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Mathematics I

Course developer

Replaced course

MateB009 [GMATB009] Mathematics I

Course abstract

The study course deals with elements of linear algebra, analytic geometry, vectors algebra, limits, differentiation of function of one variable. The study course is intended to acquire the mathematical knowledge and practical skills needed to study future special subjects, as well as to acquire skills for applying math techniques to study different problems related to Civil Engineering science and related fields. During the course, students acquire skills in working with appropriate application 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, analytic geometry, limits, differentiation of function of one variable. 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. The theory of matrices and determinants (9 h)
2. Solution of systems of linear equations (Cramers rule, Gaussian elimination method) (6 h)
3. Test 1: Linear algebra (1 h)
4. Analytical geometry on plane (2 h)
5. Straight lines on plane and applications (3 h)
6. Conic sections (4 h)
7. Space. Vectors and properties. Addition of vectors and vector subtraction (3 h)
8. The scalar product and the vector product of two vectors, applications. Scalar triple product or vector triple product, applications (4 h)
9. Test 2: Analytical geometry and vector algebra (1 h)
10. Functions and different types of functions. Sequences and limits. Number e (2 h)
11. Limit of function. Properties of limits. Indeterminate forms (3 h)
12. Special trigonometric limits. Number e as a limits (3 h)
13. Derivative of function (3 h)
14. Derivative of composite function. Logarithmic differentiation (4 h)
15. Implicit differentiation. Differentiation of a function defined parametrically (3 h)
16. Higher order derivatives (4 h)
17. Test 3: Limits of function and derivatives (1 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. Analytical geometry
Independent work 3. Vector algebra
Independent work 4. Limits of functions
Independent work 5. Derivatives of functions

Criteria for Evaluating Learning Outcomes

The student receive the test if
1. all independent works are completed at times specified by the teaching staff;
2. during the semester each test score is at least 4.
Failed tests can be repeated.
The student may overwrite unsuccessfully written test work during the study process at times specified by the teaching staff. The student can rewrite the last test in the 1st week of the individual study and examination period at the time indicated by the teaching staff.

Further reading

1. Šteiners K. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 1997. 96 lpp.
2. Šteiners K. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 1998. 116 lpp.
3. Šteiners K. Augstākā matemātika. III daļa. Rīga: Zvaigzne ABC, 1998. 192 lpp.
4. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem I daļa Zvaigzne ABC Rīga, 2003 – 256 lpp.
5. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem II daļa Zvaigzne ABC Rīga, 2004 – 192 lpp.
6. Lewin J. An Interactive Introduction to Mathematical Analysis. Cambridge University Press.2003.- 492 p

Notes

The study course is included in the compulsory part of the Bachelor’s study program “Civil Engineering”.