Infinitesimal Calculus II (MAY211)
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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  MAY211 
Semester  2 
Course Title  Infinitesimal Calculus II 
Independent Teaching Activities  Lectures, laboratory exercises (Weekly Teaching Hours: 5, Credits: 7.5) 
Course Type  General Background 
Prerequisite Courses  None (from the typical point of view). Without the knowledge earned from the course “Infinitesimal Calculus I” will be nearly impossible to follow this course. 
Language of Instruction and Examinations  Greek 
Is the Course Offered to Erasmus Students  Yes (exams in English are provided for foreign students) 
Course Website (URL)  See eCourse, the Learning Management System maintained by the University of Ioannina. 
Learning Outcomes
Learning outcomes 
This course is the sequel of the course “Infinitesimal Calculus I”. The student will get in contact with more notions and techniques in the branch of Analysis. In this course the students:


General Competences 
The course provides inductive and analytical thinking, the students evolve their computational skills and they get knowledge necessary for other courses during their undergraduate studies. 
Syllabus
Series, convergence of series and criteria for convergence of series. Dirichlet’s criterion, D’ Alembert’s criterion, Cauchy’s criterion, integral criterion. Series with alternating signs and Leibnitz’s theorem. Absolute convergence and reordering of series, Power series, radius of convergence of power series.
Uniform continuity, definition and properties. Characterization of uniform continuity via sequences. Uniform continuity of continuous functions defined on closed intervals.
Riemann integral, definition for bounded functions defined on closed intervals. Riemann’s criterion, integrability of continuous functions. Indefinite integral and the Fundamental theorem of Calculus. Mean Value theorem of integral calculus, integration by parts, integration by substitution. Integrals of basic functions, integrations of rational functions. Applications of integrals, generalized integrals, relation between generalized integrals and series.
Taylor polynomials, Taylor’s Theorem, forms of the Taylor remainder. Taylor series and expansions of some basic functions as Taylor series.
Teaching and Learning Methods  Evaluation
Delivery 
Due to the theoretical nature of this course the teaching is exclusively given in the blackboard by the teacher.  

Use of Information and Communications Technology 
The students may contact their teachers by electronic means, i.e. by email.  
Teaching Methods 
 
Student Performance Evaluation 

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:
 Thomas, Απειροστικός Λογισμός, R.L. Finney, M.D. Weir, F.R.Giordano, Πανεπιστημιακές Εκδόσεις Κρήτης, (Απόδοση στα ελληνικά: Μ. Αντωνογιαννάκης).