Course code Mate2036

Credit points 6

Total Hours in Course162

Number of hours for lectures24

Number of hours for seminars and practical classes40

Number of hours for laboratory classes8

Independent study hours90

Date of course confirmation12.04.2021

Responsible UnitInstitute of Mathematics and Physics

Matemātikas un fizikas institūts
## Svetlana Atslēga

Dr. math.

Mate1031, Mathematics I

The study course deals with analytic geometry, limits, differentiation of function of one variable, indefinite integration and numerical integration. 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.

Upon successful completion of this course:

1. Students are able to manage and demonstrate knowledge and critical understanding of analytic geometry, limits, differentiation of function of one variable, indefinite integration and numerical integration. Students manage the application of the acquired topics in practical examples related to the specialty of the Civil Engineering science and related fields. – **practical works**.

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 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**.

1. Analytical geometry on plane (2 h)

2. Straight lines on plane and applications (4 h)

3. Conic sections (3 h)

4. Functions and different types of functions. Sequences and limits. Number e (2 h)

5. Limit of function. Properties of limits. Indeterminate forms (8 h)

6. Derivative of function (5 h)

7. Derivative of composite function. Differentiation of a function defined parametrically (8 h)

8. Higher order derivatives (3 h)

9. Applications of derivatives of function of one variable (6 h)

10. Indefinite integration. Basic integration rules (3 h)

11. Integration by substitution (3 h)

12. Integration by parts (3 h)

13. Trigonometric integrals (2 h)

14. Integration of rational functions with quadratic denominator (3 h)

15. Definite integrals (3 h)

16. Integration by substitution in the definite integrals. Integration by parts (3 h)

17. Application of the definite integrals. Area of the region between curves (6 h)

18. Area of a surface of revolution. Volumes of solid revolution (5 h)

Assessment: Exam.

In writing form the following independent work must be completed at times specified by the teaching staff:
**Independent work 1.** Analytical geometry
**Independent work 2.** Limits of functions
**Independent work 3.** Derivatives of functions
**Independent work 4.** Indefinite integration
**Independent work 5.** Definite integration
**Independent work 6.** Application of the definite integrals

The **written exam** can be arranged at the time indicated by the teaching staff, if all the independent works are defended.

1. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. I daļa. Rīga: Zvaigzne, 1988. 534 lpp.

2. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. II daļa. Rīga: Zvaigzne, 1988. 527 lpp

3. Volodko I. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 2007. 294 lpp.

1. Šteiners K. Augstākā matemātika. III daļa. Rīga: Zvaigzne ABC, 1998. 192 lpp.

2. Šteiners K. Augstākā matemātika. IV daļa. Rīga: Zvaigzne ABC, 1998. 168 lpp.

3. Lewin J. An Interactive Introduction to Mathematical Analysis. Cambridge University Press.2003.- 492 p

The study course is included in the compulsory study course of First level professional higher education study programme “Civil Engineering”.