Course code Mate4019

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 lect.

Liene Strupule

Mg. math.

Course abstract

The study course deals with elements of linear algebra, vectors algebra, analytic geometry, mathematical analysis, 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 food product technologies 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 and differentiation of function of one variable. Students manage the application of the acquired topics in practical examples related to the specialty of the Food Product technology 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 (Lecture – 1h, practical work – 2h, laboratory work -1h)
2. Solution of systems of linear equations (Cramers rule) (Lecture – 1h, laboratory work – 1h)
3. Vectors and properties. Addition of vectors and vector subtraction (Lecture – 1h, practical work – 2h)
4. The scalar product and the vector product of two vectors, applications (Lecture –2h, practical work – 1h, laboratory work – 1h )
5. Scalar triple product or vector triple product, applications (Lecture –1h, practical work – 1h, laboratory work – 1h )
6. Test 1: Linear algebra. Vector algebra(practical work – 1h)
7. Analytical geometry on plane. Straight line (Lecture –1h, practical work – 1h)
8. Conic sections (Lecture –1h, practical work – 1h, laboratory work – 1h )
9. Limit of function. Properties of limits. Indeterminate forms (Lecture –1h, practical work – 1h)
10. Continuity of function (Lecture – 1h, laboratory work – 1h)
11. Derivative of function (Lecture – 1h, practical work – 1h)
12. Rules of derivative (Lecture – 2h, practical work – 2h)
13. Derivative of composite function (Lecture – 1h, practical work – 1h, laboratory work – 1h )
14. Differentiation of a function defined parametrically (Lecture – 1h, practical work – 1h)
15. Implicit differentiation (Lecture – 1h, laboratory work – 1h)
16. Test 2: Limits of function and derivatives (practical work - 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. Siliņa B., Šteiners K. Rokasgrāmata matemātikā. Rīga:Zvaigzne ABC, 2006.-367 lpp.
3. Šteiners K., Siliņa B. Augstākā matemātika. I daļa. Rīga:Zvaigzne ABC, 1997., - 96 lpp.
4. Šteiners K., Siliņa B. Augstākā matemātika. II daļa. Rīga:Zvaigzne ABC, 1998., - 116 lpp.
5. Šteiners K., Siliņa B. Augstākā matemātika. III daļa. Rīga:Zvaigzne ABC, 1998., - 192 lpp.
6. Šteiners K., Siliņa B. Augstākā matemātika. IV daļa. Rīga:Zvaigzne ABC, 1999., - 168lpp.

Further reading

1. Uzdevumu krājums augstākajā matemātikā. Dz. Bože, L.Biezā, B.Siliņa, A.Strence. Rīga:Zvaigzne, 2001. 332lpp
2. Volodko I. Augstākā matemātika. I daļa, Rīga:Zvaigzne ABC, 2007. 294lpp.
3. Čerņajeva S., Vintere A. Mācību līdzeklis augstākās matemātikas pamatu apguvei. Rīga – Jelgava:2016.-198 lpp.
4. Brūvere S., Čerņajeva S. Mācību līdzeklis un patstāvīgā darba uzdevumi augstākās matemātikas kursa pamatu apguvei. Jelgava:LLU, 2006. 159 lpp.
5. Brūvere S., Rukmane V. Mācību līdzeklis augstākajā matemātikā LLU inženierzinātņu specialitāšu studijām I daļa. Jelgava:LLU, 2003. 96 lpp.
6. Jēgere I., Baumanis A. Uzdevumi patstāvīgam darbam matemātikā. Matemātika I, Matemātika II. Jelgava:LLU, 2000, 51 lpp.

Notes

Compulsory course of the second level professional higher education study program “Food Product Technology”.