# Calculus II

 Title ΛΟΓΙΣΜΟΣ ΙΙ / Calculus II Code ΜΑ0102 Faculty Engineering School Electrical and Computer Engineering Cycle / Level 1st / Undergraduate Teaching Period Spring Coordinator Nikolaos Atreas Common No Status Active Course ID 20000613

 Academic Year 2018 – 2019 Class Period Spring Faculty Instructors Weekly Hours 6 Class ID 600135678
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 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).
Keywords
Multivariable calculus and vector calculus
Educational Material Types
• Notes
• Book
Course Organization
Lectures652.2
Exams652.2
Total1505
Student Assessment
Description
Written examination at the end of the semester.
Student Assessment methods
• Written Exam with Problem Solving (Summative)
Bibliography
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.
Last Update
27-02-2018