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Mathematics I

Course developers

Course abstract

The course deals with linear algebra, vector algebra, analytic geometry, limits of function, differentiation and applications. The course of study 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 forest 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, differentiation of function of one variable. Students manage the application of the acquired topics in practical examples related to the specialty of the forest engineering science, wood processing 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 (4h)
2. Solution of systems of linear equations (3h)
3. Vectors and properties. The scalar product and the vector product of two vectors, applictions. Scalar triple product or vector triple product, applications (6h)
4. Analytic geometry on plane, the area of the triangle (4h)
5. The equations of the line on plane. Angle between two lines. Intersection of two given lines. (4h)
6. Conic sections: circle, ellipse, hyperbola, parabola (4h)
7. Test 1: Linear algebra. Vector Algebra. Analytic geometry (1h)
8. Limit of function. Properties of limits. Indeterminate forms (5h)
9. Derivative of function and its interpretation. Derivative of composite function. Implicit differentiation. Differentiation of a function defined parametrically. Higher order derivatives (8h)
10. Test 2: Limits of function. Derivatives and applications (1h)

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. Analytical geometry
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.

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. 192 lpp.
5. Šteiners K. Augstākā matemātika. IV daļa. Rīga: Zvaigzne ABC 1999. 168 lpp.

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. Stewart J. Calculus. Bellmont CA: Brooks/Cole, Cengage Learning, 2012. 146 p.
8. Bird J.O. Engineering Mathematics. London; New York:Bellmont Routledge/Taylor & Francis Group, 2017. 709 p.
9. Stroud K.A. Engineering Mathematics. South Norwalk, CT: Industrial Press, 2013. 1155 p.

Notes

Compulsory course for professional Bachelor’s study programmes “Forest Engineering” and “Wood Processing”.