Summary

We study the fundamental concepts of analysis, calculus and the integral of real-valued functions of a real variable.

Content

Keywords

Real numbers, function, sequence,convergent/divergent sequence, limit, subsequence, limit of a function, continuous function, series of real numbers, convergent/divergent series, absolute convergence, derivative, class C^k, mean value theorem, Taylor's theorem, Taylor series, Riemann integral, indefinite integral, intermediate value theorem.

Learning Outcomes

• The intended learning outcomes of this course are that students acquire the following capacities:
• Reason rigorously to analyse problems
• Choose appropriate analytical tools for problem solving.
• Be able to conceptualise in view of the applications of analysis.
• Apply efficiently mathematical concepts for problem solving by means of examples and exercises
• Analyze and to solve new problems.
• Master the basic tools of analysis as, for example, notions of convergence, sequences and series.
• Studying rigorously real functions we intend that students will demonstrate a deep understanding of calculus

Teaching methods

Ex cathedra/online lectures and exercise sessions with tutors and student assistants.

Assessment methods

Written exam

Supervision