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Bachelor's Degree
Environmental Engineering (Evening)
Course Structure Diagram with Credits
Engineering Mathematics Course Details
Course Information  

Course Title  Code  Semester  T + P  ECTS 
Engineering Mathematics  CEV201  3  3 + 0  4 
Prerequisites  None 
Language  Turkish 
Level  Bachelor's Degree 
Type  Compulsory 
Coordinator  Assoc.Prof. AYTEN GENÇ 
Instructors  Assoc.Prof. AYTEN GENÇ 
Goals  Students will learn the solution methods of ordinary differential equations which can be observed in mathematical modeling of engineering problems. 
Contents  Definition of differential equations,Types and classifications, Solutions and general and particular solutions, Some specific solution methods (variation of parameters, integral factors, ..) Second order diferential equations, Solutions of constant parameter second order diferential equations,Variation of constant methods, Variable coefficient differential equations, System of differential equations 
Work Placement(s)  Absent 
Number  Learning Outcomes 
1  Students can classify ordinary, partial, lineer and homogen differential equations. 
2  Students can solve first order differential equations by applying separation of variables, variation of parameters and integral factors and can evaluate general and particular solutions ofdifferential equations. 
3  Students can solve second order constant coefficient differential equations. 
4  Students can solve second order constant coefficient differential equations by applying undetermined coefficient methods. 
5  Students can solve second order differential equations by using the method of undetermined coefficients. 
Mode of Delivery  FacetoFace 
Planned Learning Activities & Teaching Methods  Lecture, Team work, questionanswer 
Assessment Methods  Midterm exam (11 week), Homework, Final exam 
Course Content  

Week  Topics  Study Materials 
1  Classification of differential equations: ordinary, partial, linear, homogen  Students will read pages 1321 of the textbook. 
2  General solutions of differential equations: boundary and initial conditions  Students will read pages 1321 of the textbook. 
3  Method of separation of variables for solving diferential equations  Students will read pages 1321 of the textbook 
4  Homogen differential equations and solutions  Students will read pages 3339 of the textbook 
5  Methods of variation of parameters for solving first order linear differental equations.  Students will read pages 2333 of the textbook 
6  Methods of u*v for solving first order linear differental equations.  Students will read pages 2333 of the textbook 
7  Methods of integration factor for solving first order linear differental equations and example problems  Students will read pages 4045 of the textbook 
8  Modeling examples from environmental engineering: filling of tanks, variations in pollutant concentrations with time.  Students will read pages 4045 of the textbook 
9  Bernoulli differential equations and its solution methods.  Students will read pages 125128 of the textbook 
10  Exact differential equations and solution methods  Students will read pages 4048 of the textbook 
11  Integration factor in solving nonexact differential equations.  Students will read pages 4048 of the textbook 
12  Second order constant coefficient differential equations  Students will read pages 102110 of the textbook 
13  Examples of second order constant coefficient differential equations  Students will read pages 102110 of the textbook 
14  Method of undetermined coefficients  Students will read pages 113120 of the textbook 

Sources  

Textbook  Akyıldız, E., Alpay Ş., Erkip, A., "Differential Equations", METU publications, 1990. 
Additional Resources  Kreyzig,E. "Advanced Engineering Mathematics", John and Willey Sons, 2008. 
Assessment System  Quantity  Percentage 

InTerm Studies  
Midterms  1  90 
Assignments  5  10 
InTerm Total  6  100 
Contribution of InTerm Studies to Overall  40  
Contribution of Final Exam to Overall  60  
Total  100 
Course's Contribution to PLO  

No  Key Learning Outcomes  Level  
1  2  3  4  5  
1  Engineering graduates with application skills of fundamental scientific knowledge in the engineering practice.  x  
2  Determines, defines, formulates and solves problems in engineering; fort his aim selects and applies the appropriate analytical models and modeling techniques.  
3  Analyses a system, system component or process and in order to meet the requirements, designs under realistic conditions; thus applies modern techniques of design.  x  
4  Selects and uses modern techniques and devices necessary for engineering applications.  
5  Designs and carries out experiments, collects data, analyzes and comments on the findings.  
6  Works effectively and individually on multi disciplinary teams.  x  
7  Accesses knowledge, and to do this, does research, uses databases and other data sources.  
8  Is aware of the importance of lifelong learning; follows advances in science and technology and updates his knowledge continuously.  x  
9  Uses communication and information technology at least at advanced level of European Computer Driving License  x  
10  Communicates effectively both orally and in writing; uses a foreign language at least at B1 level of European Language Portfolio.  
11  Communicates using technical drawing.  
12  Has the awareness of Professional ethics and responsibility.  x  
13  Has awareness about Project management, workplace applications, health of workers, environment and work security; and about legal consequences of engineering applications.  
14  Indicates that he is aware of the universal and social effects of engineering solutions and applications; is aware of entrepreneurship and innovativeness and is knowledgeable about the problems of the current age.  x  
15  Makes use of conceptual and applied knowledge in mathematics, science and in his own area in accordance for engineering solutions. 
ECTS ALLOCATED BASED ON STUDENT WORKLOAD BY THE COURSE DESCRIPTION  

Activities  Quantity  Duration (Hour)  Total Work Load (h) 
Course Duration  14  3  42 
Hours for offtheclassroom study (Prestudy, practice)  12  3  36 
Assignments  5  5  25 
Midterms  1  3  3 
Final examination  1  3  3 
Total Work Load (h)  109  
Total Work Load / 30 (h)  3.63  
ECTS Credit of the Course  4 