LV EN RU DE FR

Engineering mathematics I

Course developer

Course abstract

The aim of the course is to acquire mathematical knowledge and skills necessary for the practical use of mathematical methods. The course deals with repeated and deeper understanding the number and algebra, the elements of linear and vector algebra and analytic geometry. Study course promotes mathematical thinking, practical transfer of knowledge to real tasks, problem solving by engineering students. 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 knowledges and critical understanding the numbers and simple calculations, linear algebras, analytic geometry elements. Students manage the application of the acquired topics in practical examples related to the specialty of the Engineering – 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 work.

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)

1. Fractions, decimals and percentages. Indices, standard form and engineering notation. Error and approximations. (2h)
2. Calculation and evaluation of formulae. Brackets. Polynomial division. Solving simple equations. Transposition of formulae. Solving quadratic equation. (2h)
3. Functions: logarithms, exponential, trigonometric. (2h)
4. Areas of common shapes (SI units), volumes and surfaces areas of common solid. (2h)
5. Matrices. Determinants. (4 h)
6. Systems of linear equations and their solutions (Cramer’s Rule, Gauss-Jordan Elimination method). (2 h)
Test 1. Numbers and algebra. Elements of linear algebra. (1h)
7. Analytical geometry in plane. Line and curves in plane. (4h)
8. 3-D Cartesian coordinate frame. Vectors, basic concepts and simple operations. (2h)
9. Multiplication of two vectors as scalar and vector product and its applications. (2h)
10. Scalar triple products and it interpretation. (4h)
11. Line and plane in 3-D space. (2h)

Test 2. Elements of analytical geometry and vector algebra. (1h)

Requirements for awarding credit points

Have passed the 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:
Independent work 1 – Numbers and calculation;
Independent work 2 - Elements of Linear algebra;
Independent work 2 - Analytical geometry;

Independent work 3 – Vector algebra.

Criteria for Evaluating Learning Outcomes

The student can receive the accumulative exam if:
- all independent works are completed (all tasks are executed correctly);
- 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 lecturer.
The accumulative exam mark is the average mark of of all tests.
The written exam can be arranged at the time indicated by the lecturer, if all the independent works are defended (all tasks are performed correctly)..

Compulsory reading

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.

Further reading

1. Lewin J. An Interactive Introduction to Mathematical Analysis. Cambridge: Cambridge University Press, 2003. 492 p.
2. Stroud K. A., Booth D. J. Engineering mathematics. South Norwalk, CT: Industrial Press, Incorporated, 2013. 1155 p.
31. Bird J. Engineering Mathematics. 5th edition. Abingdon, Oxon; New your, NY: Routledge, 2007. 709 p. Pieejams: https://jpmccarthymaths.files.wordpress.com/2012/09/john_bird_engineering_mathematics_0750685557.pdf
4. Singh K. Engineering Mathematics Through Applications. 2nd edition. Basingstoke: Palgrave Macmillan, 2011. 927p.
5. Jang W., Choi Y., Kim J., Kim M., Kim H., Im Y. Engineering Mathematics with MatLab. W Jang., Y. Choi, J. Kim, M. Kim, H. Kim, Y. Im. Boca Raton: CRS Press, 2018. 741 p.
6. Stewart J. Calculus: Early transcendentals (Mathematics). 7th ed. Belmont, CA: Brooks/Cole, Cengage Learning, 2012. 1170 p.

Periodicals and other sources

Engineering mathematics through applications Singh K. [online] [14.09.2019]. Available: https://www.macmillanihe.com/companion/Singh-Engineering-Mathematics-Through-Applications/fully-worked-solutions/

Math 221 First semester calculus [online] [14.09.2019]. Available: https://www.math.wisc.edu/~angenent/Free-Lecture-Notes/free221.pdf

Notes

Compulsory course for Bachelor’s study programme “Biosystems Machinery and Technologies”. 1st year, 1st semester.