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Applied Mathematics I

Course developers

Replaced course

MateB007 [GMATB007] Applied Mathematics I

Course abstract

The aim of study course is provide knowladges of mathematic for further practical use of mathematical methods. Students learn linear algebra, analytical geometry in the plane, limit of function, terms and laws of differential calculus of one and two argument functions, as well as elements of mathematical statistics and their applications.
In the lectures, they get acquainted with the application of the given laws in everyday life and technique.
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. Know and are able to demonstrate knowledge and critical understanding of the elements of linear algebra, analytical geometry, calculation of function limits and derivatives of one and two argument functions. Knows the application of the acquired topics in practical processes related to the specialty of food technology. - 3 tests
2. Is 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 apply statistical elements for scientific research, data analysis and evaluation Able to use appropriate application software for calculations - 24 practical works and 8 laboratory works
3. Working in a group or performing work independently, is 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 - 8 independent works

Course Content(Calendar)

1. Elements of linear algebra. Matrices, operations with them and it’s application in preparation of food products recipes and production program (4h).
2. Elements of linear algebra. Determinants. Systems of linear equations and their solutions using Cramer’s rule and it’s application in food extrusion process (5h).
3. Equation of a straight line in the plane. Basic problems of a straight plane, their application in the study of linear processes (4h).
Test 1. Elements of linear algebra and analytic geometry (1h).
4. Limit of the function, its properties. Uncertainty and it’s prevention. Determination the point and type of discontinuity of function and it’s application in thermal processing in food industries (6h).
5. Differential calculations of one-argument functions, their application in calculations of pasteurization and sterilization flow (8h).
Test 2. Limit of the function. Derivatives and its applications (1h).
6. Application of differential calculus in optimization of various processes (2h).
7. Differential calculations of two-argument functions, their application (6h).
Test 3. Differential calculus of two-argument functions. Application of differential calculus of one-argument and two-argument functions in optimization of various processes (1h)
Analysis and evaluation of statistical data using Excel program:
1. Statistical elements for research, data analysis and evaluation: Distribution rows of case size range (2h).
9. Confidence intervals for mean values and variances (2h).
10. Statistical hypotheses, testing of hypothesis (2h).
11. Correlation and regression analysis (3h).

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 – 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 – Differential argument functions
Using the appropriate application software, the following independent work must be completed:
Independent work 6 – Distribution rows of case size range
Independent work 7 - Confidence intervals for mean values and variances. Statistical hypotheses, testing of hypothesis
Independent work 8 - Correlation and regression

Criteria for Evaluating Learning Outcomes

The course is completed without additional knowledge test 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.
An unsuccessfully written test can be rewritten at the time indicated by the lecturer.

In the case of unsuccessful work in the semester student answers for all the topics together in the form of a written test in the period of the individual studies and examinations.

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: Zvaigzne1988. – 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”