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Mathematics II

Course developer

Prior knowledge

Mate1031, Mathematics I

Course abstract

The study course deals with analytic geometry, limits, differentiation of function of one variable, indefinite integration and numerical integration. 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 Civil Engineering science and related fields.

Learning outcomes and their assessment

Upon successful completion of this course:
1. Students are able to manage and demonstrate knowledge and critical understanding of analytic geometry, limits, differentiation of function of one variable, indefinite integration and numerical integration. Students manage the application of the acquired topics in practical examples related to the specialty of the Civil Engineering science and related fields. – practical works.
2. 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 works.
3. 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. Analytical geometry on plane (2 h)
2. Straight lines on plane and applications (4 h)
3. Conic sections (3 h)
4. Functions and different types of functions. Sequences and limits. Number e (2 h)
5. Limit of function. Properties of limits. Indeterminate forms (8 h)
6. Derivative of function (5 h)
7. Derivative of composite function. Differentiation of a function defined parametrically (8 h)
8. Higher order derivatives (3 h)
9. Applications of derivatives of function of one variable (6 h)
10. Indefinite integration. Basic integration rules (3 h)
11. Integration by substitution (3 h)
12. Integration by parts (3 h)
13. Trigonometric integrals (2 h)
14. Integration of rational functions with quadratic denominator (3 h)
15. Definite integrals (3 h)
16. Integration by substitution in the definite integrals. Integration by parts (3 h)
17. Application of the definite integrals. Area of the region between curves (6 h)
18. Area of a surface of revolution. Volumes of solid revolution (5 h)

Requirements for awarding credit points

Assessment: Exam.

Description of the organization and tasks of students’ independent work

In writing form the following independent work must be completed at times specified by the teaching staff:
Independent work 1. Analytical geometry
Independent work 2. Limits of functions
Independent work 3. Derivatives of functions
Independent work 4. Indefinite integration
Independent work 5. Definite integration
Independent work 6. Application of the definite integrals

Criteria for Evaluating Learning Outcomes

The written exam can be arranged at the time indicated by the teaching staff, if all the independent works are defended.

Compulsory reading

1. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. I daļa. Rīga: Zvaigzne, 1988. 534 lpp.
2. Kronbergs E., Rivža P., Bože Dz. Augstākā matemātika. II daļa. Rīga: Zvaigzne, 1988. 527 lpp
3. Volodko I. Augstākā matemātika. II daļa. Rīga: Zvaigzne ABC, 2007. 294 lpp.

Further reading

1. Šteiners K. Augstākā matemātika. III daļa. Rīga: Zvaigzne ABC, 1998. 192 lpp.
2. Šteiners K. Augstākā matemātika. IV daļa. Rīga: Zvaigzne ABC, 1998. 168 lpp.
3. Lewin J. An Interactive Introduction to Mathematical Analysis. Cambridge University Press.2003.- 492 p

Notes

The study course is included in the compulsory study course of First level professional higher education study programme “Civil Engineering”.