Course code Mate4014

Credit points 3

Mathematics I

Total Hours in Course81

Number of hours for lectures16

Number of hours for seminars and practical classes16

Number of hours for laboratory classes8

Independent study hours41

Date of course confirmation12.04.2021

Responsible UnitInstitute of Mathematics and Physics

Course developer

author Datoru sistēmu un datu zinātnes institūts

Līga Zvirgzdiņa

Dr. oec.

Course abstract

The course deals with the elements of linear algebra and analytic geometry, mathematical analysis, differential calculus of single-valued functions and their applications in the Forest Science. The study course contributes to mathematical thinking. During the course students learn skills in working with appropriate software applications, such as "Matlab"

Learning outcomes and their assessment

Upon successful completion of this course:
1. Students are able to manage and demonstrate knowledges and critical understanding of linear algebras, analytic geometry elements, calculation of function limits and derivatives of functions. Students manage the application of the acquired topics in practical examples related to the specialty of the Forest Science. – tests
2. Students are able to show understanding of the corresponding concept and regularities, to perform necessary caluculations and operations. Students are able to use appropriate software for calculations. - practical and laboratory work

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 studies

Course Content(Calendar)

1. Matrices. Determinants. (3 h)
2. Systems of linear equations and their solutions. (4 h)
3. Curves, its equations. Line, line segment, triangular area in the Cartesian coordinate system. (2h)
4. Equation of a straight line in the plane. The angle between 2 straight lines. Parallelity and perpendicularity condition for 2 straight lines. Coordinates for intersection of two straight lines (5h)
5. Conic sections: circle, ellipse, hyperbola, parabola (3h)
Test 1. Elements of linear algebra and analytic geometry.
6. Limit of the function, its properties. Indeterminate forms of limit and their solutions. (5h)
7. Derivatives, its geometric and physical interpretation. Derivation rules and formulas. Higher-order derivatives. (5h)
8. Use of a derivative in the study of functions. Monotonicity. Finding functional maxima and minima. Second derivative test. Inflection point. Asymptote of a curve. Differential. (6h)
9. Applications of derivatives. (5h)

Test 2. Limit of the function. Derivatives and its applications.

Requirements for awarding credit points

Formal test (Pass/Fail assessment).

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:
Independent work 1 - Elements of Linear algebra
Independent work 2 - Analytical geometry
Independent work 3 - Limit theory
Independent work 4 - Derivatives of functions

Independent work 5 - Aplications of Function derivatives

Criteria for Evaluating Learning Outcomes

The course is completed without additional knowledge examination if the results of the semester are summarized as:
- all independent works are completed (all tasks are executed correctly);
- during the semester each test score is at least 4.
Failed tests can be repeated.
In the case of unsuccessful work in the semester student answers for all the topics together in the period of the individual studies and examinations.

Compulsory reading

1. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika I daļa. Rīga: Zvaigzne, 1988 – 534 lpp.
2. Šteiners K., Siliņa B. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 1997., - 96 lpp
3. Šteiners K., Siliņa B. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 1998. - 116 lpp
4. Šteiners K. Augstākā matemātika. III daļa. Rīga: Zvaigzne ABC 1998. – 192lpp.
5. Šteiners K. Augstākā matemātika. IV daļa. Rīga: Zvaigzne ABC 1999. – 168lpp.

6. Volodko I. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 2007. - 294 lpp.

Further reading

1. Čerņajeva S., Vintere A. Mācību līdzeklis augstākās matemātikas pamatu apguvei. Rīga-Jelgava: 2016. – 198 lpp.
2. Brūvere S., Čerņajeva S. Mācību līdzeklis un patstāvīgā darba uzdevumi augstākās matemātikas kursa pamatu apguvei. Jelgava: LLU, 2006. - 159 lpp.
3. Brūvere S., Rukmane V. Mācību līdzeklis augstākajā matemātikā LLU inženierzinātņu specialitāšu studijām I daļa. Jelgava: LLU, 2003. - 96 lpp.
4. Jēgere I., Baumanis A. Uzdevumi patstāvīgam darbam matemātikā. Matemātika I, Matemātika II. Jelgava: LLU, 2000. - 51 lpp.
5. Uzdevumu krājums augstākajā matemātikā. Dz.Bože, L.Biezā, B.Siliņa, A.Strence. Rīga: Zvaigzne, 2001. - 332 lpp.
6. Siliņa B., Šteiners K. Rokasgrāmata matemātikā. Rīga: Zvaigzne ABC, 2006. - 367 lpp.

7. Lewin J. An Interactive Introduction to Mathematical Analysis. Cambridge University Press, 2003.- 492 P

Notes

Compulsory course for Bachelor’s study programme “Forest Science”.