LV EN RU DE FR

Mathematics I

Course developer

Replaced course

Mate1021 [GMAT1020] Mathematics I

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 elements of linear algebra, vector algebra, calculus, differentiation of function of one variable and 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 linear algebra, vectors algebra, limits, differentiation of function of one variable. Students manage the application of the acquired topics in practical examples related 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– practical works 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. Matrices and determinants. Evaluation of a determinant and matrices (10 h)
2. Solutions of systems of linear equations (8 h)
3. Vector algebra: dot product of two vectors, cross product of two vectors, triple scalar product (6 h)
4. Test 1. Linear algebra. Vector algebra (2 h)
5. Evaluating limits. Indeterminate forms. Continuity of a function. Applications of limits (8 h)
6. Differentiation of function of one variable (8 h)
7. Applications of differentiation. Optimization problems (4 h)
8. Test 2. Limits. Differentiation of function of one variable (2 h)

Requirements for awarding credit points

Assessment: Test (pass/fail).

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. Elements of linear algebra
Independent work 2. Vector algebra
Independent work 3. Limits of functions
Independent work 4. Derivatives of functions, applications

Criteria for Evaluating Learning Outcomes

The student receive the tes if
- all independent works are completed at time specifies by the teaching staff;
- during the semestrer 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.

Compulsory reading

1. Volodko I. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 2007. – 294 lpp
2. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika I daļa. Rīga: Zvaigzne, 1988. – 534 lpp.
3. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika II daļa. Rīga: Zvaigzne, 1988. – 527 lpp.
4. 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. I , II, III daļa. Rīga: Zvaigzne ABC, 1997. - 96 lpp.,1998. - 116 lpp., 1998. - 192 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.
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”.