Course code Mate1024

Credit points 3

Total Hours in Course81

Number of hours for lectures8

Number of hours for seminars and practical classes24

Independent study hours49

Date of course confirmation12.04.2021

Responsible UnitInstitute of Mathematics and Physics

Matemātikas un fizikas institūts
## Svetlana Atslēga

Dr. math.

Mate1023, Mathematics I

The study course deals with elements of analytic geometry, 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.

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. 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 (3 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 (6 h)

6. Derivative of function (4 h)

7. Derivative of composite function. Differentiation of a function defined parametrically (6 h)

8. Higher order derivatives (2 h)

9. Applications of derivatives of function of one variable (4 h)

Assessment: Exam.

In writing form and by using the appropriate software, 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

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

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

https://www.macmillanihe.com/companion/Singh-Engineering-Mathematics-Through-Applications/fully-worked-solutions/

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