• Basic information
• Learning outcomes
• Contents
• Assessment
• Workload

Learning outcomes

Upon successful completion of this course, students will be able to:

1. Classify differential equations

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
   3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

   Method of assessment

   1. Written exam
   2. Homework assignment
2. To solve first and higher order differential equations and systems of linear differential equations

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
   3. Describing, formulating, and analyzing real-life problems using mathematical and statistical techniques.
   4. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

   Method of assessment

   1. Written exam
   2. Homework assignment
3. To solve the differential equations by applying Laplace transform

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
   3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

   Method of assessment

   1. Written exam
   2. Homework assignment
4. To solve differential equations with variable coefficients

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
   3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.

   Method of assessment

   1. Written exam
   2. Homework assignment
5. Power series solutions of differential equations

   Contribution to Program Outcomes

   1. Having the knowledge about the scope, applications, history, problems, and methodology of mathematics that are useful to humanity both as a scientific and as an intellectual discipline.
   2. Communicating between mathematics and other disciplines, and building mathematical models for interdisciplinary problems.
   3. Having improved abilities in mathematics communications, problem-solving, and brainstorming skills.
   4. Using technology as an efficient tool to understand mathematics and apply it.

   Method of assessment

   1. Written exam
   2. Homework assignment

Contents
Week 1:	Basic definitions. Separable Equations and Equations Reducible to This Form
Week 2:	Linear Equations, Bernoulli and Riccati Equations
Week 3:	Exact Differential Equations and Integrating Factors Special Integrating Factors
Week 4:	Problems in Mechanics and Physics Rate Problems
Week 5:	The formulation of initial value problem (Cauchy problem) The Fundamental Existence and Uniqueness Theorem
Week 6:	Basic Theory of High Order Linear Differential Equations Homogeneous Linear Equation, The system of fundamental solutions, Wronskian and Abel’s Theorem. The Homogeneous Linear Equation with Constant Coefficients
Week 7:	The Method of Undetermined Coefficients, Variation of Parameters
Week 8:	The Cauchy-Euler Equation The Linear Equation with Variable Coefficients, Reduction of Order
Week 9:	Power Series Solutions About an Ordinary Point Solutions About Singular Points
Week 10:	Mid-term examination The Method of Frobenius Bessel’s Equation and Bessel Functions
Week 11:	Definition, Existence, and Basic Properties of the Laplace Transform The Inverse Transform
Week 12:	The Convolution Laplace Transform Solution of Linear Differential Equations with Constant Coefficients
Week 13:	Homogeneous Linear Systems with Constant Coefficients (Three cases: Distinct Real Eigenvalues, Repetated Real Eigenvalues and Complex Eigenvalues)
Week 14:	Variation of Parameters for Nonhomogeneous Systems
Week 15*:	-
Week 16*:	Final exam
Textbooks and materials:	Diferansiyel Denklemler Ders Notları GYTE Yayınları (2001) Alinur Büyükaksoy ve Gökhan Uzgören
Recommended readings:	Shepley L. Ross, Differential Equations, 3rd Ed., Wiley (2007). W.E. Boyce and R.C DiPrima, Elementary Differential Equations and Boundary Value Problems, John Willey and Sons Inc. 9th Edition (2009).
	* Between 15th and 16th weeks is there a free week for students to prepare for final exam.

Assessment
Method of assessment	Week number	Weight (%)
Mid-terms:	6-12	40
Other in-term studies:		0
Project:		0
Homework:	4,10	10
Quiz:		0
Final exam:	16	50
	Total weight:	(%)

Workload
Activity	Duration (Hours per week)	Total number of weeks	Total hours in term
Courses (Face-to-face teaching):	3	14
Own studies outside class:	2	14
Practice, Recitation:	1	14
Homework:	5	4
Term project:	0	0
Term project presentation:	0	0
Quiz:	0	0
Own study for mid-term exam:	5	1
Mid-term:	2	1
Personal studies for final exam:	10	1
Final exam:	2	1
		Total workload:
		Total ECTS credits:	*
	* ECTS credit is calculated by dividing total workload by 25. (1 ECTS = 25 work hours)