Calculus II

Course Information
TitleΛΟΓΙΣΜΟΣ ΙΙ / Calculus II
SchoolElectrical and Computer Engineering
Cycle / Level1st / Undergraduate
Teaching PeriodSpring
CoordinatorNikolaos Atreas
Course ID20000613

Class Information
Academic Year2018 – 2019
Class PeriodSpring
Faculty Instructors
Weekly Hours6
Class ID
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 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 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 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
  • Work in an interdisciplinary team
  • 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 (Μaxwell laws, Gauss low for electric flux, electric field calculation).
Multivariable calculus and vector calculus
Educational Material Types
  • Notes
  • Book
Course Organization
Reading Assigment200.7
Student Assessment
Written examination at the end of the semester.
Student Assessment methods
  • Written Exam with Problem Solving (Summative)
Course Bibliography (Eudoxus)
1. Φ.Ι. Ξένος, Λογισμός ΙΙ. 2. Μ. Κωνσταντινίδου, Κ. Σεραφειμίδης, Λογισμός συναρτήσεων πολλών μεταβλητών και διανυσματική ανάλυση. 3. Θ. Ρασσιάς, Μαθηματική Ανάλυση 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) 3. Τ. Rassias, Mathematical Αnalysis II.
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