Course code Mate1037

Credit points 4.50

# Mathematics II

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

### Course developers

Matemātikas un fizikas institūts

Dr. math.

lect.

## Liene Strupule

Mg. math.

### Prior knowledge

Mate1003, Mathematics I

### Replaced course

MateB008 [GMATB008] 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 functions of two variables, elements of analytic geometry, 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 functions of two variables, analytic geometry, 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. 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. Functions of two variables. Applications – 7h
2. Conic sections: ellipse, parabola, hyperbola – 4h
3. Test 1. Functions of two variables. Conic sections – 1h
4. Integral calculus. Basic integration rules. Integration techniques: substitution, integration by parts. Integration of rational, irrational, and trigonometric functions – 19h
5. Test 2. Integral calculus – 1h
6. Definite integrals. Applications of integration: area between curves, volumes of solids of revolution – 15h
7. Test 3. Definite integrals. Applications of integration -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. Functions of two variables. Applications
Independent work 2. Conic sections
Independent work 3. Indefinite integrals
Independent work 4. Definite integrals

### Criteria for Evaluating Learning Outcomes

The course is completed without additional knowledge examination if
1. the study course Mathematics I (Mate1003) must be passed
2. the results of the semester are summarized as all independent works are completed (all tasks are completed correctly)
3. 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. 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.
7. Stewart J. Calculus. Bellmont CA: Brooks/Cole, Cengage Learning, 2012. 146 p.
8. Bird J.O. Engineering Mathematics. London; New York:Bellmont Routledge/Taylor & Francis Group, 2017. 709 p.