Infinitesimal Calculus III (MAY311)

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

• J. E. Marsden, A. Tromba: Vector Calculus, 6th edition, W. H. Freeman and Company, 2012
• M. Spivak: Calculus on Manifolds, Addison-Wesley, 1965
• Ι. Γιαννούλης: Διανυσματική Ανάλυση, ΣΕΑΒ, 2015 (in Greek)