-W.E. Boyce, R.C. DiPrima, D.B. Meade, Boyce’s Elementary Differential Equations and Boundary Value Problems, 11th Edition, John Wiley & Sons, Inc., 2017
Other Sources
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Course Schedules
Week
Contents
Learning Methods
1. Week
Introduction; Classification of Differential Equations, First Order Differential Equations, Linear Equations; Method of Integrating Factors
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
8. Week
The Laplace Transform; Definition of the Laplace Transform; Solution of Initial Value Problems
Lecture and applications - Midterm Exam
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
16. Week
17. Week
Assessments
Evaluation tools
Quantity
Weight(%)
Midterm(s)
1
40
Final Exam
1
60
Program Outcomes
PO-1
Adequate knowledge in mathematics, science and engineering subjects pertaining to the relevant discipline; ability to use theoretical and applied knowledge in these areas in the solution of complex engineering problems.
PO-2
Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO-3
Ability to design a complex systemi process, device or product under realistic constraints and conditions, in such a way as to meet the desired results; ability to apply modern design methods for this purpose.
PO-4
Ability to select and use modern techniques and tools needed for analyzing and Solving complex problems encountered in engineering practice; ability to employ information technologies effectively.
PO-5
Ability to design and conduct experiments, gather data, analyze and interpret results for investing complex engineering problems or discipline specific research questions.
PO-6
Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7
Ability to communicate effectivley, both orally and in writing; knowledge of a minimum of one foreign language; ability to write effective reports and comprehend written reports, prepare design and production reports, make effective presentations, and give and receive clear and intelligible instruction.
PO-8
Awareness 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
Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
PO-10
Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
PO-11
Knowledge about the global and social effects of engineering practices on health, environment, and safety, and contemporary issues of the century reflected into the field of engineering; awareness of the legal consequences of engineering solutions.
Learning Outcomes
LO-1
Understands the solutions of some types of differential equations and identifies the classification of differential equations. (KOWLEDGE)
LO-2
Express linear equations, integration factor, seperable differential equations, exact differential equation and the method of integration factor. (KOWLEDGE)
LO-3
Understands the Eulers method and interprets the Existence and Uniqueness Theorem. (KOWLEDGE)
LO-4
Understands the homogenuous equations with constant coefficeients and express the solutions of linear homogenuous equations by using the Wronskian. (KOWLEDGE)
LO-5
Describes complex roots and repeated roots of the characterictic equation and interprets the order reducing method. (KOWLEDGE)
LO-6
Understands the non-homogenuous differential equations, the method of undetermined coefficients and the method of variation of parameters. (KOWLEDGE)
LO-7
Understands the general theory of high-order differential equations. (KOWLEDGE)
LO-8
Understands the series solutions near an ordinary point and applies it to Euler equations. Express regular singular points. (KOWLEDGE)
LO-9
Understands the series solutions near a regular singular point. (KOWLEDGE)
LO-10
Express the Laplace transform and explains the solutions of initial value problems. (KOWLEDGE)
LO-11
Explains the fundamental theory of first order linear differential equations, understands systems of homogenuous linear differential equations and applies comlex eigenvalues. (KOWLEDGE)
LO-12
Understands the fundamental matrices, repeted eigenvalues and systems of non-homogenuous linear differential equations. (KOWLEDGE)
