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Engineering mathematics IV

Course developer

Prior knowledge

Mate3027, Engineering mathematics III

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 the complex numbers, 1st and 2nd order differential equations, number and power series and methods and applications of them. Introduce with Fourier series and double integral. Study course promotes mathematical thinking and spatial perception, 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. Complex numbers, types of representation, operations with them. (4h)
2. Simplest type of differential equation. First-order separable equations. (3h)
3. Linear and homogeneous first-order differential equations. (3h)
4. 2nd and higher order differential equations. 2nd order linear homogeneous differential equation with constant coefficients. (2h)
5. 2nd order linear inhomogeneous differential equation with constant coefficients. (2h)
6. System of linear 1st order differential equations. (2h)
Task 1 First and 2nd order differential equation. (1h)
7. Sequences and series. Numerical series. Converges of positive numerical series. (2h)
8. Sufficient conditions of converges of positive numerical series. (2h)
9. Alternating harmonic series. (2h)
10. Series of function. Power series, interval of convergence. (2h)
11. Taylor and Maclaurin series. Function approximation with series. (2h)
12. Fourier series. (2h)
13. Double integral, calculation and application. (2h)

Task 2 Numerical and power series. (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 – Complex numbers
Independent work 2 – 1st order differential equations
Independent work 3 – 2nd order differential equations

Independent work 4 – Numerical and power series

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;
- taken a semester final test.
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 60% of all tests plus 40% of the final test mark.
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 222 Second semester calculus [online] [14.09.2019]. Available: https://www.math.wisc.edu/~angenent/Free-Lecture-Notes/free222.pdf

Notes

Compulsory course for Bachelor’s study programme “Biosystems Machinery and Technologies”. 2nd year, 2nd semester.