This page is for archival purposes only!
Students should use
ODTU-Class
There will be 28 lectures given by the instructors, each lasting 2 class hours. The actual timing of lectures may differ slightly from section to section because of university holidays, but the total number is the same for all sections.
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:
Sep.26-30 |
1 |
Chapter 1. Introduction §1.1: Some basic mathematical models; Direction fields. §1.3: Classification of differential equations. |
| 2 |
Chapter 2. First Order Differential Equations §2.1: Linear equations; Method of integrating factors. §2.2: Separable equations (also homogeneous equations - see p49 #30). |
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Week 2:
Oct.3-7 |
3 |
More examples of separable and linear equations §2.3: Modeling with first order equations (tank problems). |
| 4 |
§2.4: Differences between linear and nonlinear equations (existence and uniqueness theorems). §2.5: Autonomous equations and population dynamics (equilibrium solutions of autonomous equations). |
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Week 3:
Oct.10-14 |
5 |
§2.6: Exact equations and integrating factors. |
| 6 |
Chapter 3. Second Order Linear Equations §3.1: Homogeneous equations with constant coefficients. §3.2: Fundamental solutions of linear homogeneous equations; The Wronskian. |
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Week 4:
Oct.17-21 |
7 |
§3.2: The Wronskian (continued). §3.3: Complex roots of the characteristic equation. |
| 8 |
§3.4: Repeated roots; Reduction of order. §3.5: Nonhomogeneous equations; Method of undetermined coefficients. |
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Week 5:
Oct.24-28 |
9 |
§3.5: Undetermined coefficients (continued). §3.6: Variation of parameters. |
| 10 |
§3.7: Mechanical and electrical vibrations. |
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| MIDTERM EXAM 1 13:40-15:40 on Sunday, October 30 | ||
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Week 6:
Oct.31-Nov.4 |
11 |
§3.8: Forced vibrations. |
| 12 |
Chapter 4. Higher Order Linear Equations §4.1: General theory of nth order linear equations. §4.2: Homogeneous equations with constant coefficients. §4.3: The method of undetermined coefficients (reading assignment). |
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Week 7:
Nov.14-18 |
13 |
Chapter 6. The Laplace Transform §6.1: Definition of the Laplace transform. |
| 14 |
§6.2: Solution of initial value problems. |
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Week 8:
Nov.21-25 |
15 |
§6.3: Step functions. §6.4: Differential equations with discontinuous forcing functions. |
| 16 |
§6.5: Impulse functions. §6.6: The convolution integral. |
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Week 9:
Nov.28-Dec.2 |
17 |
Chapter 7. Systems of First Order Linear Equations §7.1: Introduction. §9.1: The phase plane: Linear systems. |
| 18 |
§7.2: Review of matrices. |
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| MIDTERM EXAM 2 13:40-15:40 on Saturday, December 3 | ||
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Week 10:
Dec.5-9 |
19 |
§7.2: Review of matrices (continued). §7.3: Systems of linear algebraic equations; Linear independence, eigenvalues, eigenvectors. |
| 20 |
§7.3: Linear independence, eigenvalues, eigenvectors (continued). §7.4: Basic theory of systems of first order linear equations. |
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Week 11:
Dec.12-16 |
21 |
§7.5: Homogeneous linear systems with constant coefficients. |
| 22 |
§7.6: Complex eigenvalues. §7.7: Fundamental matrices. |
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Week 12:
Dec.19-23 |
23 |
§7.8: Repeated eigenvalues. |
| 24 |
§7.9: Nonhomogeneous linear systems (variation of parameters only). |
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Week 13:
Dec.26-30 |
25 |
Chapter 10. Partial Differential Equations and Fourier Series §10.A: Derivation of the Heat Conduction Equation. §10.1: Two-point boundary value problems. |
| 26 |
§10.2: Fourier series. §10.3: The Fourier convergence theorem (briefly). |
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Week 14:
Jan.2-6 |
27 |
§10.4: Even and odd functions. |
| 28 |
§10.5: Separation of variables, heat conduction in a rod. |
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| FINAL EXAM 9:00-11:30 on Sunday, January 15 SZ-22, SZ-23, SZ-24, SZ-25 | ||