MM501: Calculus I (for Computer Science and BSc.scient.oecon.) (5 ECTS)

Ubegrænset deltagerantal, dog højst 30 studerende pr. hold for eksaminatorierne.
i 2. kvartal er ansvarlig underviser lektor Kristian Debrabant.

Prerequisites:
None

Academic preconditions:
Danish high school mathematics (high level) must be passed.

Course introduction
To prepare the students for the fundamental applications of mathematics in the natural and technical sciences and for further studies in mathematics.

Expected learning outcome
At the end of the course the student should be able to

* apply methods and results of differentiation and integration for functions of one variable to solve mathematical problems with-in the
scope of the course syllabus, including mathematical models used in science;
* compute mean, variance and standard deviation for a random variable with a given probability density function;
* decide whether a given function is a probablity density function, and fit parameters so a given function becomes a probability density function;
* solve simple algebraic equations in one complex variable, do simple arithmetic operations on complex numbers and convert between rectangular and polar representations of a complex number;
* present, formulate and carry out basic mathematical arguments needed for mathematical problems for the above topics

Subject overview
1) Differentiation and integration of standard functions (including logarithms, exponentials and power functions, the hyperbolic functions, the inverse trigonometric functions and rational functions.
2) The mean value theorem, Taylor polynomials for functions of a single variable, estimation of the error term in Taylor approximations, l'Hopital's rules for calculating limits.
3) Linear differential equations of first and second order and separable first order differential equations (solution methods and applications).
4) Riemann sums, the Riemann integral, The Fundamental Theorem of Calculus.
5) Probability theory: Random variables, density functions, mean, variance and standard deviation, the Gaussian distribution.
6) Complex numbers, the n roots of unity, the complex exponential function, the complex quadratic equation.
7) Functions of several variables and their partial derivatives.

Literature

Meddeles ved kursets start.