Fundamentals of mathematical analysis

Higher education teachers: Mramor Kosta Neža

Subject description

Prerequisits:

• Enrollment in the study year.

Content (Syllabus outline):

• Real numbers, natural numbers and induction, complex numbers, sequences, limit of sequence types.
• Functions: Basic features, graphs. Elementary functions, interpolation. Continuity and limits of functions, properties of continuous functions, bisection and secant method for solving nonlinear equations.
• Differentiation: Definition and geometric interpretation of the derivative. The rules for calculating and derivative. Differentials and linear approximations, Newton's method for solving nonlinear equations. Properties of differentiable functions. The use of derivative: drawing graphs, calculating the limit, the stationary points and local extreme, global extreme, examples of optimization functions, Taylor polynomials and Taylor series, applications.
• Integration: Indefinite integrals, elementary integral, basic integration rules. The definite integral and a surface area. Basic numerical methods for calculating the definite integral (trapezoidal and Simpson method). The relationship between the indefinite integral and certain, example of non-elementary functions.

Objectives and competences:

The goal is to consolidate knowledge and understanding of mathematical analysis such as convergence, derivatives and integrals, to show their basic properties and their use is in solving problems in computer science and generally in sciences.

Intended learning outcomes:

After completing this course the student will be able to apply basic concepts of mathematical analysis and understand the mathematical formulas and models based on them.

Learning and teaching methods:

• Lectures, calculation exercises with oral presentations, homework assignments.
• Particular emphasis is on an ongoing study with coursework and group work in class.

Study materials