This is a killer method thanks for posting. Also, you shouldn't worry about us taking notes - we can pause the video if need be :) Worst thing about going back to class in person this term is not being able to pause the instructor's lecture video.
@wesh388
6 ай бұрын
Thank you for posting this! You explain it so much better than my professor did
@prof.williams8183
6 ай бұрын
Thank you, i appreciate it!
@Zeltricks
4 жыл бұрын
I'm not a student of yours, but this helped me a lot with my homework. Thank you!
@prof.williams8183
4 жыл бұрын
Glad it was helpful!
@rebecca.hinrichs
2 жыл бұрын
Great explanation & visuals! Labeling the parts of the equation as you go was really helpful for me to follow you. I just watched 4 other vids & this is the one that clicked for me. Thank you sir!!!
@prof.williams8183
2 жыл бұрын
Glad the video was helpful!
@harissohail4536
2 жыл бұрын
The video is great, but I have to mention this: look at the subtitles at 15:12
@prof.williams8183
2 жыл бұрын
🤣
@moizarif1284
3 жыл бұрын
are you assuming C4X for root 0 (no-homogenous) or am i missing something ?
@prof.williams8183
3 жыл бұрын
yes, it is a double root and since it must be linearly independent the 2nd 0 root must be multiplied by x (if there was 3 roots of 0 there would be another c_5x^2 term and the last would become c_6e^(-2x) for the non-homogeneous).
@moizarif1284
3 жыл бұрын
@@prof.williams8183 Thank you So much !
@MuhammadUmair-zc6iv
3 жыл бұрын
you are a great teacher,
@prof.williams8183
3 жыл бұрын
Thank you!
@malaikashahid5721
Жыл бұрын
How we recognize homogeneous and non homogeneous equation ??
@prof.williams8183
Жыл бұрын
whether or not there is an equation on both sides of the equal sign. The Ch. 1.1 video discusses this as well as the beginning of 4.3 and 4.4 videos.
@carultch
Жыл бұрын
It's convention to put all the dependent variable terms, and derivatives of the dependent variable (usually y) on the left side, and to put the constants and functions of only the independent variable (usually t for time, but it could be x) on the right hand side. Think of the application of mechanical vibrations. The system properties that determine the free oscillation response, are on the left. The right hand side represents the forcing function of time, that also influences the oscillation. Such as gravity as a constant that simply offsets the neutral position, or an external forcing function of time that applies its own continued stimulus.
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