Calculus

In this course the basic concepts from calculus are treated. The course is roughly divided into three parts. The first part of the course focusses on single variable calculus. This parts main subjects are general understanding of functions of a single variable and integration of these functions. General understanding of functions contains a variety of topics, including inverse (trigonometric) functions, limits, derivatives, implicit differentiation, Taylor polynomials and l'Hospital's rule. Subsequently, the subject of integration mainly focusses on the common integration techniques the substitution rule, integration by parts and integration by partial fraction definition and ends with a treatise of improper integrals. Several differentiation and integration techniques are then combined when covering first order linear and separable differential equations.

The second part of the course focusses on multivariate calculus. After starting with some general geometrical concepts such as the dot and cross product, as well as graphs and contour plots for functions of several variables, one of the main subjects of this part is partial derivatives and various related topics, including tangent planes, linear approximations, the chain rule, directional derivatives, the gradient and extreme values. This part finishes with a treatise of double and triple integrals, including polar, cylindrical and spherical coordinates, as well as general changes of coordinates.

The final part of the course focusses on vector calculus. In this part, vector fields are introduced. In addition, line integrals are covered both for scalar functions and for vector fields and connected to double integrals by means of Greens theorem.