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 TPM - EISAKTEOI APO 2022 KAI EXĪS
Registered students: 0
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|
| Academic Year | 2016 – 2017 |
| Class Period | Spring |
| Faculty Instructors | |
| Instructors from Other Categories |
|
| Weekly Hours | 5 |
| Class ID | 600031962
|
| Section | Instructors |
|---|---|
| 1. ΓΕ0400 | Theodora Ioannidou, Zafeiria Roumelioti |
Class Schedule
| Building | Πολυτεχνείο (πτέρυγα Β) |
| Floor | Ισόγειο |
| Hall | ΑΙΘΟΥΣΑ 5.41/542 (224) |
| Calendar | Δευτέρα 12:00 έως 14:00 |
| Building | Πολυτεχνείο (πτέρυγα Β) |
| Floor | Ισόγειο |
| Hall | ΑΙΘΟΥΣΑ 5.41/542 (224) |
| Calendar | Τρίτη 12:00 έως 15:00 |
Course Type 2016-2020
- Background
Course Type 2011-2015
General Foundation
Mode of Delivery
- Face to face
Digital Course Content
- e-Study Guide https://qa.auth.gr/en/class/1/600031962
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
Prerequisites
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
Keywords
Multivariable functions, Vector calculus
Educational Material Types
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 180 | 6.4 | ✓ | ✓ | |
| Total | 180 | 6.4 |
Student Assessment
Description
Written examination at the end of the semester.
Student Assessment methods
- Written examination
Bibliography
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
Last Update
12-05-2015
