Course code Mate1029

Credit points 4.50

# Mathematics I

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 confirmation19.02.2014

Responsible UnitInstitute of Mathematics and Physics

prof.

Dr. math.

reserch

## Aivars Āboltiņš

Dr. sc. ing.

### Replaced course

MateB001 [GMATB001] Mathematics I

### Course abstract

The aim of the course is to deal with elements of linear algebra, vectors algebra, analytic geometry, differentiation of function of one variable. 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 linear algebra, vectors algebra, analytic geometry, differentiation of function of one variable. 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. The theory of matrices and determinants (6 h)
2. Solution of systems of linear equations (Cramers rule, Gaussian elimination method) (2 h)
3. Test 1: Linear algebra (1 h)
4. Analytical geometry on plane. Straight line and conic sections (6 h)
5. Space. Vectors and properties. Addition of vectors and vector subtraction (3 h)
6. The scalar product and the vector product of two vectors, applications (3 h)
7. Scalar triple product or vector triple product, applications (4 h)
8. Straight line and planes in space (2h)
9. Test 2: Analytical geometry and vector algebra (1 h)
10. Functions and different types of functions. Sequences and limits. Number e (3 h)
11. Limit of function. Properties of limits. Indeterminate forms (3 h)
12. Special trigonometric limits. Number e as a limits (3 h)
13. Continuity of function. Derivative of function (3 h)
14. Derivative of composite function. Logarithmic differentiation (3 h)
15. Implicit differentiation. Differentiation of a function defined parametrically (3 h)
16. Higher order derivatives (4 h)
17. Increasing and decreasing functions, extrema and the first derivative test. Concavity and the second derivative test (3 h)
18. Applications of derivative (optimization, L’Hopital’s rule) (2 h)
19. Test 3: Limits of function and derivatives (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

### 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. Elements of linear algebra
Independent work 2. Analytical geometry
Independent work 3. Vector algebra
Independent work 4. Limits of functions

Independent work 5. Derivatives of functions

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

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

1. Šteiners K. Augstākā matemātika. I daļa. Rīga: Zvaigzne ABC, 1997. 96 lpp.
2. Šteiners K. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 1998. 116 lpp.
3. Šteiners K. Augstākā matemātika. III daļa. Rīga: Zvaigzne ABC, 1998. 192 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”.