Τμήμα Ωκεανογραφίας και Θαλασσίων Βιοεπιστημών

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Mathematics II
School:
Of the Environment
Academic Unit:
Department of Marine Sciences
Level of studies:
Undergraduate
Course Code:
191ΜΥ22Υ
Semester:
Β
Course Title:
Mathematics II
Credits
6
Course Type:
General background.
Prerequisite Courses:
There are no official prerequisites. However, Mathematics I (calculus of one variable) is an essential prerequisite for the course.
Language of Instruction and Examinations:
Greek
Is the course offered to Erasmus students:
Yes. In case of participation of Erasmus students, the course is offered in English.
  • (2) Learning Outcomes
  • Learning Outcomes

It is expected that students should learn the material presented in the Syllabus.

  • General Competences

The course aims to applications in oceanography. In particular, students should be able to understand the mathematical formalism of fluid mechanics.

  • (3) Syllabus

1st 2nd and 3nd week. Vector calculus, the space ℝ3, scalar product, exterior product, vector functions (curves), velocity as the derivative of a vector function.

4th week. Matrices and determinants.

5rd and 6th week. Functions of several variables (scalar fields), level sets, graph of a function of two variables, partial derivatives.

7th and 8th week. Gradient of a scalar field, properties of the gradient, vector fields, divergence and curl, vector identities.

9th week. Extrema.

10th week. Taylor’s theorem, Taylor’s series, Taylor’s theorem in many dimensions.

11th and 12th week. Linear spaces, subspaces, bases and dimension, linear systems, equation of the plane, geometric interpretation of linear systems. Linear maps.

13th week. Applications in geometry and physics.

  • (4) Teaching and Learning Methods - Evaluation
  • Delivery:

Face-to-face

  • Use of Information and Communication Technology:

The Calculus Laboratory aims in the acquaintance of students with MATHEMATICA.

  • Teaching Methods:
Activity Semester workload
Lectures/Turorials
50
Tutorials
10
Lectures
10
Independent study
67
Lectures-Seminars
10
Final exam
3
Course total
150
  • Student Performance Evaluation:

Final written examination.

Student’s papers are accessible to them. Students may ask detailed information about their evaluation.

  • (5) Attached Bibliography

– Suggested bibliography:

Class Notes: 140 pages (in Greek).

M.R. Spiegel, Ανώτερα Μαθηματικά, σειρά Schaum’s, β΄ έκδοση, εκδόσεις Τζιόλας.

R.L. Finney, M.D. Weir, F.R. Giordano, Απειροστικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης.

–Additional bibliography:

J.E. Marsden and A.J. Tromba, Διανυσματικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης.

H.M. Schey, Div, Grad, Curl, and All That: An Informal Text on Vector Calculus, (W.W. Norton and Company 2005).

Bachman, Advanced Calculus Demystified (McGraw-Hill 2007).