| Course title | Applied Mathematics I |
| Course code | MateB007 |
| Credit points (ECTS) | 4 |
| Total Hours in Course | 108 |
| Number of hours for lectures | 18 |
| Number of hours for seminars and practical classes | 26 |
| Number of hours for laboratory classes | 0 |
| Independent study hours | 64 |
| Date of course confirmation | 24/01/2024 |
| Responsible Unit | Institute of Mathematics and Physics |
| Course developers | |
| Dr. math., prof. Natālija Sergejeva Dr. paed., prof. (Emeritus) Anda Zeidmane |
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| There is no prerequisite knowledge required for this course | |
| Replaced course | |
| Mate3029 [GMAT3028] Applied Mathematics I |
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| Course abstract | |
| The aim of the study course is to provide knowledge in mathematics, which is necessary for further practical use of mathematical methods for use.
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 works, the use of MatLab and Excel programs in solutions of specific tasks is mastered. |
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| Learning outcomes and their assessment | |
| After successful completion of this course, the student will have obtained:
Knowledge and understanding of elements of linear algebra, analytic geometry, calculation of limits of functions, differential calculus of functions of one and two arguments, as well as knowledge of practical application of learned topics, with in processes related to the specialty of food technology – 3 tests Skills to show understanding of the relevant concepts and laws, to perform the necessary mathematical actions and operations, creating a chain of logical judgments and correct mathematical language, as well as skills to apply statistical elements for scientific research, data analysis and evaluation. Ability to use appropriate application software to perform calculations - 16 practical works and 8 laboratory works The competence to apply mathematical calculations appropriate to the problem situation of the specialty, to perform professional evaluation and interpretation of intermediate and final results of calculations, working in a group or doing work independently - 8 individual independent works |
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| 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 (3h).
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 (4h). 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 (7h). Test 2. Limit of the function. Derivatives and its applications (1h). 6. Application of differential calculus in optimization of various processes (1h). 7. Differential calculations of two-argument functions, their application (5h). 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: 8.Statistical elements for research, data analysis and evaluation: Distribution rows of case size range (2h). 9. Confidence intervals for mean values and variances (1h). 10. Statistical hypotheses, testing of hypothesis (2h). 11. Correlation and regression analysis (2h). |
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| 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 (MATLAB), 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 (EXCEL), 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 |
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| 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. |
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| 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] |
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| 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 |
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| Notes | |
| Compulsory course for Bachelor’s study programme “Food Quality and Innovations Bachelor” | |