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

prof.

Dr. math.

reserch

## Aivars Āboltiņš

Dr. sc. ing.

### Prior knowledge

Mate1029, Mathematics I

### Course abstract

The aim of the course is to deal with function of two variables and it’s applications, indefinite integration and numerical integration. 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

Upon successful completion of this course:
1. Knowledge - students are able to manage and demonstrate knowledge and critical understanding of function of two variables and it’s applications, indefinite integration and numerical integration. Students manage the application of the acquired topics in practical examples related to the specialty of the Engineering science and related fields – tests.
2. Skills - 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. Competence - 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)

Full time intramural studies:
1. Applications of derivatives of function of one variable (3 h)
2. Functions of two variables. Continuity of function of two variables (2 h)
3. Partial derivatives of function of two variables (2 h)
4. Extrema of functions of two variables (3 h)
5. Test 1: Functions of two variables (1 h)
6. Indefinite integration. Basic integration rules (2 h)
7. Integration by substitution (2 h)
8. Integration by parts (2 h)
9. Integration of rational function (2 h)
10. Trigonometric integrals (2 h)
11. Integration of irrational functions (3 h)
12. Test 2: Indefinite integrals
13. Definite integrals (2 h)
14. Integration by substitution in the definite integrals. Integration by parts (3 h)
15. Application of the definite integrals. Area of the region between curves (2 h)
16. Arc Length (2 h)
17. Area of a surface of revolution. Volumes of solid revolution (3 h)
18. Improper integral (2 h)
19. Test 3: Definite integrals
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

### Requirements for awarding credit points

Assessment: Test (pass/fail).

### 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. Functions of two variables
Independent work 3. Indefinite integration
Independent work 4. Definite integrals

Independent work 5. Application of the definite integrals

### Criteria for Evaluating Learning Outcomes

The student receive the test 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.

1. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. I daļa. Rīga: Zvaigzne, 1988. 534 lpp.
2. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. I daļa. Rīga: Zvaigzne, 1988. 527 lpp.

3. Volodko I. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 2007. 294 lpp.

1. Šteiners K. Augstākā matemātika. III daļa. Rīga: Zvaigzne ABC, 1998. 192 lpp.
2. Šteiners K. Augstākā matemātika. IV daļa. Rīga: Zvaigzne ABC, 1998. 168 lpp.
4. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem I daļa Zvaigzne ABC Rīga, 2003 – 256 lpp.
5. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem II daļa Zvaigzne ABC Rīga, 2004 – 192 lpp.

6. 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” and of the professional higher education study program “Technical expert”.