Introduction to Differential Equations (Differential Equations 2)

A basic introduction the concept of Differential Equations and how/why we use them.

[ProfessorLeonard]

Hey there! For ordinary Diff. eq's the number of arbitrary constants typically match the ORDER of the diff. eq. So, second order, two arbitrary constants, etc. This is generally true for Diff eq's IF, and I mean IF, the highest order derivative can be solved EXPLICITLY in the diff. eq. Problems occur when those derivatives are defined IMPLICITLY in the diff. eq. So, that's why most texts, and teachers, can make the assumption that the number of arbitrary constants match the order; it's because we can almost always solve for the highest-order derivative explicitly in the examples we are able to solve with the techniques we have. Does this make sense? Long story made short.... implicitly defined derivatives cause complications to this general rule.

[XpPotions]

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[meathead]

1. Explains Diff Eqs better than anyone else? Check.
2. Bench presses 275 lbs without breaking a sweat? Check.

Sir, you got a new subscriber. Well deserved.

[TitanFlare]

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[jacksonr]

Professor Leonard you are truly helping SO many people with these lectures for free. Literally helping new doctors, scientists, and engineers enter our society every year. People like you are the unsung superstars. Teaching in a way that is thorough and inspires interest in the topic. THANK YOU!

[andrejangelovski]

Thank you, professor Lenard for staying true to your words and for the great value that you provide with all these videos.

[xianbalderrama]

2 dislikes, probably some x and y professors in the university that can't explain math in this level to their students like Professor Leonard can do.

[mathman]

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[robertmay]

You are my go-to Prof. for Calculus. In fact my only teacher. I am a self-learner. I thank you for your easy explanations. makes C understandable

[tashina]

Thank You Professor Leonard!

I am pursuing my electrical engineering degree and have a 10 month old. I watch your videos on my phone all the time, when I am doing dishes, when I would have to wake up at 2 am to feed the baby whenever I get 10 minutes to myself. Thanks to your wonderful teaching I have aced calculus 1, 2 and I just aced calculus 3. I don’t know how I would have passed without your guidance. Thank you! Thank you! Thank You!

[claireschmitt]

Starting my diff eq class today. Your videos were 100% the reason I was able to succeed and get an A in multivariable calc. Ready to do the same with this class!

[ericsills]

There is so much love and care in your voice as you teach, I can't even imagine you'd yell at a teenager who comes home late.

[BashaerB-hc]

I've learned more in 10 minutes than what my professor was trying to teach me in over 5 lectures.... Thank you so much! May God Bless your soul.

[jimmytorres]

Why would anyone dislike this beautiful and smart man? I mean, he is literally the best professor I’ve ever seen and he gives us all this courses for free

[photon]

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[tticusFinch]

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[jaredknezevich]

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[GreeeenT]

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[zilehumaumair]

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[xzavierreed]

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