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Contents
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| Week 1: |
Improper Integrals; Definition of Laplace Transforms; |
| Week 2: |
Properties of Laplace Transforms; Inverse Laplace Transforms; |
| Week 3: |
Convolution and the Unit Step Function; Solution of Linear Differential Equations with Constant Coefficients by Laplace Transforms; |
| Week 4: |
Solution of systems of LDEs with Constant Coefficient by Laplace Transforms. |
| Week 5: |
Linear differential equations with variable coefficients: Change of Dependent Variable; Reduction of Order; Reduction to the Canonical Form; Change of Independent Variable; Methods Based on Factorization of the Operator.Nonlinear DEs of order two and higher: Without Dependent Variable; Without Independent Variable; Homogeneous Eqs., Total Deqs; Sarrus Method; |
| Week 6: |
Midterm exam I |
| Week 7: |
Variation of parameters.Integration in series: Analytic Functions; Ordinary and Singular Points; Power-Series Solution about an Ordinary Point; |
| Week 8: |
Regular Singular Points and the Method of Frobenius; The Expansion for Large Values of x.The Legendre, Bessel and Hypergeometric equations: Elementary and Transcendental Functions; The Legendre Equation; The Bessel Equation; The Hypergeometric Equation.Boundary value problems: Initial Value Problems; Existence and Uniqueness Theorems; Second Order Boundary Value Problems; Uniqueness of Solutions; |
| Week 9: |
Eigenvalue Problems; Sturm-Liouville Problems; Properties of Sturm-Liouville Problems; |
| Week 10: |
Systems of linear first order differential equations: Linear Systems of ODEs; Homogeneous LS with Constant Coefficients; Distinct Real Eigenvalue; |
| Week 11: |
Repeated Eigenvalue, Complex Eigenvalue; Nonhomogeneous Linear Systems; Variation of Parameters; |
| Week 12: |
Midterm exam II |
| Week 13: |
Linear and nonlinear method of variation of parameters. Theory of differential and integral inequalities; |
| Week 14: |
Qualitative and quantitative theory; |
| Week 15*: |
Basic stability theory and Lyapunovs second method;
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| Week 16*: |
Final exam |
| Textbooks and materials: |
Diferansiyel Denklemler Teorisi(E. Hasonov, G. Uzgören, İ. A. Büyükaksoy).
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| Recommended readings: |
Differential Equations with BVP(D.G, Zill,M.R,Cullen)
Ordinary Differential Equations(V. Lakshmikantham,V. Raghavendra).
Nonlinear Variation of Parameters for Dynamical Systems(S.G., Deo, V. Lakshmikantham)
Stability Analysis of Dynamical Systems (V.Lakshmikantham)
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* Between 15th and 16th weeks is there a free week for students to prepare for final exam.
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