## Curriculum in Mathematics Pre-semester

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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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