Course code MateB010
Credit points 5
Mathematics II
Total Hours in Course120
Number of hours for lectures24
Number of hours for seminars and practical classes40
Number of hours for laboratory classes0
Independent study hours71
Date of course confirmation24.01.2024
Responsible UnitInstitute of Mathematics and Physics
Course developer
Svetlana Atslēga
Dr. math.
Prior knowledge
MateB009, Mathematics I
Replaced course
Mate1022 [GMAT1021] 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 Civil Engineering science and related fields.
The study course deals with differentiation of function of two variables, elements of analytic geometry, integral calculus, linear correlation and linear regression. Students will acquire skills in working with appropriate software such as Matlab
Learning outcomes and their assessment
Upon successful completion of this course:
1. Students are able to manage and demonstrate knowledge and critical understanding of differentiation of function of two variables, analytic geometry, integral calculus. Students manage the application of the acquired topics in practical examples related to the specialty of the Civil Engineering science 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 and laboratory 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)
Full time studies:
1. Partial derivatives of functions of two variables. Applications (12 h)
2. Conic sections: ellipse, hyperbola, parabola (8 h)
3. Test 1. Derivatives of function of two variables. Conic sections (2 h)
4. Integration. Indefinite Integration. Basic integration rules. Integration by substitution and integration by parts, integration of rational functions (16 h)
5. Test 2. Integral calculus (2 h)
6. Integration. Definite integrals. Applications of integration: area of a plane region, arc length and volume of a solid of revolution (18 h)
7. Test 3. Integration and Applications (2 h)
8. Linear regression and correlation (4 h)
Part-time studies:
All topics specified for full-time studies are covered, but the number of contact hours is half of the number specified in the calendar.
Requirements for awarding credit points
In writing form and by using the appropriate software, the following independent work must be completed (all tasks are executed correctly) at times specified by the teaching staff:
Independent work 1. Differentiation of function of two variables
Independent work 2. Conic sections
Independent work 3. Indefinite integrals
Independent work 4. Definite integrals, applications
Independent work 5. Linear regression and correlation
Description of the organization and tasks of students’ independent work
In writing form and by using the appropriate software, the following independent work must be completed (all tasks are executed correctly) at times specified by the teaching staff:
Independent work 1. Differentiation of function of two variables
Independent work 2. Conic sections
Independent work 3. Indefinite integrals
Independent work 4. Definite integrals, applications
Independent work 5. Linear regression and correlation
Criteria for Evaluating Learning Outcomes
The student can receive the accumulative exam score if
- the study course Mathematics I (MateB009) 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.
5. Roland E. Larson. Brief calculus: an applied approach. Belmont, CA: Brooks/Cole, Cengage Learning, c2009. xxi, 569,112 lpp.
Further reading
1. Šteiners K. Augstākā matemātika. IV ,V daļa. Rīga: Zvaigzne ABC, 1998. - 168 lpp., 2000. - 129 lpp.
2. Kuldeep S. Engineering mathematics through applications. Basingstoke: Palgrave Macmillan, 2011. xvi, 927 lpp.
3. Paul Blachard. Differential equations. Belmont: Thomson Brooks/Cole, c2006. xviii, 828 lpp.
4. Uzdevumu krājums augstākajā matemātikā. / Dz.Bože, L.Biezā, B.Siliņa, A.Strence. Rīga: Zvaigzne, 2001. 332 lpp.
Notes
The study course is included in the compulsory part of the Bachelor’s study program “Civil Engineering”.