Course code Mate4020

Credit points 3

# Mathematics II

Total Hours in Course120

Number of hours for lectures16

Number of hours for seminars and practical classes32

Number of hours for laboratory classes8

Independent study hours64

Date of course confirmation12.04.2021

Responsible UnitDepartment of Mathematics

### Course developer lect.

## Liene Strupule

Mg. math.

### Prior knowledge

Mate4019, Mathematics I

### Course abstract

The study course deals with function of one and two variables and it’s applications, indefinite integration and numerical integration, ordinary differential equations. The study course is intended to acquire the mathematical knowledge and practical skills needed to study future special subjects, as well as to acquire skills for applying math techniques to study different problems related to food product technologies and related fields. 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 function of one and two variables and it’s applications, indefinite integration and numerical integration, ordinary differential equations. Students manage the application of the acquired topics in practical examples related to the specialty of food product technologies and related fields. – tests.
2. Students are able to show understanding of the corresponding concept and regularities, to perform necessary calculations and operations. Students are able to use appropriate software for calculations. – practical and 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 – independent works.

### Course Content(Calendar)

1. Applications of derivative. Increasing and decreasing functions and extrema. (Lecture – 1h, practical work – 1h)
2. Concavity and the second derivative test. (Lecture –1h, practical work – 1h)
3. Asymptotes of a function.( Practical work – 2h, laboratory work – 1h)
4. Applications of derivative in different problems.(Practical work – 1h)
5. Indefinite integration. Basic integration rules. (Lecture – 1h, practical work – 1h)
6. Integration by substitution. (Lecture – 1h, practical work – 2h)
7. Integration by parts. (Lecture – 1h, practical work – 2h, laboratory work – 1h)
8. Integration of rational functions with quadratic denominator. (Practical work – 1h)
9. Integration of rational function (Lecture – 1h, practical work – 1h, laboratory work – 1h)
10. Test 1: Indefinite integrals. (Practical work – 1h)
11. Definite integrals. (Lecture – 1h, practical work – 2h, laboratory work – 1h)
12. Integration by substitution in the definite integrals. ( Lecture – 1h, practical work – 1h)
13. Integration by parts in the definite integrals. (Lecture – 1h, practical work – 2h, laboratory work – 1h)
14. Application of the definite integrals. Area of the region between curves. (Practical work – 1h)
15. Volumes of solid revolution. ( Practical work – 1h, laboratory work – 1h)
16. Test 2: Definite integrals and applications. (Practical work – 1h)
17. Functions of two variables. Continuity of function of two variables. Partial derivatives of function of two variables. (Lecture – 1h, practical work – 2h)
18. Extrema of functions of two variables. (Lecture – 1h, practical work – 1h, laboratory work – 1h)
19. First order ordinary differential equations. Equations with separable variables. ( Lecture – 1h, practical work – 2h)
20. Homogenous equations. (Lecture – 1h, practical work – 1h)
21. Linear equations.( Lecture – 1h, practical work – 2h, laboratory work – 1h)
22. Second order differential equations. Second order homogeneous linear equations. (Lecture – 1h, practical work – 1h)
23. Second order nonhomogeneous linear equations. (Lecture – 1h, practical work – 1h)
24. Test 3: First and second-order equations. (Practical work – 1h)

### 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 (all tasks are executed correctly) at times specified by the teaching staff:
Independent work 1. Applications of derivatives
Independent work 2. Indefinite integration
Independent work 3. Definite integrals and applications
Independent work 4. Functions of two variables
Independent work 5. First and second order differential equations

### Criteria for Evaluating Learning Outcomes

The student can receive the accumulative exam if:
1. all independent works are completed at times specified by the teaching staff;
2. 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 teaching staff.
The accumulative exam mark is
- 90% of the average mark of all tests
- 10% for completed independent works.

The written exam can be arranged at the time indicated by the teaching staff, if all the independent works are defended (all tasks are performed correctly).

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2. Siliņa B., Šteiners K. Rokasgrāmata matemātikā. Rīga:Zvaigzne ABC, 2006.-367 lpp.
3. Šteiners K., Siliņa B. Augstākā matemātika. III daļa. Rīga:Zvaigzne ABC, 1998., - 192 lpp.
4. Šteiners K., Siliņa B. Augstākā matemātika. IV daļa. Rīga:Zvaigzne ABC, 1999., - 168lpp.