Mathematics 1

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 be able to:
- identify and sketch graphs of elementary functions, to determine the domain of the given function
- find the derivative of the given function
- apply the dervative in practice (tangents and normals, maximum, minimum and inflection points) and to interpret the shape of graphs
- 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. Sets of numbers.
2. Functions: Notion. Composite functions. Inverse function.
3. Elementary functions.
4. Functions: Limits. Continuity.
5. Derivative and application: Notion. Interpretation. Derivative techniques.
6. Differential. Higher order derivatives.
7. Theorems of differential calculus. Maximum, minimum points.
8. Inflection points. Asymptotes. Graphs sketching.
9. Sequences: Notion. Limits.
10. Series: Convergence of numeric series. Power series. Taylor series.
11. Matrices and vectors: Matrix algebra. Determinants. Inverse matrix.
12. Linear systems of equations.
13. Vector algebra.
14. Solid analityc geometry.
15. Course review. Revision.

Format of instruction:

Student responsibilities

Regular attendance of classes.