The aim of this course is to provide a perfect understanding of linear differential equations to the students as well as the ability to solve them.
Prerequisite(s)
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Corequisite(s)
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Special Requisite(s)
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Instructor(s)
Professor Remzi Tunç MISIRLIOĞLU, Assoc. Prof. Songül ESİN
Course Assistant(s)
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Schedule
Group A: Monday 13:00-14:30 / Wednesday 09:00-10:30
Group B: Monday 09:00-10:30 / Wednesday 11:00-12:30
Group C: Monday 11:00-12:30 / Wednesday 13:00-14:30
Office Hour(s)
Prof. dr. Remzi Tunç MISIRLIOĞLU: Friday 15:00-16:00
Associate Professor. Songul ESİN: Wednesday 09:30-10:30
Teaching Methods and Techniques
Lectures and Recitation
Principle Sources
W.E. Boyce and R.C. DiPrima, Elementary Differential Equations and Boundary Value Problems, 9th Edition, John Wiley & Sons, Inc., 2010
Other Sources
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Course Schedules
Week
Contents
Learning Methods
1. Week
Solutions of Some Differential Equations; Classification of Differential Equations
Lecture
2. Week
Separable Equations; Exact Equations and Integrating Factors
Lecture
3. Week
Linear Equations; The Existence and Uniquness Theorem
Lecture
4. Week
Homogeneous Equations with Constant Coefficients; Solutions of Linear Homogeneous Equations; the Wronskian
Lecture
5. Week
Complex Roots of the Characteristic Equation; Repeated Roots; Reduction of Order (Midterm Exam 1 - 09.03.2013, 14:00)
Lecture, Exam
6. Week
Nonhomogeneous Equations; Method of Undetermined Coefficients; Variation of Parameters; General Theory of nth Order Linear Equations
Lecture
7. Week
Homogeneous Equations with Constant Coefficients; The Method of Undetermined Coefficients; The Method of Variation of Parameters
Lecture
8. Week
Series Solutions Near an Ordinary Point; Euler Equations; Regular Singular Points
Lecture
9. Week
Series Solutions Near a Regular Singular Point, Part I
Lecture
10. Week
Series Solutions Near a Regular Singular Point, Part II (Midterm Exam 2 - 13.04.2013, 14:00)
Lecture, Exam
11. Week
Definition of the Laplace Transform; Solution of Initial Value Problems; Step Functions
Lecture
12. Week
Impulse Functions; The Convolution Integral
Lecture
13. Week
Basic Theory of Systems of First Order Linear Equations; Homogeneous Linear Systems with Constant Coefficients; Complex Eigenvalues
Lecture
14. Week
Fundamental Matrices; Repeated Eigenvalues; Nonhomogeneous Linear Systems
Lecture
15. Week
Final Exam Week
Final Exam
16. Week
Final Exam Week
Final Exam
17. Week
Final Exam Week
Final Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
2
60
Final Exam
1
40
Program Outcomes
PO-1
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied information in these areas to model and solve engineering problems.
PO-2
Ability to identify, formulate, and solve complex engineering problems; ability to select and apply proper analysis and modelling methods for this purpose.
PO-3
Ability to design a complex system, process, device or product under realistic constraints and conditions, in such a way so as to meet the desired result; ability to apply modern design methods for this purpose. (Realistic constraints and conditions may include factors such as economic and environmental issues, sustainability, manufacturability, ethics, health, safety issues, and social and political issues according to the nature of the design.)
PO-4
Ability to devise, select, and use modern techniques and tools needed for engineering practice; ability to employ information technologies effectively.
PO-5
Ability to design and conduct experiments, gather data, analyse and interpret results for investigating engineering problems.
PO-6
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7
Ability to communicate effectively, both orally and in writing; knowledge of a minimum of one foreign language.
PO-8
Recognition of the need for lifelong learning; ability to access information, to follow developments in science and technology, and to continue to educate him/herself.
PO-9
Awareness of professional and ethical responsibility.
PO-10
Information about business life practices such as project management, risk management, and change management; awareness of entrepreneurship, innovation, and sustainable development.
PO-11
Knowledge about contemporary issues and the global and societal effects of engineering practices on health, environment, and safety; awareness of the legal consequences of engineering solutions.
Learning Outcomes
LO-1
define differential equations and their classifications
LO-2
identify linear and nonlinear differential equations
LO-3
solve both homogeneous and nonhomogeneous linear differential equations
LO-4
apply linear differential equations theory on related engineering problems
LO-5
recognize linear differential equation systems and exponential matrices
LO-6
solve problems involving both homogeneous and nonhomogeneous linear differential equation systems
LO-7
define direct and inverse Laplace transform
LO-8
apply Laplace transform technique to linear differential equations and differential equation systems
LO-9
describe series solutions to linear differential equations with variable coefficients
LO-10
solve linear differential equations with variable coefficients by using Frobenius method
