# Foundation course in Mathematics

7.5 ECTS credits

Instruction is in the form of lectures, exercises, and laboratory sessions.

Main course components:

- Basic logic and set theory: symbols and concepts, basic principles of logical reasoning and proofs

- Basic analytical geometry such as conic sections

- Algebraic simplification, completing the square, factor theorem, equations such as trigonometric equations, inequalities, and absolute values

- Geometric and arithmetic sums, the sigma symbol

- Complex numbers: Cartesian and polar form, de Moivres formula, binomial equations, complex exponential functions

- Elementary functions: the concept of function, domain of definition, range of function, composition of functions, inverse functions

- Basic functions: polynomial, power, logarithmic, exponential, trigonometric and inverse trigonometric functions, their definitions, properties, graphs and rules for calculation

- Limits of sequences and functions, continuity, properties of continuous functions

- Definition of the derivative and calculation laws, chain rule, derivatives of elementary functions, implicit differentiation, the mean value theorem

- Basic applications of derivatives: tangents and normals, increasing and decreasing functions.

- Function studies: graph construction, extreme points, asymptotes, concavity

- Applications of derivatives: extreme value problems, linearisation, Taylor polynomial with error term using big-O notation and the Lagrange's form, l'Hopital's rules.

Main course components:

- Basic logic and set theory: symbols and concepts, basic principles of logical reasoning and proofs

- Basic analytical geometry such as conic sections

- Algebraic simplification, completing the square, factor theorem, equations such as trigonometric equations, inequalities, and absolute values

- Geometric and arithmetic sums, the sigma symbol

- Complex numbers: Cartesian and polar form, de Moivres formula, binomial equations, complex exponential functions

- Elementary functions: the concept of function, domain of definition, range of function, composition of functions, inverse functions

- Basic functions: polynomial, power, logarithmic, exponential, trigonometric and inverse trigonometric functions, their definitions, properties, graphs and rules for calculation

- Limits of sequences and functions, continuity, properties of continuous functions

- Definition of the derivative and calculation laws, chain rule, derivatives of elementary functions, implicit differentiation, the mean value theorem

- Basic applications of derivatives: tangents and normals, increasing and decreasing functions.

- Function studies: graph construction, extreme points, asymptotes, concavity

- Applications of derivatives: extreme value problems, linearisation, Taylor polynomial with error term using big-O notation and the Lagrange's form, l'Hopital's rules.

Progressive specialisation:
G1N (has only upper‐secondary level entry requirements)

Education level:
Undergraduate level

Admission requirements:
General admission requirements plus field-specific eligibility A9 (Physics 2, Chemistry 1, Mathematics 4) or field-specific eligibility 9 (Physics B, Chemistry A, Mathematics E)

Selection:

Selection is usually based on your grade point average from upper secondary school or the number of credit points from previous university studies, or both.

### This course is included in the following programme

- Bachelor Programme in Physics (studied during year 1)
- Mathematics Programme (studied during year 1)
- Master of Science in Computer Engineering (studied during year 1)
- Master of Science in Energy and Environmental Engineering (studied during year 1)
- Master of Science in Industrial Engineering and Management (studied during year 1)
- Master of Science in Chemical Engineering (studied during year 1)
- Master of Science in Mechanical Engineering (studied during year 1)
- Master of Science in Engineering Physics (studied during year 1)