Course code Mate3030

Credit points 3

# Applied Mathematics II

Total Hours in Course81

Number of hours for lectures12

Number of hours for seminars and practical classes16

Number of hours for laboratory classes4

Independent study hours49

Date of course confirmation12.04.2021

Responsible UnitInstitute of Mathematics and Physics

prof.

## Natālija Sergejeva

Dr. math.

Matemātikas un fizikas institūts

## Anda Zeidmane

Dr. paed.

### 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)

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2. Volodko I. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 2009. – 392 lpp
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5. Granato D., Ares G. Mathematical and Statistical Methods in Food Science and Technology IFT Press Wiley Blackwell, 2014 -536 pp
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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”