Infinitesimal Calculus III (MAY311)

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Undergraduate Courses Outlines - Department of Mathematics

General

School

School of Science

Academic Unit

Department of Mathematics

Level of Studies

Undergraduate

Course Code

MAΥ311

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)

http://users.uoi.gr/giannoul/AL3.html

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

Syllabus

  • 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

Delivery

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 Eudoxus. Additionally: