(hour/week) >
Prerequisites 
 
Course Language  English  
Course Type  Required  
Course Level  First Cycle  
Mode of Delivery    
Teaching Methods and Techniques of the Course  Problem Solving Case Study Q&A Simulation  
Course Coordinator    
Course Lecturer(s)  
Assistant(s) 
Course Objectives  This course includes classification, applications and solution methods of partial differential equations. Fourier series for periodic functions, solution of heat and wave equation by separation method, solution methods of Laplace equation in rectangular and polar coordinates are aimed. 
Learning Outcomes  The students who succeeded in this course;

Course Description  In this course basic concepts and classification of partial differential equations will be discussed. The heat, wave and Laplace equation will be given and the solution methods will be taught. 
Related Sustainable Development Goals  
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Major Area Courses  
Supportive Courses  
Media and Managment Skills Courses  
Transferable Skill Courses 
Week  Subjects  Required Materials 
1  Mathematical background for the study of partial differential equations  Erwin Kreyszig, “Advanced Engineering Mathematics”,10Th Edition, (John Wiley and Sons), Sections 9.5, 9.7, 9.8 
2  Description of partial differential equations. Classification and model definitions. First order partial differential equations  Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 1.1. to 1.7 
3  Modelling first order partial differential equations. Solving by the method of characteristics  Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 2.1. to 2.4 
4  Modelling continuity equation, wave equation and traffics flow and applications  Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), Sections 2.1. to 2.4 
5  Partial Laplace transform. Solving first order partial differential equations by partial Laplace transform.  “http://www.math.ttu.edu/~gilliam /ttu/s10/m3351_s10/c15_laplace_trans_pdes.pdf” Chapter 15 
6  Heat Equation. Solution by separation of variables. Existence and Uniqueness of Solutions.  Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.5. 
7  Heat and diffusion equations examples and interpretation of the solution results  Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.510.7 
8  Midterm Exam I  
9  The wave equation. Solution by seperation of variables. Existence and Uniqueness of Solutions.  Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.6. 
10  The Laplace's equation in rectangular coordinates. Solution by separation of variables. Existence and Uniqueness of Solutions.  Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.7. 
11  Laplace's equation in polar coordinates and its solution by the method of separation of variables.  Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), Section 10.7. 
12  Solving second order partial differential equations by partial Laplace transform.  “http://www.math.ttu.edu/~gilliam/ttu/s10/m3351_s10/c15_laplace_trans_pdes.pdf” Chapter 15 
13  Numerical solutions of heat equation  David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), Sections: 9.1,9.2 
14  Numerical solutions of wave equation  David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), Sections: 9.1,9.2 
15  Semester review  
16  Final exam 
Course Notes/Textbooks  Kent Nagle, Edward B. Saff and Arthur David Snider, “Fundamentals of Differential Equations and Boundary Value Problems” 6th Edition, (Pearson, 2011), ISBN13: 9780321747747. 
Suggested Readings/Materials  Yehuda Pinchover and Jacob Rubistein, “An Introduction to Partial Differential Equations”, (Cambridge University Press, 2005), ISBN13:9780521848862 Erwin Kreyszig, “Advanced Engineering Mathematics”,10Th Edition, (John Wiley and Sons), ISBN: 9780470458365 David R. Kincaid and E. Ward Cheney, “Numerical Analysis”, (Brooks/Cole, 1991), ISBN10: 0534130143 
Semester Activities  Number  Weigthing 
Participation  
Laboratory / Application  
Field Work  
Quizzes / Studio Critiques  
Portfolio  
Homework / Assignments  1  20 
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterm  1  30 
Final Exam  1  50 
Total 
Weighting of Semester Activities on the Final Grade  2  50 
Weighting of EndofSemester Activities on the Final Grade  1  50 
Total 
Semester Activities  Number  Duration (Hours)  Workload 

Course Hours (Including exam week: 16 x total hours)  16  4  64 
Laboratory / Application Hours (Including exam week: 16 x total hours)  16  
Study Hours Out of Class  14  3  42 
Field Work  
Quizzes / Studio Critiques  
Portfolio  
Homework / Assignments  1  10  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterms  1  14  
Final Exams  1  20  
Total  150 
#  Program Competencies/Outcomes  * Contribution Level  
1  2  3  4  5  
1  To be able master and use fundamental phenomenological and applied physical laws and applications,  X  
2  To be able to identify the problems, analyze them and produce solutions based on scientific method,  X  
3  To be able to collect necessary knowledge, able to model and selfimprove in almost any area where physics is applicable and able to criticize and reestablish his/her developed models and solutions,  X  
4  To be able to communicate his/her theoretical and technical knowledge both in detail to the experts and in a simple and understandable manner to the nonexperts comfortably,  
5  To be familiar with software used in area of physics extensively and able to actively use at least one of the advanced level programs in European Computer Usage License,  
6  To be able to develop and apply projects in accordance with sensitivities of society and behave according to societies, scientific and ethical values in every stage of the project that he/she is part in,  
7  To be able to evaluate every all stages effectively bestowed with universal knowledge and consciousness and has the necessary consciousness in the subject of quality governance,  
8  To be able to master abstract ideas, to be able to connect with concreate events and carry out solutions, devising experiments and collecting data, to be able to analyze and comment the results,  
9  To be able to refresh his/her gained knowledge and capabilities lifelong, have the consciousness to learn in his/her whole life,  
10  To be able to conduct a study both solo and in a group, to be effective actively in every all stages of independent study, join in decision making stage, able to plan and conduct using time effectively.  
11  To be able to collect data in the areas of Physics and communicate with colleagues in a foreign language ("European Language Portfolio Global Scale", Level B1).  
12  To be able to speak a second foreign at a medium level of fluency efficiently  
13  To be able to relate the knowledge accumulated throughout the human history to their field of expertise. 
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest