Course code Mate1038

Credit points 2

# Mathematics III

Total Hours in Course80

Number of hours for lectures16

Number of hours for seminars and practical classes16

Independent study hours48

Date of course confirmation19.10.2022

Responsible UnitDepartment of Mathematics

### Course developers

Matemātikas katedra

Dr. math.

lect.

## Liene Strupule

Mg. math.

### Prior knowledge

Mate1003, Mathematics I

Mate1037, Mathematics II

### 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 complex numbers, ordinary differential equations, series and power series.

### Learning outcomes and their assessment

Upon successful completion of this course:
1. Students are able to manage and demonstrate knowledge and critical understanding of complex numbers, ordinary differential equations, series, power series. 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. Complex numbers -4h
2. First-order ordinary differential equations and their applications – 6h
3. Second-order ordinary differential equations and their applications – 5h
4. Test 1. First-order and second-order ordinary differential equation – 1h
5. Series and convergence. Alternating series. – 6h
6. Power series. Repesentation of functions by power series. Applications – 9h
7. Test 2. Series. Power series. Applications – 1h

### 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. First-order ordinary differential equations
Independent work 2. Second-order ordinary differential equations
Independent work 3. Series
Independent work 4. Power series

### Criteria for Evaluating Learning Outcomes

The student can receive the accumulative exam score if
1. the study courses Mathematics I (Mate1003), Mathematics II (Mate1037) must be passed
2. all independent works are defended successfully until the beginning of period of individual studies and examinations.

The mark of the accumulative exam consists of the average mark of all tests
Laboratory work that has not been passed on time can be completed in a time allotted by the academic staff, but not more than two per one visit.
The exam can be arranged at the time indicated by the academic staff if all independent works are successfully defended.

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