We ek |
Date | Lec- ture |
Contents |
1 | 0901 |
Labour Day | |
0903 | L01 |
outline; §0.2 examples and terminology of differential equations (DEs) |
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0905 | L02 | PART I. First order ODEs
§1.1 integrals as solutions §1.2 slope fields |
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2 | 0908 | L03 | §1.2 slope fields, unique existence of
solutions §1.3 separable equations |
0910 | L04 | §1.3 separable equations continued
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0912 | L05 | §1.4 linear equations and integrating factor |
|
3 | 0915 | L06 |
(§1.5 is skipped)
Braun's §1.9: exact equations |
0917 | L07 | Braun's §1.9: integration factor for exact equation §1.6 autonomous equations |
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0919 | L08 | §1.6 phase line analysis for autonomous equations
§1.7 numerical methods, Euler method |
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4 | 0922 | L09 | §1.7 examples for Euler
method
PART II. Second order linear ODEs §2.1 terminology, solution space for homogeneous second order linear ODEs |
0924 | L10 | §2.2 Constant coefficient homogeneous second order
linear
ODEs: distinct and equal real root cases
|
|
0926 |
L11 | §2.2.1-2.2.2 complex numbers and Euler's formula, complex
roots case |
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5 | 0928 |
L12 | §2.2.2 example, and remark on §2.3 §2.4 mechanical vibrations §2.4.1 some examples |
1001 |
midterm exam 1 | ||
1003 |
L13 | §2.4.2 free undamped vibration, and §2.4.3 free damped
vibration
|
|
6 | 1006 |
L14 | §2.5 nonhomogeneous equations, the method of
undetermined coefficients |
1008 |
L15 |
§2.5.2 more examples of undetermined
coefficients §2.5.3 variation of parameters |
|
1010 |
L16 | Examples of variation of parameters §2.6 forced oscillation |
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7 | 1013 |
Thanksgiving Day | |
1015 |
L17 |
§2.6 forced
oscillation continued,
Tacoma Narrows Bridge (1940) PART III. Laplace transform §6.1 Laplace transform: definition and examples |
|
1017 |
L18 | More examples of Laplace transform, step functions,
properties |
|
8 | 1020 |
L19 | inverse Laplace transform §6.2 Transforms of derivatives and ODEs |
1022 |
L20 | solving ODEs with discontinuous forces, shifting properties |
|
1024 |
L21 | §6.2.5 Laplace transform of integral
§6.3 Laplace transform of convolution and its application to ODEs We skip transfer functions (§6.2.4) and integral equations (§6.3.3 and part of §6.2.5) |
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9 | 1027 |
L22 | §6.4 Dirac delta function in ODE We skip §6.4.4 on beam bending since it is a boundary value problem |
1029 |
L23 |
PART IV.
Linear systems of ODEs §3.1 systems of nonlinear ODEs, solutions of special cases |
|
1031 |
L24 | (We skip §3.2 which is a review of matrices) §3.3 Linear systems of first order ODEs, solution spaces and general solutions §3.4 eigenvalue method |
|
10 | 1103 |
L25 | §3.4 eigenvalue method: different real eigenvalues case, complex conjugate eigenvalues
case |
1105 |
midterm exam 2 |
||
1107 |
L26 | §3.7 eigenvalue method: repeated eigenvalues case |
|
11 | 1110 |
L27 | §3.5 phase plane analysis |
1112 |
L28 | §3.9.1 nonhomogeneous system: methods of undetermined
coefficients
and variation of parameters, lecture
notes (matrix exponential is a special case of variation of parameters; we skip eigenvalue method, §3.6, §3.8, §3.9.2, and §3.9.3) |
|
1114 |
L29 | examples of variation of parameters
PART V. Nonlinear systems of ODEs §8.1 autonomous systems, trajectories on phase plane, fixed points |
|
12 | 1117 |
L30 | §8.1 linearization about fixed points §8.2 definition of stability |
1119 |
L31 | §8.2 stability of nonlinear fixed point and its
linearization |
|
1121 |
L32 |
§8.2 continued teaching evaluation |
|
13 |
1124 |
L33 |
§8.2.4 conservative systems §8.3.1 pendulum |
1126 |
L34 |
§8.3.2 predator-prey and competition models (global phase protrait will not be in final exam) |
|
1128 |
conclusion and review |