Infinitesimal Calculus IV (MAY411)
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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 
MAY411 
Semester  4 
Course Title 
Infinitesimal Calculus IV 
Independent Teaching Activities 
Lectures (Weekly Teaching Hours: 5, Credits: 7.5) 
Course Type 
General Background 
Prerequisite Courses   
Language of Instruction and Examinations 

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 VFomV stands for Vector Function of multiple Variables.
Comprehension:
Applying:
Evaluating: Teaching undergraduate and graduate courses. 

General Competences 

Syllabus
Definition of multiple integral using lower and upper sums over closed rectangles, set of zero volume, Lebesgue Criterion for Riemann Integrability, Jordan measurable sets and the definition of the integral over such sets, Fubini Theorem, Cavalieri Principle, elementary regions in two and three dimensional spaces, change of variables and their basic applications, evaluation of integrals using the aforementioned methods. Definition of integrals over paths for parametrizes functions an vector fields, definition of path length, parametrizes paths, parametrized transformations, gradient fields and path independent integrals, Green Theorem. Surfaces and parametrization of surface integrals. Definition of surface integral for real functions and for vector fields. Area of surface. Stokes and Gauss Theorems. Uniform convergence of function’s sequences and series. Fourier series.
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:
 