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School of Chemical and Environmental Engineering

Now offering two distinct diplomas: Chemical Engineering and Environmental Engineering

Ordinary differential equations

1. COURSE INFORMATION:

SchoolEnvironmental Engineering
Course LevelUndergraduate
Course IDMATH 203Semester3rd
Course CategoryRequired
Course ModulesInstruction Hours per WeekECTS
Lectures3
Th=3, E=0, L=0
5
Course Type Scientific area
Prerequisites 
Instruction/Exam LanguageGreek
The course is offered to Erasmus studentsYes
Course URLhttps//www.eclass.tuc.gr/courses/MHPER310/   (in Greek)

 

2. LEARNING OUTCOMES

Learning Outcomes

In many problems / systems of everyday life we ​care about  the change of a quantity (variable) of our interest w.r.t. time (rate of change). In order to model (mathematically) and solve these problems we use differential equations. The role of d.e. is therefore a protagonist in many scientific fields, especially in engineering. The purpose of this undergraduate course is to introduce basic concepts and techniques to students in order to be able to solve ordinary differential equations. Furthermore, applications of d.e. are being presented in basic problems/fields of Mechanics, Electromagnetism, Environment and so on.

The aim of the course is also, to give the students the ability to use differential equations to model natural phenomena / situations, to be able to solve such equations and to interpret the solutions of the equations.

The course is addressed to the sophomore students of the School / Department of Environmental Engineering of the Technical University of Crete.
General Competencies/Skills
 
  • Work autonomously
  • Review, analyse and synthesise data and information, with the use of necessary technologies)
  • Team work
 

3. COURSE SYLLABUS

 
  • Introduction.
  • 1st  and 2nd order d.e.: separation of variables, homogenous, exact, Bernoulli, Ricati, Euler, integrating factors.
  • Newton's differential equation and applications in engineering problems.
  • Linear independence, Wronskian.
  • Linear differential equations with constant coefficients.
  • Laplace transform method.
  • Applications in Engineering and Electricity
  • 1st order systems with constant coefficients..
  • Power series method
 

4. INSTRUCTION and LEARNING METHODS - ASSESSMENT

Lecture MethodDirect (face to face)
Use of Information and Communication TechnologySpecialized software, Power point presentations, E-class support
Instruction OrganisationActivityWorkload per Semester
(hours)
- Lectures39
- Review exercises6
-Software applications6
- Autonomous study74
Course Total125

Assessment Method

Ι. Written final examination (100%).
  • Questions of theoretical knowledge.
  • Theoretical problems to be resolved.
II. “Bonus” exercises (10% in addition to the final exam).

OR

I. Midterm and final exam (100%=50%+50%)

II.“Bonus” exercises (10% in addition to the project grade).

5. RECOMMENDED READING

 
  • W. E. Boyce - R. C. Diprima, Elementary differential equations and boundary value problems,  1999, Ed. E.M.P. (in Greek)
  • Trahanas S., elementary differential equations,  2008, Ed C.U.P.. (in Greek)
  • Y.A.Cengel, W.J.Palm III, Differential equations for engineers and scientists, 2017,Ed Tziola. (in Greek)
  • E-class notes
 

6. INSTRUCTORS

Course Instructor: 
Lectures: 
Tutorial exercises: 
Laboratory Exercises: