Indefinite Integration. Basic integration rules. Integration by substitution and integration by parts, integration of rational functions (14 h)
13. Test 4: Integral calculus (2 h)

Requirements for awarding credit points

The course is assessed through an examination

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
Independent work 4. Differentiation of function of one variable.
Independent work 5. Differentiation of function of two variables.
Independent work 6. Indefinite integrals

Criteria for Evaluating Learning Outcomes

The student can receive the accumulative exam score if
- all independent works are defended successfully until the beginning of period of individual studies and examinations
- during the semester each test score is at least 4.
The mark of the accumulative exam consists of the average mark of all tests.
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.
The exam can be arranged at the time indicated by the academic staff if all independent works are successfully defended.

Compulsory reading

1. Volodko I. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 2007. – 294 lpp
2. Volodko I. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 2009. – 392 lpp  
3. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika I daļa. Rīga: Zvaigzne, 1988. – 534 lpp.
4. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika II daļa. Rīga: Zvaigzne, 1988. – 527 lpp.
5. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem I daļa.. Rīga: Zvaigzne ABC, 2003. 256 lpp.
6. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem II daļa.. Rīga: Zvaigzne ABC, 2004. 192 lpp.

Further reading

1. Šteiners K. Augstākā matemātika. I , II, III daļa. Rīga: Zvaigzne ABC, 1997. - 96 lpp.,1998. - 116 lpp., 1998. - 192 lpp.
2. Roland E. Larson. Brief calculus: an applied approach. Belmont, CA: Brooks/Cole, Cengage Learning, c2009 xxi, 569,112 lpp.
3. Kuldeep S. Engineering mathematics through applications. Basingstoke: Palgrave Macmillan, 2011. xvi, 927 lpp.
4. 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”.