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Mathematics II

Course developer

Prior knowledge

Mate1021, Mathematics I

Replaced course

MateB010 [GMATB010] Mathematics II

Course abstract

The study course deals with function of one and two variables and it’s applications, indefinite integration and numerical integration, probability, laws of probability, distributions. 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. 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. Students are able to manage and demonstrate knowledge and critical understanding of function of one and two variables and it’s applications, indefinite integration and numerical integration, probability, laws of probability, distrbutions. Students manage the application of the acquired topics in practical examples related to the specialty of the Civil Engineering science and related fields. – tests
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 and laboratory 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. Applications of derivatives of function of one variable (4 h)
2. Functions of two variables. Partial derivatives of function of two variables (3 h)
3. Extrema of functions of two variables (4 h)
4. Test 1: Functions of one and two variables (1 h)
5. Indefinite integration. Basic integration rules (4 h)
6. Integration by substitution (5 h)
7. Integration by parts (3 h)
8. Trigonometric integrals (3 h)
9. Integration of rational functions with quadratic denominator (3 h)
10. Test 2: Indefinite integrals (1 h)
11. Definite integrals (3 h)
12. Integration by substitution in the definite integrals. Integration by parts (4 h)
13. Application of the definite integrals. Area of the region between curves (3 h)
14. Area of a surface of revolution. Volumes of solid revolution (4 h)
15. Laws of probability (3 h)
16. Discrete random variables and probability distributions (3 h)
17. Continuous random variables and probability distributions (4 h)
18. Test 3: Definite integrals. Probability. Distributions (1 h)

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. Applications of derivatives. Functions of two variables
Independent work 2. Indefinite integration
Independent work 3. Definite integration
Independent work 4. Application of the definite integrals
Independent work 5. Discrete variables. Continuous variables. Distributions

Criteria for Evaluating Learning Outcomes

The student can receive the accumulative exam if:
1. all independent works are completed at times specified by the teaching staff;
2. 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 teaching staff.
The accumulative exam mark is
- 90% of the average mark of all tests
- 10% for completed independent works.

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).

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.
4. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem I daļa Zvaigzne ABC Rīga, 2003 – 256 lpp.
5. Bula I., Buls J. Matemātiskā analīze ar ģeometrijas un algebras elementiem II daļa Zvaigzne ABC Rīga, 2004 – 192 lpp.
6. Lewin J. An Interactive Introduction to Mathematical Analysis. Cambridge University Press.2003.- 492 p

Notes

The study course is included in the compulsory part of the Bachelor’s study program “Civil Engineering”.