# Mathematics II

 Title ΜΑΘΗΜΑΤΙΚΑ ΙΙ / Mathematics II Code ΓΕ0400 Faculty Engineering School Civil Engineering Cycle / Level 1st / Undergraduate Teaching Period Spring Common No Status Active Course ID 20000099

### Programme of Study: PPS TMĪMATOS POLITIKŌN MĪCΗANIKŌN (2018-2019)

Registered students: 506
OrientationAttendance TypeSemesterYearECTS
Core program for all studentsCompulsory Course216

 Academic Year 2019 – 2020 Class Period Spring Faculty Instructors Weekly Hours 5 Class ID 600155115
SectionInstructors
1. ΓΕ0400

### Class Schedule

 Building Πολυτεχνείο - πτέρυγα Β (Πολιτικών Μηχ.) Floor Ισόγειο Hall ΑΙΘΟΥΣΑ 5.41/542 (224) Calendar Δευτέρα 10:00 έως 13:00 Building Πολυτεχνείο - πτέρυγα Β (Πολιτικών Μηχ.) Floor Ισόγειο Hall ΑΙΘΟΥΣΑ 5.41/542 (224) Calendar Τρίτη 12:00 έως 14:00
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)
Prerequisites
General Prerequisites
Calculus I
Learning Outcomes
After the succesful completion of the course, the students are able to: 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
Keywords
Multivariable functions, Vector calculus
Educational Material Types
• Book
Course Organization