At the end of this course the student should be able to:
- Have a good understanding of the knowledge of the basic applied mathematics for engineers, within the wide area of the mathematical physics, which is adequate to his/her science.
- Know the new notions in the form of definitions and theorems that concern the basic contents of the course "Applied Mathematics", in order to be able to apply them.
- Combine and make worthy of the knowledge that he/she acquired to other fields of the theoretical and applied mathematics, in which certain notions and principles of the present course are necessary and useful.
At the end of the course the student will have further developed the following skills and competences:
- Ability to demonstrate knowledge and understanding of essential concepts, principles and applications that are related to the applied mathematics and the necessary tools for the solution of problems of technological interest.
- Ability to apply such knowledge to the solution of problems in other fields of the wide conception of theoretical and applied mathematics, related to the science of Chemical Engineering, or to the solution of multidisciplinary problems.
- Study skills needed for continuing profession development.
There are no prerequisite courses. It is, however, recommended that students should have the basic knowledge of the differential and integral calculus of one and many variables, of the vectors analysis, as well as of the linear algebra, which they were taught to the corresponding undergraduate courses "Single Variable Calculus and Linear Algebra" and "Multivariable Calculus and Vector Analysis". Moreover, it is requisite the basic knowledge in subjects of ordinary and partial differential equations, which they were taught to the corresponding undergraduate courses "Ordinary Differential Equations" and "Partial Differential Equations".
Mathematical physics, analytical and hybrid mathematical methods of applied sciences, modeling of physical problems. Partial differential equations with boundary and initial value problems, theory and main applications to:
– Fluid dynamics and creeping hydrodynamics.
– Magnetic fluids with conductive properties.
– Electromagnetism and low frequency scattering.
– Electric and magnetic activity of the brain.
– Cancer tumour growth.
– Wave propagation in elasticity.
– Plasma theory and mathematical prototyping.
– Ellipsoidal coordinate system and applications.
Interrelation with physics and mechanics, theoretical background and basic problems solution techniques.
- J. Hass, C. Heil and M.D. Weir, "Thomas Infinitesimal Calculus" (translation Y. Kotsopoulos), Institute of Technology & Research – University of Crete Publications, Herakleion, 2018 (Eudoxos / code 77107082).
- G. Strang, "Linear Algebra and Applications" (translation P. Pamfilos), Institute of Technology & Research – University of Crete Publications, Herakleion, 2009 (Eudoxos / code 204).
- S. Trachanas, "Ordinary Differential Equations", Institute of Technology & Research – University of Crete Publications, Herakleion, 2008 (Eudoxos / code 222).
- S. Trachanas, "Partial Differential Equations", Institute of Technology & Research – University of Crete Publications, Herakleion, 2009 (Eudoxos / code 228).
Teaching with solving exercises (3 hours/week) and personal study.
Written – oral examination or / and exercises series.