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Applied Mathematics II

Course developers

Course abstract

The aim of the study course is to deepen the mathematical knowledge required for further practical use of mathematical methods. Students learn the graphical method of linear programming, integral calculus, first order differential equations and their applications.
In practical work, skills are acquired, using the acquired laws, to perform calculations in solutions of specific food production tasks (problems).
In laboratory work, the use of Matlab and Excel programs in solutions of specific tasks is mastered.

Learning outcomes and their assessment

Upon successful completion of this course the students:
1. Knows and are able to demonstrate knowledge and critical understanding of compilation and calculation of linear programming tasks, integral calculus, as well as differential calculus. Knows the application of the acquired topics in practical processes related to the specialty of food technology. - 2 tests
2. Are able to show an understanding of the relevant concepts and laws, perform the necessary mathematical operations and operations, forming a logical chain of judgments and correct mathematical language. Able to use appropriate application software for calculations - 16 practical works and 4 laboratory works
3. Working in a group or performing work independently, are able to apply mathematical calculations appropriate to the problem situation of the specialty, perform professional evaluation and interpretation of intermediate results and final results of the calculations - 4 independent works

Course Content(Calendar)

1. Compilation and calculation of linear programming tasks with a graphical method, their use in compiling a recipe (5h).
2. Integrals. Calculation of indefinite integral by direct integration, methods of substitution and integration by parts (9h).
Test 1. Linear programming problems and calculations of indefinite integral (1h).
3. Calculations of the definite integral, their application in area calculation, economics and calculations in extrusion processes (9h).
4. First order differential equations, their calculation and application. (7h).
Test 2. Calculations of the definite integrals and first order differential equations and their applications (1h).

Requirements for awarding credit points

Have passed the 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:
1. Independent work. Linear programming
2. Independent work. Integral calculation - indefinite integral
3. Independent work. Integral calculus - the definite integral 4. Independent work. Calculations of first order differential equations

Criteria for Evaluating Learning Outcomes

A student can receive the accumulative exam if:
1. All independent works are completed (all tasks are performed correctly);
2. During the semester, the evaluation of each test is at least 4 points (the mark of the accumulative exam is formed by the average mark of all tests).
The student can rewrite an unsuccessfully written test during the study process, at more times indicated 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.
If the conditions for receiving the cumulative exam are not met, the student takes a written exam during the period of individual studies and examinations (admission to the exam - all independent works are included)

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, 19Statisk88. – 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.
7. Winters R, Winters A, Amedee RG. Statistics: A brief overview. Ochsner J. 2010;10:213–6. [PMC free article] [PubMed] [Google Scholar]

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. Cambridge Umiversity press UK - 492 P.
5. Granato D., Ares G. Mathematical and Statistical Methods in Food Science and Technology IFT Press Wiley Blackwell, 2014 -536 pp
6. 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
7. Uzdevumu krājums augstākajā matemātikā. / Dz.Bože, L.Biezā, B.Siliņa, A.Strence. Rīga: Zvaigzne, 2001. 332 lpp.
8. Descriptive Statistics Using Excel and Stata (Excel 2003 and Stata 10.0+) https://www.princeton.edu/~otorres/Excel/excelstata.htm
9. Real Statistics Using Excel https://www.real-statistics.com/excel-environment/data-analysis-tools/

Notes

Compulsory course for Bachelor’s study programme “Food Quality and Innovations Bachelor”