# 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: 436
OrientationAttendance TypeSemesterYearECTS
CORECompulsory Course216

 Academic Year 2021 – 2022 Class Period Spring Faculty Instructors Nikolaos Atreas 5hrs Weekly Hours 5 Class ID 600198676

### 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 11:00 Building Πολυτεχνείο - πτέρυγα Γ (ΤΗΜΜΥ & Τοπογράφων Μηχ.) Floor Όροφος 1 Hall Α5 (7) Calendar Τετάρτη 14:00 έως 16:00 Building Πολυτεχνείο - κτίριο Α (Εδρών) Floor Υπόγειο 1 Hall ΜΙΚΡΟ ΑΜΦΙΘΕΑΤΡΟ ΠΟΛΥΤΕΧΝΙΚΗΣ (240) Calendar Πέμπτη 15:00 έως 18:00
Course Type 2021
General Foundation
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)
• 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
Lectures652.2
Exams802.7
Total1806
Student Assessment
Description
Written examination at the end of the semester.
Student Assessment methods
• Written Exam with Problem Solving (Formative, Summative)
• Written examination
Bibliography
Course Bibliography (Eudoxus)
1. Μ. Κωνσταντινίδου, Κ. Σεραφειμίδης, Λογισμός συναρτήσεων πολλών μεταβλητών και διανυσματική ανάλυση. 2. Θ. Ρασσιάς, Μαθηματικά ΙΙ.