This page is for archival purposes only!
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.
|
Week 1:
Sept.22-26 |
1 |
Introduction, Directional Fields Chapter 2. First Order Differential Equations §2.2: Separable equations (also homogeneous equations - see #30 on page 49). |
| 2 |
§2.1: Linear equations; Method of integrating factors. |
|
|
Week 2:
Sept.29-Oct.3 |
3 |
§2.3: Modeling with first order equations (tank problems). |
| 4 |
§2.4: Differences between linear and nonlinear equations (existence and uniqueness theorems). §2.6: Exact equations and integrating factors. |
|
|
Week 3:
Oct.6-10 |
5 |
Chapter 7. Systems of First Order Linear Equations §7.1: Introduction. §7.2: Review of matrices. |
| 6 |
§7.3: Systems of linear algebraic equations; Linear independence, eigenvalues, eigenvectors. |
|
|
Week 4:
Oct.13-17 |
7 |
§7.4: Basic theory of systems of first order linear equations. §7.5: Homogeneous linear systems with constant coefficients. |
| 8 |
§7.5: Homogeneous linear systems with constant coefficients (continued). §7.6: Complex eigenvalues. |
|
|
Week 5:
Oct.20-24 |
9 |
§7.7: Fundamental matrices. |
| 10 |
§7.8: Repeated eigenvalues. §7.9: Nonhomogeneous linear systems (variation of parameters only). |
|
|
Week 6:
Oct.27-31 |
11 |
Chapter 4. Higher Order Linear Equations §4.1: General theory of nth order linear equations. |
| Holiday: Wed., Oct. 29 | ||
|
Week 7:
Nov.3-7 |
12 |
§4.2: Homogeneous equations with constant coefficients. |
| 13 |
Chapter 3. Second Order Linear Equations §3.2: Linear independence and the Wronskian. |
|
|
Week 8:
Nov.10-14 |
14 |
§3.3: Complex roots of the characteristic equation. |
| 15 |
§3.4: Repeated roots; Reduction of order. |
|
|
Week 9:
Nov.17-21 |
16 |
§3.5: Nonhomogeneous equations; Method of undetermined coefficients. |
| 17 |
§4.3: The method of undetermined coefficients. |
|
|
Week 10:
Nov.24-28 |
18 |
§3.6: Variation of parameters. |
| 19 |
§3.7: Mechanical and electrical vibrations. |
|
|
Week 11:
Dec.1-5 |
20 |
§3.8: Forced Vibrations. |
| 21 |
Chapter 6. The Laplace Transform §6.1: Definition of the Laplace transform. §6.2: Solution of initial value problems. |
|
|
Week 12:
Dec.8-12 |
22 |
§6.3: Step functions. |
| 23 |
§6.4: Differential equations with discontinuous forcing functions. |
|
|
Week 13:
Dec.15-19 |
24 |
§6.5: Impulse functions. §6.6: The convolution integral. |
| 25 |
Chapter 10. Partial Differential Equations and Fourier Series §10.A: Derivation of the Heat Conduction Equation. §10.1: Two-point boundary value problems. |
|
|
Week 14:
Dec.20-26 |
26 |
§10.2: Fourier series. §10.3: The Fourier convergence theorem (briefly). |
| 27 |
§10.4: Even and odd functions. |
|
|
Week 15:
Dec.29-30 |
28 |
§10.5: Separation of variables, heat conduction in a rod. |
| FINAL EXAM | ||