Courses

Multivariable Functions

General

Course Contents

Multivariable functions, definition, limits, continuity.
Vectors and Analytic geometry of space, equations of lines and planes.
Partial derivatives and basic theorems.
Total differential, gradient, implicit differentiation, tangent planes.
The chain rule, coordinate systems.
Taylor’s formula for multivariable functions.
Curves in space and component functions
Extreme values of multivariable functions.
Double and triple integrals.
Substitutions in multiple integrals, polar, cylindrical, spherical coordinates
Applications in Engineering, in Physics.

Educational Goals

The course is designed to provide the basic tools of advanced mathematics, including mainly elements of differential and integral calculus of multivariable functions. In particular, it focuses on the detailed presentation of mathematical concepts, theorems and propositions but also on problem-solving techniques related to them. For this purpose, extensive use is made of examples that find use in practical applications from the field of engineering.
As an elective course, it offers the engineer the opportunity to satisfy his / her interest in mathematics by further cultivating the mathematical way of thinking by developing skills of mathematical transcendence and methodology and applying them to the solution of practical problems on two and three dimensions.
Consistent and successful course attendance has as expected learning outcomes for the student:
to achieve the gradual theoretical logical subtraction from the real functions of one variable into real functions of two, three and more variables, to enable him to understand and process three-dimensional data with the help of representations of functions in 3d-space, to provide him with methods for the study and analysis of multivariable functions, to understand the concepts of double and triple integrals and connect them with practical applications, to identify and distinguish problem-solving methods related to the differentiation and integration of multivariable functions, to make him / her capable to apply the above methods to engineering problems, to analyze and interpret the obtained results.

General Skills

Research, analysis and synthesis of data and information, using corresponding technologies, Adaptation to new situations, Independent work, Teamwork – distribution of responsibilities, Intellectual competences, Societal competence.

Teaching Methods

Lectures, Exercises, Projected Presentations, Online Synchronous and Asynchronous Teaching Platform (moodle).

Students Evaluation

Assessment Language: Greek / English. Final Written Examinations. Submission of weekly assignments.
Evaluation criteria: Application of definitions, algorithms or propositions. Combination and synthesis of concepts and proof or computational procedures. Taking initiatives to implement problem-solving strategies.

Recommended Bibliography

1. Thomas’ Calculus, 14th edition, by Joel Hass, Christopher Heil, Maurice Weir
2. Vector Calculus, 3rd edition by Jerold E. Marsden, Antony J. Tromba