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Mathematics III

Course developer

Prior knowledge

MateB009, Mathematics I

MateB010, Mathematics II

Replaced course

Mate2031 [GMAT2032] Mathematics III

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 complex numbers, ordinary differential equations, series and power series, applications. 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 complex numbers, ordinary differential equations and series and their applications. 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)

1. Complex numbers. Basic operations (5 h)
2. First order ordinary differential equations. Equations with separable variables (4 h)
3. Linear ordinary differential equations, Bernoulli differential equations (5 h)
4. Test 1, Complex numbers. First-order ordinary differential equations. (2 h)
5. Second order differential equations (3 h)
6. Second order homogeneous and nonhomogeneous linear equations (6 h)
7. The system of differential equations (2 h)
8. Test 2. Second-order equations. The system of differential equations (2 h)
9. Series with positive terms. Convergence for series. Series with positive terms. Cauchy convergence test, ratio test, comparison test, integral test. Alternating series (9 h)
10. Power series. Interval of convergence of the power series. Taylor series and MacLaurin series. Representation of functions by power series (4 h)
11. Numerical integration using power series. Solving ordinary differential equations using power series (4 h)
12. Test 3. Series with positive terms and series of functions (2 h)

Requirements for awarding credit points

The course is assessed through an examination

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. Complex numbers First order differential equations
Independent work 2. Second order differential equations. Systems of differential equations
Independent work 3. Series with positive terms
Independent work 4. Power series

Criteria for Evaluating Learning Outcomes

The student can receive the accumulative exam score if
- the study course Mathematics I (MateB009), Mathematics II (MateB010) 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”.