W.E. Boyce, R.C. DiPrima, Elementer Diferansiyel Denklemler ve Sınır Değer Problemleri, Çev., M. Uğuz, Ç. Ürtiş, 10. Baskıdan Çeviri, Palme Yayıncılık, 2016.
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Course Schedules
Week
Contents
Learning Methods
1. Week
Introduction; Classification of Differential Equations, Linear Equations; Method of Integrating Factors; Variation of Parameters
Lecture and applications
2. Week
Separable Differential Equations; Homogeneous Equations; Exact Equations and Integrating Factors; The Existence and Uniqueness Theorem
Lecture and applications
3. Week
Second-Order Linear Differential Equations; Homogeneous Equations with Constant Coefficients, Solutions of Linear Homogeneous Equations; the Wronskian
Lecture and applications
4. Week
Complex Roots of the Characteristic Equation; Repeated Roots; Reduction of Order
Lecture and applications
5. Week
Nonhomogeneous Equations; Method of Undetermined Coefficients, Variation of Parameters
Lecture and applications
6. Week
Higher-Order Linear Differential Equations; General Theory of nth Order Linear Equations; Homogeneous Equations with Constant Coefficients
Lecture and applications
7. Week
The Method of Undetermined Coefficients; The Method of Variation of Parameters
Lecture and applications - Midterm Exam
8. Week
The Laplace Transform; Definition of the Laplace Transform; Solution of Initial Value Problems
Lecture and applications
9. Week
System of First-Order Linear Equations; Review of Matrices; Systems of Linear Algebraic Equations; Linear Independence, Eigenvalues, Eigenvectors
Lecture and applications
10. Week
Basic Theory of Systems of First Order Linear Equations; Homogeneous Linear Systems with Constant Coefficients; Complex Eigenvalues
Lecture and applications
11. Week
Fundamental Matrices, Repeated Eigenvalues, Nonhomogeneous Linear Systems
Lecture and applications
12. Week
Series Solution of Second-Order Linear Equations; Series Solutions Near an Ordinary Point
Lecture and applications
13. Week
Euler Equations; Regular Singular Points
Lecture and applications
14. Week
Series Solutions Near a Regular Singular Point
Lecture and applications
15. Week
Final Exam
Exam
16. Week
Final Exam
Exam
17. Week
Final Exam
Exam
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
60
Final Exam
1
40
Program Outcomes
PO-1
Interpreting advanced theoretical and applied knowledge in Mathematics and Computer Science.
PO-2
Critiquing and evaluating data by implementing the acquired knowledge and skills in Mathematics and Computer Science.
PO-3
Recognizing, describing, and analyzing problems in Mathematics and Computer Science; producing solution proposals based on research and evidence.
PO-4
Understanding the operating logic of computer and recognizing computational-based thinking using mathematics as a discipline.
PO-5
Collaborating as a team-member, as well as individually, to produce solutions to problems in Mathematics and Computer Science.
PO-6
Communicating in a foreign language, and interpreting oral and written communicational abilities in Turkish.
PO-7
Using time effectively in inventing solutions by implementing analytical thinking.
PO-8
Understanding professional ethics and responsibilities.
PO-9
Having the ability to behave independently, to take initiative, and to be creative.
PO-10
Understanding the importance of lifelong learning and developing professional skills continuously.
PO-11
Using professional knowledge for the benefit of the society.
Learning Outcomes
LO-1
Understands the solutions of some types of differential equations and identifies the classification of differential equations.
LO-2
Express linear equations, integration factor, seperable differential equations, exact differential equation and the method of integration factor
LO-3
Understands the Eulers method and interprets the Existence and Uniqueness Theorem
LO-4
Understands the homogenuous equations with constant coefficeients and express the solutions of linear homogenuous equations by using the Wronskian.
LO-5
Describes complex roots and repeated roots of the characterictic equation and interprets the order reducing method
LO-6
Understands the non-homogenuous differential equations, the method of undetermined coefficients and the method of variation of parameters
LO-7
Understands the general theory of high-order differential equations
LO-8
Understands the series solutions near an ordinary point and applies it to Euler equations. Express regular singular points.
LO-9
Understands the series solutions near a regular singular point
LO-10
Express the Laplace transform and explains the solutions of initial value problems
LO-11
Explains the fundamental theory of first order linear differential equations, understands systems of homogenuous linear differential equations and applies comlex eigenvalues.
LO-12
Understands the fundamental matrices, repeted eigenvalues and systems of non-homogenuous linear differential equations.
