Algengar spurningar

Stær4CA05

The course provides an introduction to calculus where the main emphasis is laid on the theoretical aspects of the material. Several different types of mathematical proofs are studied in detail (e.g. direct proofs, indirect proofs and proofs by mathematical induction). Students are introduced to the construction of the real number system and use the axioms for the real numbers to proof simple rules. Sequences and series are studied in more detail than in prior courses, with emphasis on the limits of sequences and convergence tests for series. The main properties of continuous and differentiable functions are studied and students apply, for instance, the definition of limits of functions, and the mean- and intermediate-value theorems in proofs. The rule of l’Hopital is further used for computation of limits. The mathematical typesetting system LaTeX is introduced and students are expected to use it.