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Students should use
ODTU-Class
The table below is a rough guideline for the content of course lectures. Professors may reorder their lectures as necessary/desired. Section and page numbers below are from the textbook, Elementary Differential Equations and Boundary Value Problems, Boyce and DiPrima, 9th ed., 2010.
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Week 1:
Jun.24-28 |
1 |
Introduction, Directional Fields Chapter 2. First Order Differential Equations §2.2: Separable equations (also homogeneous equations - see p49 #30). |
| 2 |
§2.1: Linear equations; Method of integrating factors. §2.3: Modeling with first order equations (tank problems). |
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| 3 |
§2.4: Differences between linear and nonlinear equations (existence and uniqueness theorems). |
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| 4 |
§2.6: Exact equations and integrating factors. |
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| 5 |
Chapter 7. Systems of First Order Linear Equations §7.1: Introduction. §7.2: Review of matrices. |
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Week 2:
Jul.1-5 |
6 |
§7.3: Systems of linear algebraic equations; Linear independence, eigenvalues, eigenvectors. |
| Short Exam 1: 02.07.13, 17:40-18:40 | ||
| 7 |
§7.4: Basic theory of systems of first order linear equations. §7.5: Homogeneous linear systems with constant coefficients. |
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| 8 |
§7.5: Homogeneous linear systems with constant coefficients. §7.6: Complex eigenvalues. |
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| 9 |
§7.7: Fundamental matrices. |
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| 10 |
§7.8: Repeated eigenvalues. §7.9: Nonhomogeneous linear systems (variation of parameters only). |
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Week 3:
Jul.8-12 |
11 |
Chapter 4. Higher Order Linear Equations §4.1: General theory of nth order linear equations. |
| 12 |
§4.2: Homogeneous equations with constant coefficients. |
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| 13 |
Chapter 3. Second Order Linear Equations §3.2: Fundamental solutions of linear homogeneous equations. |
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| 14 |
§3.3: Linear independence and the Wronskian. §3.4: Complex roots of the characteristic equation. |
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| 15 |
§3.5: Repeated roots; Reduction of order. |
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Week 4:
Jul.15-19 |
16 |
§3.6: Nonhomogeneous equations; Method of undetermined coefficients. |
| Short Exam 2: 16.07.13, 17:40-18:40 | ||
| 17 |
§4.3: The method of undetermined coefficients. |
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| 18 |
§3.7: Variation of parameters. |
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| 19 |
§3.8: Mechanical and electrical vibrations. |
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| 20 |
§3.9: Forced Vibrations. |
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Week 5:
Jul.22-26 |
21 |
Chapter 6. The Laplace Transform §6.1: Definition of the Laplace transform. |
| Short Exam 3: 23.07.13, 17:40-18:40 | ||
| 22 |
§6.2: Solution of initial value problems. §6.3: Step functions. |
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| 23 |
§6.4: Differential equations with discontinuous forcing functions. |
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| 24 |
§6.5: Impulse functions. §6.6: The convolution integral. |
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| 25 |
Chapter 10. Partial Differential Equations and Fourier Series §10.A: Derivation of the Heat Conduction Equation. §10.1: Two-point boundary value problems. |
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Week 6:
Jul.29-Aug.3 |
26 |
§10.2: Fourier series. §10.3: The Fourier convergence theorem (briefly). |
| 27 |
§10.4: Even and odd functions. |
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| 28 |
§10.5: Separation of variables, heat conduction in a rod. |
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| 29 | ||
| FINAL EXAM | ||