Undergraduate
Faculty of Engineering and Architecture
Civil Engineering
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Differential Equations

Course CodeSemester Course Name LE/RC/LA Course Type Language of Instruction ECTS
MCB1005 4 Differential Equations 4/0/0 CC English 6
Course Goals
 Teaching differential equation techniques required for engineering problems.
Prerequisite(s) -
Corequisite(s) -
Special Requisite(s) -
Instructor(s) Professor SONGÜL ESİN, Professor R. TUNÇ MISIRLIOĞLU, Assist. Prof. Dr. GÜLDEN GÜN POLAT
Course Assistant(s) -
Schedule Section A: Monday 13:00-14:30, Wednesday 09:00-10:30; Şube B: Monday 09:00-10:30, Wednesday 11:00-12:30; Şube C: Monday 11:00-12:30, Wednesday 13:00-14:30;
Office Hour(s) Tunç Mısırlıoğlu: Friday 15:00-16:00, İKÜ-CATS; Songül Esin: Wednesday 15:00-16:00, İKÜ-CATS;
Teaching Methods and Techniques -Lecture and applications
Principle Sources -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 -
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-1Adequate 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-2Ability to formulate, and solve complex engineering problems; ability to select and apply proper analysis and modeling methods for this purpose.
PO-3Ability 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-4Ability 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-5Ability to design and conduct experiments, gather data, analyze and interpret results for investing complex engineering problems or discipline specific research questions.
PO-6Ability to work efficiently in intra-disciplinary and multi-disciplinary teams; ability to work individually.
PO-7Ability 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-8Awareness 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-9Knowledge on behavior according ethical principles, professional and ethical responsibility and standards used in engineering practices.
PO-10Knowledge about business life practices such as project management, risk management, and change management; awareness in entrepreneurship, innovation; knowledge about sustainable development.
PO-11Knowledge 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-1Understands the solutions of some types of differential equations and identifies the classification of differential equations. (KOWLEDGE)
LO-2Express linear equations, integration factor, seperable differential equations, exact differential equation and the method of integration factor. (KOWLEDGE)
LO-3Understands the Eulers method and interprets the Existence and Uniqueness Theorem. (KOWLEDGE)
LO-4Understands the homogenuous equations with constant coefficeients and express the solutions of linear homogenuous equations by using the Wronskian. (KOWLEDGE)
LO-5Describes complex roots and repeated roots of the characterictic equation and interprets the order reducing method. (KOWLEDGE)
LO-6Understands the non-homogenuous differential equations, the method of undetermined coefficients and the method of variation of parameters. (KOWLEDGE)
LO-7Understands the general theory of high-order differential equations. (KOWLEDGE)
LO-8Understands the series solutions near an ordinary point and applies it to Euler equations. Express regular singular points. (KOWLEDGE)
LO-9Understands the series solutions near a regular singular point. (KOWLEDGE)
LO-10Express the Laplace transform and explains the solutions of initial value problems. (KOWLEDGE)
LO-11Explains the fundamental theory of first order linear differential equations, understands systems of homogenuous linear differential equations and applies comlex eigenvalues. (KOWLEDGE)
LO-12Understands the fundamental matrices, repeted eigenvalues and systems of non-homogenuous linear differential equations. (KOWLEDGE)
Course Assessment Matrix:
Program Outcomes - Learning Outcomes Matrix
 PO 1PO 2PO 3PO 4PO 5PO 6PO 7PO 8PO 9PO 10PO 11