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Mathematics III

Course developer

Prior knowledge

Mate1021, Mathematics I

Mate1022, Mathematics II

Replaced course

MateB011 [GMATB011] Mathematics III

Course abstract

The study course deals with confidence intervals and hypothesis testing, linear correlation and linear regression, complex numbers, ordinary differential equations and series and their applications. 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 confidence intervals and hypothesis testing, linear correlation and linear regression, ordinary differential equations and series and their applications. 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. Confidence intervals for the mean. Hypothesis testing (2 h)
2. Linear regression and correlation between two variables. Multiple regression and correlation (4 h)
3. Complex numbers. Basic operations (3 h)
4. First order ordinary differential equations. Equations with separable variables (5 h)
5. Linear ordinary differential equations, Bernoulli differential equations (5 h)
6. Test 1: Complex numbers. First-order ordinary differential equations. (1 h)
7. Second order differential equations (3 h)
8. Second order homogeneous and nonhomogeneous linear equations (8 h)
9. The system of differential equations (3 h)
10. Test 2: Second-order equations. The system of differential equations (1h)
11. Series with positive terms. Convergence for series. Series with positive terms. Cauchy convergence test, ratio test, comparison test, integral test (5 h)
12. Alternating series (3 h)
13. Series of functions. Power series. Interval of convergence of the power series. Taylor series and MacLaurin series. Representation of functions by power series (5 h)
14. Numerical integration using power series. Solving ordinary differential equations using power series (7 h)
15. Test 3: Series with positive terms and series of functions (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. Confidence intervals. Hypothesis testing
Independent work 2. Correlation and regression
Independent work 3. Complex numbers First order differential equations
Independent work 4. Second order differential equations. Systems of differential equations
Independent work 5. Series with positive terms
Independent work 6. Power series

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. IV daļa. Rīga: Zvaigzne ABC, 1998. 168 lpp.
2. Šteiners K. Augstākā matemātika. V daļa. Rīga: Zvaigzne ABC, 2000. 129 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”.