Kursu reģistrs

Statuss(Aktīvs)

Course title	Mathematics III
Course code	MateB002
Credit points (ECTS)	4
Total Hours in Course	108
Number of hours for lectures	18
Number of hours for seminars and practical classes	26
Number of hours for laboratory classes	8
Independent study hours	56
Date of course confirmation	24/01/2024
Responsible Unit	Institute of Mathematics and Physics

Course developers
Dr. math., prof. Natālija Sergejeva
Prior knowledge
Mate1030, Mathematics II MateB001, Mathematics I
Replaced course
Mate2034 [GMAT2034] Mathematics III
Course abstract
Methods of solving ordinary differential equations, elements of series theory and their applications are learned in the study course. The study course is intended to acquire the mathematical knowledge and practical skills necessary for learning future special subjects, as well as to acquire skills in the application of mathematical techniques to identify various problems related to engineering and related fields. During the course, students learn 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 understanding of ordinary differential equations, methods of solving them, series theory and the use of multiple integrals. Students are to use the acquired knowledge when solving practical tasks related to engineering problems - tests. 2. Students are able to demonstrate understanding of the corresponding concept and regularities, to perform necessary calculations and operations. Students are able to use appropriate application software for calculations - practical and laboratory works. 3. Working independently or working in a group, are able to apply mathematical calculations appropriate to the problem situation of the specialty, perform professional evaluation and interpretation of intermediate and final results of calculations - independent works.
Course Content(Calendar)
Full-time studies: 1. Complex numbers, the forms of complex numbers and operations with complex numbers. – 5h 2. First order ordinary differential equations (equations with separable variables, linear equations), their application. – 7h 3. Second and higher order differential equations. Reducible second order differential equations. - 2h 4. Second order homogeneous and nonhomogeneous linear equations with constant coefficients, their application. – 10h 5. Test 1: First and second order differential equations, their applications. – 1h 6. Series. Convergence of series with positive terms. – 6h 7. Alternating series. - 2h 8. Series of functions. Interval of converge of power series. – 4h 9. Maclaurin’s and Taylor’s series. Series expansion of functions. – 4h 10. Numerical integration using power series. Integration of ordinary differential equations using power series. – 6h 11. Test 2: Series of numbers and functions, their applications. – 1h Part-time studies: All topics specified for full-time studies are covered, but the number of contact hours is 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. Complex numbers Independent work 2. First order differential equations Independent work 3. Second order differential equations Independent work 4. Series Independent work 5. Power series
Criteria for Evaluating Learning Outcomes
The student can receive the accumulative exam if: 1. the previous study courses Mathematics I (Mate1029) and Mathematics II (Mate1030) have been completed 2. all independent works are completed at times specified by the teaching staff; 3. during the semester each test score is at least 4. An unsuccessfully written test can be rewritten by the student during the study process, at times specified by the teacher. The student can rewrite the last test in the 1st week of the period of individual study and tests at the time specified by the teacher. The accumulative exam grade is made up of the average grade of all tests. 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).
Compulsory reading
1. Volodko I. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 2009. – 392 lpp 2. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika II daļa. Rīga: Zvaigzne, 1988. – 527 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.
Further reading
1. Černajeva S., Vintere A. Mācību līdzeklis Augstākās matemātikas pamatu apguvei. Rīga - Jelgava, 2016. – 198 lpp. 2. Šteiners K. Augstākā matemātika. IV daļa. Rīga: Zvaigzne ABC, 1998. – 168 lpp. 3. Šteiners K. Augstākā matemātika. V daļa. Rīga: Zvaigzne ABC, 2000. – 129 lpp. 4. Zeidmane A. Didaktiskie materiāli augstākajā matemātikā. Pamatjēdzieni, pamatlikumi, pamatsakarības. Kopsavilkums. LLU, Jelgava. 2010. – 39 lpp- e-materiāli 5. Uzdevumu krājums augstākajā matemātikā. / Bože Dz., Biezā L., Siliņa B., Strence A. Rīga: Zvaigzne, 2001. 332 lpp. 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
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” and of the professional higher education bachelor study program “Applied Energy Engineering”.