| Course Code: |
2101C |
| Course Type: |
Theory |
| Course Category: |
Core Module |
| Hours per Week:: |
4 |
| Credit Units: |
6 |
| Semester: |
2 |
Aims
and Scope
To
teach students the
basic concepts and essential techniques in Ordinary
Differential Equations, and Vector and Multivariable Calculus.
Course Description
Ordinary Differential
Equations, Laplace transform and its applications, Vectors and the geometry of
Space, Vector functions, Partial derivatives, Multiple integrals, Vector
Calculus.
Learning Objectives
Upon successful completion of this
course students are expected to:
·
Be
able to solve linear first and second order differential equations, and apply
the Laplace transform in order to solve differential equations. Follow basic
vector analysis in three-dimensional space. Be able to compute partial derivatives
and multiple integrals of functions of two and three variables.
·
Have
acquired a solid mathematical background on the topics and the techniques
discussed in this course, and be able to use them in order to solve applied
problems.
·
Enhance
their research and analytical thinking abilities.
Bibliography
Ελληνική:
1. R.L. Finney, F.R. Giordano, M.D. Weir, Απειροστικός
Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 2012.
2. Μ. Γλαμπεδάκης, Α.
Γλαμπεδάκης, Μαθηματική Ανάλυση ΙΙ, Εκδ. Ίων, 2012.
3. Α.
Μπράτσος, Εφαρμοσμένα Μαθηματικά, Εκδόσεις Α. Σταμούλη, Αθήνα, 2002.
4. Ν.
Αλικάκος, Γ. Καλογερόπουλος, Συνήθεις Διαφορικές Εξισώσεις, Σύγχρονη Εκδοτική,
Αθήνα, 2003.
5. J.E. Marsden, A.J. Tromba,
Διανυσματικός Λογισμός, Πανεπιστημιακές Εκδόσεις Κρήτης, Ηράκλειο, 2012.
6. W.E. Boyce, R.C. DiPrima,
Στοιχειώδεις Διαφορικές Εξισώσεις και Προβλήματα Συνοριακών Τιμών,
Πανεπιστημιακές Εκδόσεις Ε.Μ.Π., 1999.
Ξενόγλωσση:
1.
G.B. Thomas, M.D. Weir, J. Hass,
Thomas' Calculus, 12th ed., Addison-Wesley, 2010.
2.
J. Stewart, Calculus, 6th
ed., Brooks/Cole, 2008.
3.
E. Kreyszig, Advanced Engineering
Mathematics, 10th ed., Wiley, 2011.
4.
J.D. Logan, A First Course in
Differential Equations, 2nd ed., Springer, 2011.
5.
K.A. Stroud, D.J. Booth, Engineering Mathematics, Industrial Press Inc., 2007.
5.
M.R. Boelkins, J.L. Goldberg, M.C. Potter, Differential Equations with Linear Algebra, Oxford University Press, 2009.
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