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Course title Applied Mathematics
Course code Mate1039
Credit points 5
ECTS creditpoints 7.50
Total Hours in Course 200
Number of hours for lectures 24
Number of hours for seminars and practical classes 40
Number of hours for laboratory classes 16
Independent study hours 120
Date of course confirmation 21/03/2018
Responsible Unit Department of Mathematics
Course developers
Dr. paed., prof. Anda Zeidmane
Dr. math., asoc. prof. Svetlana Atslēga
Dr. math., asoc. prof. Natālija Sergejeva
Mg. math., lekt. Liene Strupule

There is no prerequisite knowledge required for this course
Course abstract
The course is dedicated to acquire mathematical knowledge and skills necessary for the practical use of mathematical methods. The course deals with linear algebra, analytic geometry, limits of the function, derivatives of functions, integration, the complex numbers, 1st and 2nd order differential equations, number and power series and methods and applications of them. Introduce with Fourier series and double integral. Study course promotes mathematical thinking, practical transfer of knowledge to real tasks, problem solving by engineering students. 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, analytic geometry, limits of the function, derivatives of functions, integrals, complex numbers, 1st and 2nd order differential equations. Students manage the application of the acquired topics in practical examples related to the specialty of the Food Science. – 4 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. – 40 practical and 12 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. – 12 independent works
Course Content(Calendar)
1. Determinants. Systems of linear equations and their solutions using Cramer’s rule and it’s application in Food extrusion process. (6h)
2. Matrices, operations with them and it’s application in preparation of food products recipes and production program. (5h)
3. Equation of a straight line in the plane. Basic problems of a straight line, their application in the study of linear processes. (5h)
Test 1. Elements of linear algebra and analytic geometry (1h)
4. Limit of the function, its properties. Indeterminate forms of limit and their solutions. Determination the point and type of discontinuity of function and it’s application in Thermal Processing in Food Industries (7h)
5. Differential calculations of one argument functions, their application in calculations of pasteurization and sterilization flow. Application of differential calculus in optimization of various processes. (10h)
6. Differential calculations of two argument functions, their application (4h)
Test 2. Limit of the function. Derivatives and its applications (1h)
7. Integrals. Calculation of indefinite integral by direct integration, method of substitution and integration by parts. (8h)
8. Calculations of the definite integral, their application in the calculation of area, volumes of revolution. Using calculations of integrals in extrusion processes. (8h)
Test 3. Calculations of integrals and their application
9. Complex numbers (1)
10. 1st order differential equations, their application (5h)
11. 2nd order differential equations, it’s using in structural and textural properties evaluation of food products. (5h)
Test 4. Calculation of differential equations, their application (1h)
12. Statistics: distribution rows of case size range, confidence intervals for mean values and variances, statistical hypotheses, testing of hypothesis, correlation and regression. Analysis and evaluation of statistical data working with appropriate application software. (12h)
Requirements for awarding credit points
Assessment: Exam
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. Linear Algebra
Independent work 2. Straight line in the plane
Independent work 3. Limits of the function
Independent work 4. Differential calculations of one argument functions
Independent work 5. Calculation of indefinite integral
Independent work 6. Calculations of definite integral, their application
Independent work 7. Calculation of 1st order differential equations
Independent work 8. Calculation of 2nd order differential equations
Independent work 9. Grouped frequency distribution
Independent work 10. Confidence intervals for mean values and variances
Independent work 11. Statistical hypotheses, testing of hypothesis
Independent work 12. Correlation and regression
Criteria for Evaluating Learning Outcomes
The student can receive the accumulative exam if:
- 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.
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 lecturer.
The accumulative exam mark is the average mark of all tests. The written exam can be arranged at the time indicated by the lecturer, if all the independent works are defended (all tasks are performed correctly).
Compulsory reading
1.Volodko I. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 2007. 294 lpp
2.Volodko I. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 2009. 392 lpp  
3.Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. I daļa. Rīga: Zvaigzne, 1988. 534 lpp.
4.Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. II daļa. Rīga: Zvaigzne, 1988. 527 lpp.
5.Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem I daļa. Rīga: Zvaigzne ABC, 2003. 256 lpp.
6.Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem II daļa. Rīga: Zvaigzne ABC, 2004. 192 lpp.
Further reading
1.Cernajeva S., Vintere A. Mācību līdzeklis Augstākās matemātikas pamatu apguvei. Rīga-Jelgava, 2016. 198 lpp.
2.Šteiners K. Augstākā matemātika. I , II, III daļa. Rīga: Zvaigzne ABC, 1997. 96 lpp.; 1998. 116 lpp.; 1998. 192 lpp.
3.Zeidmane A. Didaktiskie materiāli augstākajā matemātikā. Pamatjēdzieni, pamatlikumi, pamatsakarības. Kopsavilkums. LLU, Jelgava. 2010. 39 lpp. e-materiāli
4.Lewin J. An Interactive Introduction to Mathematical Analisis. UK: Cambridge Umiversity press. 492 p.
5.Konev V. Linear algebra, Vector algebra and analytical geometry. Tomsk Polytechnic University, 2009. 114 p. file:///C:/Users/LIETOT~1/AppData/Local/Temp/Konev-Linear_Algebra_Vector_Algebra_and_Analytical_Geome-1.pdf 6.Uzdevumu krājums augstākajā matemātikā. Dz.Bože, L.Biezā, B.Siliņa, A.Strence. Rīga: Zvaigzne, 2001. 332 lpp.
Compulsory course for Bachelor’s study programme “Food Quality and Innovations Bachelor”.