Course Name  Introduction to Differential Equations II 
Code  Semester  Theory (hour/week)  Application/Lab (hour/week)  Local Credits  ECTS 

MATH 208  Spring  2  2  3  6 
Prerequisites 
 
Course Language  English  
Course Type  Required  
Course Level  First Cycle  
Mode of Delivery    
Teaching Methods and Techniques of the Course  
Course Coordinator    
Course Lecturer(s)  
Assistant(s)   
Course Objectives  This course aims to consider partial differential equations which are a type of differential equation that is, a relation involving an unknown function (or functions) of several independent variables and its (or their) partial derivatives with respect to those variables. Partial differential equations are used to formulate, and thus aid the solution of problems involving functions of several variables; such as the propagation of sound or heat, electrostatics, electrodynamics, fluid flow, and elasticity. Seemingly distinct physical phenomena may have identical mathematical formulations, and thus be governed by the same underlying dynamic. In this course how to model these physical phenomena and the solution methods for these models will be taught. 
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. 
 Core Courses  X 
Major Area Courses  
Supportive Courses  
Media and Managment Skills Courses  
Transferable Skill Courses 
Week  Subjects  Required Materials 
1  Differential equations with two independent variables. Classification of partial differential equations of the second order. Canonical forms of linear equations with constant coefficients.  “Equations of Mathematical Physics” by A.N. Tikhonov, A.A. Samarskii, Dover. Section 1.1, 1.2, 1.3. 
2  A Model for Heat Flow. Solution by method of separation of variables.  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.1, 10.2. 
3  Fourier Series for 2pi periodic functions. Convergence of Fourier Series. Pointwise convergence of Fourier Series. Differentiation and Integration of Fourier Series.  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.3. 
4  Fourier Cosine and Sine Series.  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.4. 
5  Heat Equation. Solution by separation of variables. Existence and Uniqueness of Solutions.  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.5. 
6  The wave equation. Solution by seperation of variables. Existence and Uniqueness of Solutions.  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.6. 
7  The Laplace's equation in rectangular coordinates. Solution by separation of variables. Existence and Uniqueness of Solutions.  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.7. 
8  Bessel’s Equation and Bessel’s Function.  “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 4.7. 
9  Solution of Bessel’s Equation  “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 4.8. 
10  Laplace’s equation in polar coordinates and its solution by the method of separation of variables.  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. Section 10.7. 
11  Legendre’s Differential Equation.  “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 5.5. 
12  Legendre Polynomials and Legendre Series Expansions.  “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 5.6. 
13  Associated Legendre Functions and Series Expansions.  “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 5.7. 
14  SturmLiouville Theory  “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. Section 6.1, 6.2. 
15  Review for Final Exam  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. 
16  Review of the Semester  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. 
Course Notes/Textbooks  “Fundamentals of Differential Equations and Boundary Value Problems” by Nagle, Saff, Snider, 6th Edition, Pearson. “Partial Differential Equations with Fourier Series and Boundary Value Problems”by Nakhle H. Asmar, Pearson International Edition. 
Suggested Readings/Materials  None 
Semester Activities  Number  Weigthing 
Participation  
Laboratory / Application  
Field Work  
Quizzes / Studio Critiques  
Portfolio  
Homework / Assignments  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterm  2  60 
Final Exam  1  40 
Total 
Weighting of Semester Activities on the Final Grade  2  60 
Weighting of EndofSemester Activities on the Final Grade  1  40 
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  15  3  
Field Work  
Quizzes / Studio Critiques  
Portfolio  
Homework / Assignments  
Presentation / Jury  
Project  
Seminar / Workshop  
Oral Exam  
Midterms  2  15  
Final Exams  1  26  
Total  165 
#  Program Competencies/Outcomes  * Contribution Level  
1  2  3  4  5  
1  To have a grasp of basic mathematics, applied mathematics and theories and applications of statistics.  X  
2  To be able to use theoretical and applied knowledge acquired in the advanced fields of mathematics and statistics,  X  
3  To be able to define and analyze problems and to find solutions based on scientific methods,  X  
4  To be able to apply mathematics and statistics in real life with interdisciplinary approach and to discover their potentials,  X  
5  To be able to acquire necessary information and to make modeling in any field that mathematics is used and to improve herself/himself,  X  
6  To be able to criticize and renew her/his own models and solutions,  X  
7  To be able to tell theoretical and technical information easily to both experts in detail and nonexperts in basic and comprehensible way,  X  
8  To be able to use international resources in English and in a second foreign language from the European Language Portfolio (at the level of B1) effectively and to keep knowledge uptodate, to communicate comfortably with colleagues from Turkey and other countries, to follow periodic literature,  X  
9  To be familiar with computer programs used in the fields of mathematics and statistics and to be able to use at least one of them effectively at the European Computer Driving Licence Advanced Level,  
10  To be able to behave in accordance with social, scientific and ethical values in each step of the projects involved and to be able to introduce and apply projects in terms of civic engagement,  X  
11  To be able to evaluate all processes effectively and to have enough awareness about quality management by being conscious and having intellectual background in the universal sense,  
12  By having a way of abstract thinking, to be able to connect concrete events and to transfer solutions, to be able to design experiments, collect data, and analyze results by scientific methods and to interfere,  X  
13  To be able to continue lifelong learning by renewing the knowledge, the abilities and the compentencies which have been developed during the program, and being conscious about lifelong learning,  
14  To be able to adapt and transfer the knowledge gained in the areas of mathematics and statistics to the level of secondary school,  
15  To be able to conduct a research either as an individual or as a team member, and to be effective in each related step of the project, to take role in the decision process, to plan and manage the project by using time effectively. 
*1 Lowest, 2 Low, 3 Average, 4 High, 5 Highest