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Course Curriculum
Part I: Calculus
1) Basic concepts
Sets; set relations and operations.
2) Functions
Real-valued functions of one variable; graph of function; continuity;
polynomials; rational functions; algebraic functions; natural exponential
function; trigonometric functions; natural logarithmic function.
3) Differential calculus
First derivative; tangent; linear approximation; differential; product rule;
quotient rule; chain rule.
4) Limits
Definition; evaluation
5) de L’Hôpital’s rule
Criteria for application.
6) Integral calculus
Definite integrals; fundamental theorem of calculus; indefinite integrals;
integration by parts; substitution method; partial fractions
decomposition of rational functions.
Part II: Vector algebra
1) Basic concepts
Column vectors; row vectors; addition and scaling of vectors; linear
in-/dependence of vectors; vector basis.
2) Linear systems
Gaussian elimination; matrices; addition and scaling of matrices; matrix
product; linear maps.
3) Scalar product
Orthogonality of vectors; length of vector; normalisation; angle
subtended by two vectors; representations of planes in 3-D Euclidian
space.
4) Decomposition of vectors
Components of vector with respect to given basis; projection of vector
onto other vectors.
5) Determinants
Area of parallelogram; volume of parallelepiped.
6) Vector product
Definition; properties; applications.
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