Applied Mathematics

Code

Course teacher

Associate teachers

Status of the course

Course objectives

Student are introduced to the ideas and methods of approximate solving algebraic and differential equations, interpolation and numerical integration, to concepts of the theory of probability and statistics and their application to particular example and tasks.
By developing a positive attitude toward learning, responsibility for own success and progress, and the acquisition of competencies described above, the students are expected to build a solid foundation for lifelong learning and further education.

Course enrolment requirements and entry competences required for the course

Students should have fundamental competencies related to the calculus.

Learning outcomes expected at the level of the course (4 to 10 learning outcomes)

After the passing the exam, students will be able to:
- use appropriate language, symbolic notation and graphic representation to describe the ideas and methods for numerical solving equations;
- apply the methods described above in the particular tasks;
- describe the concept and define the notions of probability theory;
- understand the concepts and apply the methods described above in real situations;
- define discrete and continuous random variables and their characteristics;
- properly interpret characteristics of random variables on particular examples;
- describe examples of important distribution and identify conditions for their use in problem solving;
- describe the concept and define the notions of statistics theory;
- use a computer and appropriate software as a tool in the statistical data processing;
- understand the process of statistical testing and parametric and non-parametric sample testing.

Course content broken down in detail by weekly class schedule (syllabus)

1st week: Introduction to the objectives and learning outcomes, curriculum, methods of evaluation and assessment criteria.
2nd week: Errors of approximate values. The types of errors. Sources of errors.
3rd week: Solving equations approximately. Graphical method. Bisection method. Iteration. Secant method. Tangent method.
4th week: Interpolation and approximation.
5th week: Numerical integration. Rectangular formula. Trapezium formula. Simpson’s formula.
6th week: Numerical solving of differential equations. Euler’s method. Taylor’s method.
Written exam.
7th week: Definition and properties of probability.
8th week: Conditional probability. Independence of events.
9th week: Random variables. Discrete and continuous random variables.
10th week: Independence of random variables.
11th week: Numerical characteristics of random variables. Mathematical expectation.
12th week: Dispersion. Mode and median. Moments. The coefficient of skewness and kurtosis.
13th week: Some important distributions. Binomial distribution. Poisson distribution. Normal distribution. Uniform distribution. Exponential distributions.
14th week: Basics of statistics. Population. Sample. Displaying data. The average value of the sample. Sample variance. Sample mode. Sample median.
15th week: Statistical testing. Parametric test. Nonparametric test. Χ2 test.
Written exam.

Format of instruction:

Student responsibilities