We ek 
Date  Lec ture 
Contents 
1  0901 
Labour Day  
0903  L01 
outline; §0.2 examples and terminology of differential equations (DEs) 

0905  L02  PART I. First order ODEs
§1.1 integrals as solutions §1.2 slope fields 

2  0908  L03  §1.2 slope fields, unique existence of
solutions §1.3 separable equations 
0910  L04  §1.3 separable equations continued


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 

0919  L08  §1.6 phase line analysis for autonomous equations
§1.7 numerical methods, Euler method 

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  §2.2.12.2.2 complex numbers and Euler's formula, complex
roots case 

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 

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) 

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 predatorprey and competition models (global phase protrait will not be in final exam) 

1128 
conclusion and review 