Course code Mate1030

Credit points 3

# Mathematics II

Total Hours in Course81

Number of hours for lectures16

Number of hours for seminars and practical classes16

Number of hours for laboratory classes8

Independent study hours41

Date of course confirmation19.02.2014

Responsible UnitInstitute of Mathematics and Physics

lect.

## Anna Vintere

Mg. math.

### Prior knowledge

Mate1029, Mathematics I

### Course abstract

The aim of the study course is to learn the application of derivatives of functions of one and two arguments. 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 Engineering science and related fields. During the course, students acquire skills in working with appropriate application software, such as “Matlab”.

### Learning outcomes and their assessment

After successfully completing this course, the student:
• Knows and is able to demonstrate knowledge and understanding of the use of derivatives of functions of one and two arguments and integral calculus. Able to use the acquired knowledge in solving practical tasks related to engineering problems – tests.
• Able to demonstrate understanding of relevant concepts and regularities, perform the necessary mathematical operations and calculations. Able to use appropriate application software to perform calculations – practical and laboratory works.
• Working independently or working in a group, is able to apply mathematical calculations appropriate to the problem situation of the specialty, perform professional evaluation and interpretation of intermediate and final results of calculations – independent works.

### Course Content(Calendar)

Full-time studies:
1. Use of the derivative in the study of business relations: maximization of sales volume and revenue, minimization of average costs, maximization of profit. (3 h)
2. Economic-mathematical regularities in the economy of two benefits. (2 hours)
3. Indefinite integration. Basic integration rules (3 h)
4. Integration by substitution (2 h)
5. Integration by parts (2 h)
6. Integration of rational function (2 h)
7. Trigonometric integrals (2 h)
8. Integration of irrational functions (3 h)
1st TEST: Indefinite integrals (1 h)
1. Definition of definite integral. Properties and calculation of the definite integral. (3 h)
2. Integration by substitution in the definite integrals. Integration by parts (3 h)
3. Application of the definite integrals. Area of the region between curves (3 h)
4. Arc Length (2 h)
5. Area of a surface of revolution. Volumes of solid revolution (4 h)
6. Applications of the definite integral in the study of business relations: determining resource consumption; determination of production costs, sales revenue and profit growth; determination of the volume of production and the quantity of goods sold. (4 h)
2nd TEST: Indefinite integrals and its application. (1 h)

Part time extramural studies:
All topics specified for full time studies are accomplished, but the number of contact hours is one half of the number specified in the calendar.

Assessment: Test

### 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 of one variable function
Independent work 2 - Applications of derivatives of two variables function
Independent work 3 - Indefinite integration
Independent work 4 - Definite integrals
Independent work 5 - Application of the definite integrals

### Criteria for Evaluating Learning Outcomes

Credits are received cumulatively, without an additional knowledge test, if the semester study results are summarised:
• The previous study course Mathematics I (Mate1029) has been completed;
• All independent works are completed at times specified by the teaching staff;
• 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.
Independent works that have not been graded within the specified time can be defended at the times indicated by the teaching staff, no more than two at one acceptance.
If the conditions for cumulative credit are not fulfilled, the student shall, during the period of individual study and examinations, answer for all the topics covered in the semester as a whole in the form of a written assignment.

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• Čerņajeva S., Vintere A. Mācību līdzeklis augstākās matemātikas pamatu apguvei. Rīga-Jelgava: 2016. 198 lpp.
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• Lewin J. An Interactive Introduction to Mathematical Analysis. Cambridge University Press, 2003 - 492 p.

### Periodicals and other sources

https://www.macmillanihe.com/companion/Singh-Engineering-Mathematics-Through-Applications/fully-worked-solutions/

### Notes

The study course is included in the compulsory part of the Bachelor’s study program “Agricultural Engineering”, of the professional bachelor study program “Machine design and production”, of the professional higher education bachelor study program “Applied Energy Engineering”.