Mathematics II

Course Information
TitleΜΑΘΗΜΑΤΙΚΑ ΙΙ / Mathematics II
SchoolCivil Engineering
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
Course ID20000099

Programme of Study: PPS TPM - EISAKTEOI APO 2022 KAI EXĪS

Registered students: 0
OrientationAttendance TypeSemesterYearECTS

Class Information
Academic Year2018 – 2019
Class PeriodSpring
Faculty Instructors
Instructors from Other Categories
  • Zafeiria Roumelioti
Weekly Hours5
Class ID
1. ΓΕ0400Theodora Ioannidou, Zafeiria Roumelioti
Course Type 2016-2020
  • Background
Course Type 2011-2015
General Foundation
Mode of Delivery
  • Face to face
Digital Course Content
The course is also offered to exchange programme students.
Language of Instruction
  • Greek (Instruction, Examination)
General Prerequisites
Calculus I
Learning Outcomes
1. Calculate first and higher order partial derivatives and differentials, apply chain rule and model problems associated with the concept of rate of change. 2. Calculate local and global extrema of multivariable functions in optimization problems. 3. Linearize scalar/vector fields. 4. Compute double and triple integrals (in cartesian, polar, cylindrical and spherical coordinates). 5. Parametrize curves and surfaces and calculate surface area. 6. Identify linear and central vector fields and perform calculations using gradient, divergence, rotation and Laplace operators in Cartesian, cylindrical, spherical coordinates. Also, to identify conservative, irrotational, incompressible fields and compute scalar/vector potential. 7. Study qualitative characteristics of vector fields (circulation - flux) with the use of line or surface integrals. 8. Connect between the concepts of circulation and rotation and the between the concepts of flux and divergence using Green’s, Gauss and Stokes theorems. 9. Apply the basic tools of vector calculus in fluid mechanics.
General Competences
  • Apply knowledge in practice
  • Retrieve, analyse and synthesise data and information, with the use of necessary technologies
  • Advance free, creative and causative thinking
Course Content (Syllabus)
Many Variables Calculus: Surrfaces, Partial Derivatices, Chain Rule, Taylor's Expansion, Double and Triple Integrals Vector Analysis: Vector Fields, Line and Surface Integrals, Conservative Vector Fields Frenet Frame, Greens, Gauss and Stokes Theorem
Multivariable functions, Vector calculus
Educational Material Types
  • Book
Course Organization
Student Assessment
Written examination at the end of the semester.
Student Assessment methods
  • Written examination
Course Bibliography (Eudoxus)
1) Απειροστικός Λογισμός Finney, Weir, Giordano Πανεπιστημιακές εκδόσης Κρήτης Κωδικός Εύδοξος 22689021 ISBN 978-960-524-182-7 2) Διανυσματικός Λογισμός Marsden, Tromba Πανεπιστημιακές εκδόσης Κρήτης Κωδικός Εύδοξος 211 ISBN 978-960-7309-45-7
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