#### Abstract

Most first-year students find it hard to understand and acquire mathematical notions of differential calculus. This is often due to insufficient prior knowledge or because these notions are really difficult and require mathematical and logical maturity. Given the difficulties, this unit explains the matter gradually, starting with the targeted theoretical notions, which is followed by exercises and solved problems, with the aim of teaching the students how to solve tasks independently and how to apply the acquired knowledge in solving problem tasks in the area of maritime affairs. Basic notions associated with the derivation of function are explained, along with the rules and techniques of derivatives. A particular attention is paid to the application of derivation in the problems of the tangent, the normal, the differential, and the establishing the function limits. The application of derivations in the flow examination and function graph drawing are explained and followed by the application of derivations in maritime affairs.

#### Aim

Acquire knowledge and skills in those areas of differential calculus which are necessary to follow the curricula of other courses of the study program, and are expected to be implemented in maritime practice., which can be seen from the last part.

#### Learning Outcomes

- Define the notions of derivative, function limit and differential,
- Apply simple and complex derivation rules when solving tasks,
- Perform the derivation of the complex, parametrically or implicitly given function,
- Explain the concept of the real variable of real functions and the geometric interpretation of the derivative at a point,
- Apply the derivative in finding the local and global extremes of the function of a give variable, and the points of the function inflection,
- Analyze the flow of an elementary function by using derivation, and sketch its graph.

#### Previous knowledge of mathematics

*sets and functions, sequences and series, limits and continuity of the function*

#### Relatedness with solving problems in the maritime field

mechanics (problem of speed), meteorology (weather forecast – extreme sea states), electronics (graphic layouts), navigation (establishing the distance, navigability of the fairway)…

#### Contents

Google Forms

GeoGebra