Course code MateB008
Credit points 6
Mathematics II
Total Hours in Course120
Number of hours for lectures32
Number of hours for seminars and practical classes32
Number of hours for laboratory classes0
Independent study hours98
Date of course confirmation24.01.2024
Responsible UnitInstitute of Mathematics and Physics
Course developers
Svetlana Atslēga
Dr. math.
Liene Strupule
Mg. math.
Prior knowledge
MateB006, Mathematics I
Replaced course
Mate1037 [GMAT1036] 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 integral calculus, 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 integral calculus, applications, complex numbers, ordinary differential equations, series and 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– 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. Integration. Definite integrals. Applications of integration: area of a plane region, arc length and volume of a solid of revolution (17 h)
2. Test 1: Integration and Applications (2 h)
3. First-Order Differential Equations. Applications (7 h)
4. Complex Numbers (4 h)
5. Second-Order Differential Equations. Applications (11 h)
6. Test 2: First-Order and Second-Order Differential Equations (2 h)
7. Series: Convergence of an infinite series. Convergence of alternating series (7 h)
8. Power Series: interval of convergence of a power series. Power series approximation of a definite integral. Series solutions of differential equations (12 h)
9. Test 3: Series and power series (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. Integral calculus
Independent work 2. Application of integration
Independent work 3. First-order differential equations
Independent work 4. Second-order differential equations
Independent work 5. Series
Independent work 6. Power series
Criteria for Evaluating Learning Outcomes
The student can receive the accumulative exam score if
- the study course Mathematics I (MateB006) must be passed
- 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.
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. Paul Blachard. Differential equations. Belmont: Thomson Brooks/Cole, c2006. xviii, 828 lpp.
5. 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”.