# Mathematics

 Title ΜΑΘΗΜΑΤΙΚΑ / Mathematics Code 001Υ Faculty Agriculture, Forestry and Natural Environment School Forestry and Natural Environment Cycle / Level 1st / Undergraduate Teaching Period Winter Common No Status Active Course ID 420000001

### Programme of Study: UPS School of Forestry and Natural Environment (2009-today)

Registered students: 348
OrientationAttendance TypeSemesterYearECTS
KORMOSCompulsory Course115

 Academic Year 2018 – 2019 Class Period Winter Instructors from Other Categories Charalampos Bratsas Theodora Vlachou Weekly Hours 5 Class ID 600125894

### Class Schedule

 Building Γεωπονίας & Δασολογίας Floor Όροφος 1 Hall ΑΜΦΙΘΕΑΤΡΟ Α (35) Calendar Πέμπτη 09:00 έως 11:00
Course Type 2016-2020
• Background
Course Type 2011-2015
General Foundation
Mode of Delivery
• Face to face
Digital Course Content
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
• Greek (Instruction, Examination)
• English (Examination)
Prerequisites
General Prerequisites
Knowledge of Mathematics of Lyceum. Very useful for repetition is considered the book of A΄ class of General Lyceum, and the first chapter (Differential Calculus) of the book “Mathematics and Elements of Statistics for the C΄class of General Lyceum”. These books and a lot of other are available in the page http://www.pi-schools.gr/ of pedagogical institute.
Learning Outcomes
To comprehend and consolidate the notion of a function, with which they dealt in some degree in the last years of Lyceum. To use the graphic representation for the recognition of behavior of functions and to learn how to draw the graphic representation of elementary functions. To recognize the sequences and series (numerical and power series) and to find, if exist, limits and infinite sums. To differentiate various forms of functions (explicit, implicit, parametric, bivariate) and apply the derivatives in the geometry and elsewhere. To integrate elementary and relatively complicated functions with one or two variables and express various quantities as areas, volumes, etc as integrals. Also, to solve some simple differential equations and find their general and partial solution.
General Competences
• Apply knowledge in practice
• Work autonomously
• Work in an interdisciplinary team
Course Content (Syllabus)
Functions (algebraic, exponential, logarithmic, trigonometric, transcendental, implicit, parametric), Sequences (the notion of limit, convergence, criteria of convergence), Series (definition, convergence, criteria of convergence), Power Series, Derivative (Derivative Rules, logarithmic differentiation, derivative of implicit and parametric functions, power series, second and higher order derivative), Taylor Polynomial and Taylor series, Applications of derivatives (geometrical applications, Newton-Raphson method for finding the roots of an equation), Complete study of a function (extrema, curvature, asymptote, graphic representation), Integrals (integration of elementary functions, theorem of mean value, the Fundamental Theorem of Calculus), Area under or between curves, Geometric applications, Techniques of Integration (Substitution, Integration by Parts, integration of a rational function), Functions of many variables (domain and continuity, partial derivative, extrema, double integrals), Differential equations (Separable, homogenous, linear of first order)
Keywords
variable, function, sequence, series, derivative, integral, area, improper integral, numerical integration, partial derivative, double integral
Educational Material Types
• Notes
• Slide presentations
• Book
Use of Information and Communication Technologies
Use of ICT
• Use of ICT in Course Teaching
• Use of ICT in Communication with Students
Description
Some of the lectures are given with Powerpoint and using Mathematical Packages, such as GeoGebra
Course Organization