Course code Mate1033

Credit points 2

# Mathematics II

Total Hours in Course80

Number of hours for lectures16

Number of hours for seminars and practical classes16

Number of hours for laboratory classes8

Independent study hours40

Date of course confirmation12.04.2021

Responsible UnitInstitute of Mathematics and Physics

### Course developers

Matemātikas un fizikas institūts

Dr. math.

lect.

Mg. math.

reserch

## Aivars Āboltiņš

Dr. sc. ing.

### Prior knowledge

Mate4016, 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 forest 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. Students are able to manage and demonstrate knowledge and critical understanding of application of differentiation, function of two variables, indefinite and definite integrals, differential equations. Students manage the application of the acquired topics in practical examples related to the specialty of the Forest Engineering or Wood Processing. – 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 derivatives of function of one variable (2h)
2. Extrema of functions of one variables (3h)
3. Partial derivatives of function of two variables (2h)
4. Extrema of functions of two variables (3h)
5. Practical applications (2h)
6. Test 1: Extrema of functions of one and two variables (1h)
7. Indefinite integration. Basic integration rules. Integration by substitution. Integration by parts (5h)
8. Definite integrals. Integration by substitution in the definite integrals. Integration by parts (3h)
9. Application of the definite integrals (4h)
10. Test 2: Indefinite and definite integrals (1h)
11. First-order ordinary differential equations (5h)
12. Second-order ordinary differential equations (4h)
13. Applications of ordinary differential equations (4h)
14. Test 3: Differential equations (1h)

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. Functions of two variables
Independent work 3. Indefinite integration
Independent work 4. Definite integrals
Independent work 5. 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).

1.Volodko I. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 2007. 294 lpp.
2.Volodko I. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 2009. 396 lpp.

1. Āboltiņa B., Liepiņa K. Rokasgrāmata matemātikā vecāko klašu skolēniem un studentiem. Rīga: Zvaigzne ABC, 2018. 320 lpp.
2. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem I daļa. Rīga: Zvaigzne ABC, 2003. 256 lpp.
3. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem II daļa. Rīga: Zvaigzne ABC, 2004. 192 lpp.
4.Stewart J. Calculus. Bellmont CA: Brooks/Cole, Cengage Learning, 2012. 146 p.
5.Bird J.O. Engineering Mathematics. London; New York:Bellmont Routledge/Taylor & Francis Group, 2017. 709 p.
6.Stroud K.A. Engineering Mathematics. South Norwalk, CT: Industrial Press, 2013. 1155 p.

### Periodicals and other sources

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

### Notes

Compulsory course for professional Bachelor’s study programme “Forest Engineering”.