Analysis A: Limit and Continuity (5cr)

Objectives

This course introduces to the fundamentals of mathematical analysis at an adequate level of rigour. Upon successful completion of the course, a student will be able todetermine the greatest lower bound and the least upper bound in simple cases,study the convergence and the properties of sequences,find limits and study continuity of functions,use precise definitions to produce rigorous proofs of results that arise in this course using direct and indirect proof, induction and epsilon-delta technique,deliver both oral and written presentations of her/his solutions.

Content

Real numbers, the least upper bound and the greatest lower bound, the limit of a sequence, Bolzano-Weierstrass Theorem, the limit of a function and the epsilon-delta proofs, continuity of a function, Bolzano's Intermediate Value Theorem.

Prerequisites

For the students of Bachelor's Programme in Science and Engineering, no prerequisites are required.