Basic Calculus 2

Real and complex numbers, elementary topology for euclidian spaces, fundamental theorem of algebra, partial summation, sequences and series, power series, Taylor series, uniform convergence of functions, Weierstrass approximation theorem, first order differential equations, Picard-Lindelöf Theorem, linear differential equations, power series solutions of differential equations.

1. Knowledge. The student has knowledge on the basic terminology in mathematical analysis,. The student has a solid background for further studies in analysis and of differential equations. The student has knowledge of the requirements for rigor in mathematical analysis.
2. Skills. The student has basic technical computation skills that are important in mathematical analysis. The student can become acquainted with mathematical reasoning that combines different concepts and results from the course's academic content. The student is able to derive simple sentences based on the subject content of the course.

Lectures and exercises. Final grade based on written final examination. Parts of this course can be taught in English.