Infinitesimal Calculus I (MAY111)
 Ελληνική Έκδοση
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 Department of Mathematics
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General
School  School of Science 

Academic Unit  Department of Mathematics 
Level of Studies  Undergraduate 
Course Code  MAY111 
Semester  1 
Course Title  Infinitesimal Calculus I 
Independent Teaching Activities  Lectures (Weekly Teaching Hours: 5, Credits: 7.5) 
Course Type  General Background 
Prerequisite Courses   
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
Learning outcomes  Here, the acronym RFooV stands for Real Function of one Variable. Remembering:
Comprehension:
Applying:
Evaluating: Teaching undergraduate courses. 

General Competences 

Syllabus
 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
Delivery 
 

Use of Information and Communications Technology 
 
Teaching Methods 
 
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. 
Attached Bibliography
See the official Eudoxus site or the local repository of Eudoxus lists per academic year, which is maintained by the Department of Mathematics. Books and other resources, not provided by Eudoxus:
 