Upon completion of this course the student is able to:
- Give precise definitions of some important concepts from real analysis and work with them, and also, to give a rigorous proof of some important results related to these concepts,
- explain and apply the concepts convergence/divergence of a sequence of real numbers,
- explain and work with the concepts related to real-valued functions, and inverse functions,
- explain and work with the concepts related to continuity, differentiability and Riemann-integrability of real-valued functions on an interval.
Within the Analysis-line of Applied Mathematics, one learns the fundamental concepts in Real Analysis that are indispensable for the further study. Another integral part of the Analysis-line is the proper and rigorous manner of proving results. In this first course, the Axioms of Real numbers will be reviewed very briefly, and in particular, the concepts of supremum and minimum. The main focus lies on the topics of convergence of a sequence of real numbers and different properties of real-valued functions such as continuity, differentiability and integrability and the relationships among these properties.|