Curriculum in Mathematics Pre-semester

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Physics                              Chemistry                                Mathematics

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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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Physics                              Chemistry                                Mathematics

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