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|School||School of Science|
|Academic Unit||Department of Mathematics|
|Level of Studies||Undergraduate|
|Course Title||Infinitesimal Calculus I|
|Independent Teaching Activities||Lectures (Weekly Teaching Hours: 5, Credits: 7.5)|
|Course Type||General Background|
|Language of Instruction and Examinations||Language of Instruction (lectures): Greek.|
Language of Instruction (activities other than lectures): Greek and English
Language of Examinations: Greek and English
|Is the Course Offered to Erasmus Students||Yes (in English)|
|Course Website (URL)||See eCourse, the Learning Management System maintained by the University of Ioannina.|
|Learning outcomes||Here, the acronym RFooV stands for Real Function of one Variable.|
Evaluating: Teaching undergraduate courses.
- Real numbers, axiomatic foundation of the set of real numbers (emphasis in the notion of supremum and infimim), natural numbers, induction, classical inequalities.
- Functions, graph of a function, monotone functions, bounded functions, periodic functions. Injective and surjective functions, inverse of a function. Trigonometric functions, inverse trigonometric functions, exponential and logarithmic functions, hyperbolic and inverse hyperbolic functions.
- Sequences of real numbers, convergent sequences, monotone sequences, sequences defined by recursion, limits of monotone sequences, nested intervals. The notion of subsequence, Bolzano Weierstass’ Theorem, Cauchy sequences. Accumulation points of sequences, upper and lower limit of a sequence (limsup, liminf).
- Continuity of functions, accumulation points and isolated points, limits of functions, one sided limits, limits on plus infinity and minus infinity. Continuity of several basic functions, local behaviour of a continuous function. Bolzano Theorem and intermediate value theorem. Characterization of continuity via sequences, properties of continuous functions defined on closed intervals, continuity of inverse functions.
- Derivative of a function, definition and geometric interpretation, examples and applications in sciences. The derivatives of elementary functions, derivation rules, higher order derivation. Rolle’s Theorem, Mean Value Theorem, Darboux’s theorem. Derivative and the monotonicity of a function, extrema of functions, convex and concave functions, inflection points. Derivation of inverse functions. Generalized Mean Value Theorem, De L’ Hospital rule. Study of functions using derivatives.
Teaching and Learning Methods - Evaluation
|Use of Information and Communications Technology||
|Student Performance Evaluation||
Language of evaluation: Greek and English.
The aforementioned information along with all the required details are available through the course's website. The information is explained in detail at the beginning of the semester, as well as, throughout the semester, during the lectures. Reminders are also posted at the beginning of the semester and throughout the semester, through the course’s website. Upon request, all the information is provided using email or social networks.