# Mathematics ii

 Title ΓΕΝΙΚΑ ΜΑΘΗΜΑΤΙΚΑ ΙΙ / Mathematics ii Code GMC 214Y Faculty Sciences School Geology Cycle / Level 1st / Undergraduate Teaching Period Spring Coordinator Ioannis Pytharoulis Common No Status Active Course ID 40001801

 Academic Year 2013 – 2014 Class Period Spring Faculty Instructors Weekly Hours 4 Class ID 40049684
Type of the Course
• Background
Course Category
General Foundation
Mode of Delivery
• Face to face
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
• Greek (Instruction, Examination)
Prerequisites
General Prerequisites
Derivatives, partial derivatives, integrals
Learning Outcomes
Upon successful completion of this course, the students will: 1) Understand the concept of vector / vector functions 2) Understand and apply the operations among vectors and vector functions, their derivatives and integrals 3) To know and use the applications of vectors to solve problems
General Competences
• Apply knowledge in practice
• Work autonomously
Course Content (Syllabus)
Vectors in three dimensional space. Product of vectors (scalar, vector and triple) with applications to analytic geometry. Vector functions of one variable (limits, continuity, differentiation, integration). Theory of curves in the three dimensional space (tangent, perpendicular plane). Vector functions of several variables (limits, continuity, partial derivatives, total differential). Scalar and vector fields (gradient, divergence, rotation). Differentiation of scalar field along a curve and direction. Theory of surfaces (curvilinear coordinates, tangent plane and vertical vector). Line integrals of vector fields (properties, conservative fields and potential function, Green’s theorem). Line integrals of scalar fields. Area of surfaces (in Cartesian and curvilinear coordinates). Surface integrals of scalar and vector fields. Applications.
Keywords
Vectors, Scalar and vector fiends, surface, Line and surface integrals
Educational Material Types
• 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
1) All class material is available in electronic form to all students through the course web page. 2) Communication with the students by-email.
Course Organization