Semester 2

Course: Mathematical Analysis II



Course Code: ΜΚ8
Course Level: Undergratuate
Obligatory/Elective: Obligatory
Semester: 2
Division: Main Course
Group: Main Course
ECTS Credits: 5
Hours Per Week: 4
Website: eclass.uowm.gr/courses/HMMY119/
Language: Greek
Content:

The ℝn space. Quadratic surfaces. Real functions of several variables. Partial derivatives. Chain differentiation. Directional derivative. Extreme values. Taylor series. Double integrals. Triple integrals. Vector functions. Curves. Line integrals. Differentiation of scalar and vector fields. Conservative fields. Green’s theorem. Surface integrals. Gauss και Stokes theorems.

Learning Outcomes:

Upon successful completion of this course, students will be able:

  • to differentiate variables of several functions,
  • to use cylindrical and spherical coordinates,
  • to find extreme values (free/constraint) and saddle points,
  • to linearize functions and find tangent planes,
  • to perform double and triple integration,
  • to manipulate vectors,
  • to differentiate vector functions,
  • to detect irrotational and solenoidal fields,
  • to determine potentials for conservative fields,
  • to parametrically describe curves and surfaces,
  • to calculate line integrals and fluxes through surfaces of vector fields,
  • to use Green’s, Gauss, και Stokes theorems.
Pre-requirements:

Elements of the following course are required: Mathematical Analysis Ι

Teaching Methods:
Method Description Semester workload
Lectures 26
Problems solving in class 26
Homework-study 73
Total 125
Validation:

Written intermediate exam (25%), written final exam (75%)

Suggested Books:
  1. J. Marsden, A. Tromba, Διανυσματικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης, 2010. 
  2. R. L. Finney, M. D. Weir, F. R. Giordano, Απειροστικός  Λογισμός,  Πανεπιστημιακές Εκδόσεις Κρήτης, 2012. 
  3. Κωνσταντινίδου Μαρία, Σεραφειμίδης Κάρολος, Λογισμός συναρτήσεων  πολλών μεταβλητών και διανυσματική ανάλυση, Εκδότης «σοφία», 2012. 
  4. Φιλιππάκης Ε. Μιχαήλ, Εφαρμοσμένη Ανάλυση και Θεωρία Fourier, ΤΣΟΤΡΑΣ ΑΝ. ΑΘΑΝΑΣΙΟΣ, Έκδοση: 2η/2017. 
  5. Παπασχοινόπουλος Γ., Σχοινάς Χ., Μυλωνάς Ν., Λογισμός Συναρτήσεων Πολλών Μεταβλητών και Εσαγωγή στις Διαφορικές Εξισώσεις, ΕΚΔΟΣΕΙΣ Α. ΤΖΙΟΛΑ & ΥΙΟΙ Α.Ε., Έκδοση: 1η/2016.
  6. Θ. Ρασσιάς, Μαθηματικά ΙΙ, β΄ έκδοση, ΤΣΟΤΡΑΣ ΑΝ. ΑΘΑΝΑΣΙΟΣ, 2017. 
  7. T. M. Apostol, Calculus Vol. II, John Wiley & Sons, 1969. 
  8. Tang, Kwong‐Tin, Mathematical Methods for Engineers and Scientists 2 [electronic resource], Heal‐Link/Σύνδεσμος Ελληνικών Ακαδημαϊκών Βιβλιοθηκών. 
Lecturer: Bisbas Antonis