Infinitesimal Calculus III (MAY311)

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School of Science

Academic Unit

Department of Mathematics

Level of Studies


Course Code


Semester 3
Course Title

Infinitesimal Calculus III

Independent Teaching Activities

Lectures, laboratory exercises (Weekly Teaching Hours: 5, Credits: 7.5)

Course Type

General Background

Prerequisite Courses -
Language of Instruction and Examinations

Greek, 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

The main learning outcomes are the:

  • differentiability analysis of real- and vector-valued functions of several variables
  • familiarity with the Euclidean space from an analytic (topological) viewpoint
  • knowledge of the problems that arise in Analysis in several dimensions
  • preparation for the treatment of functions of several variables in more specialized courses, e.g., Partial Differential Equations, Differential Geometry, Classical Mechanics, Application of Mathematics in the Sciences
  • development of combination skills concerning knowledge from diverse areas of Mathematics (Linear Algebra, Analytical Geometry, Analysis).
General Competences
  • Search for, analysis and synthesis of data and information, with the use of the necessary technology
  • Adapting to new situations
  • Working independently
  • Criticism and self-criticism
  • Production of free, creative and inductive thinking


  • Algebraic and topological structure of the Euclidean space R^n and geometric representation of the two- and three-dimensional space. Vector-sequences and their use concerning the topology of R^n.
  • Real- and Vector-valued functions of several variables. Limits and continuity of functions.
  • Partial derivatives. Partially differentiable and differentiable functions. Directional derivative. Differential operators and curves in R^n.
  • Higher order partial derivatives. Taylor Theorem. Local and global extrema of real-valued functions. Implicit Function Theorem. Inverse Function Theorem. Constrained extrema.

Teaching and Learning Methods - Evaluation


Classroom (face-to-face)

Use of Information and Communications Technology
  • Teaching material is offered at the course's website (notes and older exams)
  • The students may contact the lecturer by e-mail
Teaching Methods
Activity Semester Workload
Lectures (13X5) 65
Working independently 100
Exercises-Homeworks 22.5
Course total 187.5
Student Performance Evaluation

Final written exam in Greek (in case of Erasmus students in English)

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: