Calculus I
Description

Positive integers, induction, real numbers, operations, ordering, the concepts of supremum and infimum. Axiom of completeness, n-th root function. Sequences, increasing and bounded sequences, sequences that converge to their supremum. Algebra of limits. Series of numbers, geometric series, absolute convergence, ratio test and n-th root test. Definition of e, exponential and logarithmic function. Limit of a function, continuity of a function, algebra of limits and continuity of functions. Intermediate value theorem, derivatives, algebra of derivatives, geometric interpretation, differential, Rolle’s theorem, mean value theorem, monotonicity, extrema, convexity and graph of a function.

In order to highlight the special educational and didactical aspects of a course, special emphasis is given on the historical evolution and scientific development of the subject as well as on its applications in technology and/or other sciences.

Division: Pure Mathematics
Program of Studies:
Undergraduate Studies
Semester: A
ECTS: 8
Hours per week (Lec/Tut/L): 3/2/0
Code: PM103
Course type: Core
Erasmus students: No




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