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)

Introduction to the objectives and learning outcomes, curriculum, methods of evaluation and assessment criteria.
Errors of approximate values. The types of errors. Sources of errors. (2 + 1)
Solving equations approximately. Graphical method. Bisection method. Iteration. Secant method. Tangent method. (4 + 2)
Interpolation and approximation. (2 + 1)
Numerical integration. Rectangular formula. Trapezium formula. Simpson’s formula. (2 + 1)
Numerical solving of differential equations. Euler’s method. Taylor’s method. (2 + 1)
Written exam. (0 + 2)
Definition and properties of probability. (2 + 1)
Conditional probability. Independence of events. (2 + 1)
Random variables. Discrete and continuous random variables. Independence of random variables. (2 + 1)
Numerical characteristics of random variables. Mathematical expectation. (2 + 1)
Dispersion. Mode and median. Moments. The coefficient of skewness and kurtosis. (2 + 1)
Some important distributions. Binomial distribution. Poisson distribution. Normal distribution. Uniform distribution. Exponential distributions. (4 + 2)
Basics of statistics. Population. Sample. Displaying data. The average value of the sample. Sample variance. Sample mode. Sample median. (2 + 1)
Statistical testing. Parametric test. Nonparametric test. Χ2 test. (2 + 1)
Written exam. (0 + 2)

Format of instruction:

Student responsibilities