Calculus II
| Title | Λογισμός ΙΙ / Calculus II |
| Code | 007 |
| Faculty | Engineering |
| School | Electrical and Computer Engineering |
| Cycle / Level | 1st / Undergraduate |
| Teaching Period | Spring |
| Coordinator | Nikolaos Atreas |
| Common | No |
| Status | Active |
| Course ID | 600000955 |
Programme of Study: Electrical and Computer Engineering
Registered students: 485
| Orientation | Attendance Type | Semester | Year | ECTS |
|---|---|---|---|---|
| CORE | Compulsory Course | 2 | 1 | 6 |
| Academic Year | 2019 – 2020 |
| Class Period | Spring |
| Faculty Instructors | |
| Class ID | 600144691
|
Class Schedule
| Building | Πολυτεχνείο - πτέρυγα Γ (ΤΗΜΜΥ & Τοπογράφων Μηχ.) |
| Floor | Όροφος 1 |
| Hall | Α3 (2) |
| Calendar | Τρίτη 09:00 έως 12:00 |
| Building | Πολυτεχνείο - πτέρυγα Γ (ΤΗΜΜΥ & Τοπογράφων Μηχ.) |
| Floor | Όροφος 1 |
| Hall | Α5 (7) |
| Calendar | Τετάρτη 09:00 έως 12:00 |
| Building | Πολυτεχνείο - πτέρυγα Γ (ΤΗΜΜΥ & Τοπογράφων Μηχ.) |
| Floor | Όροφος 1 |
| Hall | Α5 (7) |
| Calendar | Τετάρτη 14:00 έως 16:00 |
| Building | Πολυτεχνείο - πτέρυγα Γ (ΤΗΜΜΥ & Τοπογράφων Μηχ.) |
| Floor | Όροφος 1 |
| Hall | Α5 (7) |
| Calendar | Πέμπτη 16:00 έως 18:00 |
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/1/600144691
- Other: http://users.auth.gr/natreas
Erasmus
The course is also offered to exchange programme students.
Language of Instruction
- Greek (Instruction, Examination)
- English (Examination)
Prerequisites
General Prerequisites
Calculus of functions of a real variable, linear algebra and Analytic Geometry
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 curve length, surface area and related mass problems.
6. Identify linear and central vector fields and perform calculations using gradient, divergence, rotation and
Laplace operators in Cartesian, cylindrical, spherical coordinates. Also, 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. Establish connection between the concepts of circulation and rotation and between the concepts of flux and divergence, using Green’s, Gauss and Stokes theorems.
9. Apply the basic tools of vector calculus in electromagnetism(Maxwell equations, Gauss law on
electromagnetism, calculation of electric field, work, scalar potential of electric field etc. )
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)
Multivariable functions. Limits, continuity, directional derivative, partial derivative and applications. Total derivative/Tangent plane. Chain rule. Implicit functions. Taylor series. Local extrema. Lagrange multiplies. Double and triple integrals and applications. Change of variables. Curves. Vector valued functions. Vector fields. The gradient, divergence, rotation, Laplace operators. Line integrals and applications. Conservative fields. Scalar and vector potential. Surfaces. Surface integrals and applications. Green, Gauss, Stokes theorems. Αpplications in electromagnetism.
Keywords
Multivariable calculus and vector calculus
Educational Material Types
- Notes
- Book
Course Organization
| Activities | Workload | ECTS | Individual | Teamwork | Erasmus |
|---|---|---|---|---|---|
| Lectures | 65 | 2.2 | ✓ | ||
| Reading Assigment | 50 | 1.7 | ✓ | ||
| Exams | 65 | 2.2 | ✓ | ||
| Total | 180 | 6 |
Student Assessment
Description
Written examination at the end of the semester.
Student Assessment methods
- Written Exam with Problem Solving (Summative)
- Written examination
Bibliography
Course Bibliography (Eudoxus)
1. Μ. Κωνσταντινίδου, Κ. Σεραφειμίδης, Λογισμός συναρτήσεων πολλών μεταβλητών και διανυσματική ανάλυση.
2. Θ. Ρασσιάς, Μαθηματικά ΙΙ.
Additional bibliography for study
1. M. Spiegel, Ανώτερα Μαθηματικά.
2. R.L. Finney, F.R. Giordano, M.D. Weir, Απειροστικός Λογισμός (Ενιαίος τόμος για
Λογισμό Ι και ΙΙ)
Last Update
12-02-2020
