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Engineering mathematics II

Course developer

Prior knowledge

Mate3025, Engineering mathematics I

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 mathematical analysis, differential calculus of single- valued and multi-valued functions. 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 the calculation of function limits and derivatives of functions (one and multi-valuated functions). 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. Sequences and its limits. Number e. (2h)
2. Limit of the function. Infinitesimal and infinity variable, equivalent infinitesimal variables. Indeterminate forms of limit and their solutions. (2h)
3. 1st and 2nd remarkable limit. (2h)
4. Continuously of function. Derivative of function. (3h)
5. Derivative of composite function. Logarithmic differentiation. (3h)
6. Derivative of parametric and implicit functions. (2h)
7. Higher-order derivatives. (2h)
Test 1. Limit of the function. Derivatives and its applications. (1h)
8. Increasing and decreasing function, convex and not convex graph. Extreme and inflection points. (2h)
9. Use of a derivative (extremum problem, optimization problem, L’Hopital’s rule). (3h)
10. Two argument function. Continuity, the first and second partial derivatives. (2h)
11. Extreme values of 2 and multivariable function. (3h)
12. Practical tasks (compilation and solving). (4h)

Test2: Use of derivatives of function for one and multiple functions. (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 - Limit theory;
Independent work 2 - Derivatives of functions;
Independent work 2 - Applications of derivatives;

Independent work 3 - Multivariable function.

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 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, 2nd semester.