Mathematics

Code

Course teacher

Associate teachers

Status of the course

Course objectives

To introduce students to the basic elements of calculus and linear algebra.

Course enrolment requirements and entry competences required for the course

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

After finishing this course the student is expected to:
- identify and sketch graphs of elementary functions, to determine the domains of more complex functions
- find the derivatives of the given functions
- know the graphical applications of the dervative (tangents and normals, maximum, minimum and inflection points, sketching and interpreting graphs)
- know techniques of integration (integration by substitution, integration by parts)
- use the definite integral -applications to geometry
- solve the system of linear equations (by matrix inversion, by Gaussian elimination)

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

1. Sets: Notion. Algebra of sets.
2. Number sets.
3. Functions: Notion. Inverse function.
4. Elementary functions. Limits.
5. Continuity. Sequences: Notion. Limits.
6. Derivative and application: Notion. Interpretation. Derivation techniques.
7. Differential. Higher order derivatives.
8. Theorems of differential calculus. Maximum, minimum points.
9. Inflection points. Asymptotes. Curve sketching.
10. Integral and application: Indefinite integral. Techniques of integration.
11. Definite integral.
12. Using the definite integral.
13. Matrices and vectors: Matrix algebra. Determinants. Inverse matrix.
14. Linear systems of equations. Vector algebra.
15. Course review. Revision.

Format of instruction:

Student responsibilities

Regular attendance of classes.