Differential Equations and Linear Algebra Course Lecture 1: What is it all about?

Our goal is to study systems that change over time, in both continuous and discrete ways. This lecture covers big ideas, as well as a couple simple examples of difference equations and differential equations (both for exponential growth in populations). There is also an emphasis on what it means for a discrete function to solve a difference equation and a continuous (and differentiable, or smooth) function to solve a differential equation. (a.k.a. Continuous and Discrete Dynamical Systems, Lecture 1)

(0:00) Introduction and textbooks.
(4:16) Main goal for the course, and how we will achieve it.
(8:43) Main applications and an example (unforced undamped harmonic oscillator).
(19:23) Main methods and how linear algebra plays into this.
(24:46) Difference equation example (population growth based on doubling time).
(44:53) Now you try it (based on tripling time).
(47:51) Differential equation example (its really the same function, but not the inputs and outputs are continuous (real number) quantities).
(1:00:10) Predator-prey model, including the phase plane and a solution.

Mathematics course by Bill Kinney

#differentialequations #linearalgebra #differentialequationsandlinearalgebra

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[smarthumanism]

Great lectures full of inspiration. I didn't know math is so interesting and inspirational. Brilliant! I am really grateful to you.

[georgesadler]

Professor Kinney, thank you for an awesome Introduction to Differential Equations and its overall impact on life on planet earth. I took this class in the mid 1980's at the old Catonsville Community College in Baltimore County, Maryland and I enjoyed it from that moment on. I used Differential Equations and Linear Algebra in all my third- and fourth-year Electrical Engineering classes at the University of Maryland College Park in the late 1980's.

[kudancer]

This professor is so incredible. Everyone talks
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3Blue1Brown which is excellent
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[TJ-hsqm]

56:21 Say our reference population is represented by the equation p(t) = p0*e^t (call it R) which we compare against a second population. However, since time t is slowed down in the second population by 0.693 in e^(0.693t), we can only observe a population growth represented by the equation p(t) = p0 * e^(0.693t) (lets call that the S curve). S is nothing but p(t) = p0*2^t
[ ln(2^t) = ln(2) * t => 2^t = e^(ln(2)*t) = e^(0.693)t] and the slope of S is 0.693 of the slope of reference R. Essentially, the population S represented by 2^t (or e^(0.693t)) grows 31% slower than the population represented by R. For example, with the reference R, we see a doubling of the population every 0.69 of a month, while it takes a full month for S to double.

[rinnotstimpy]

Thanks for this I go to UDC and wanted a idea of what this class would be like in fall 2022 Differ Eq W/Linear Algb...seems to use a little Calculus which Im ok with, haven't watched this whole video yet but thanks for some information on what Im heading into.

[ghislainleonel]

Thanks for this intro. Looking forward to the rest of the course

[marcinr]

Great! Can't wait for the course to start :D
BTW: Will it be recorded with students in the class?

[pintblAnkwaziT]

Hey professor, hope you’re well. I just finished Calculus III and I’m ready to start learning more stuff (I am not formally in school - I’m just buying textbooks and working through these on my time). Should I jump straight into your ODE course first, or take this before that course? Thanks!

[kaimingyang]

Hey professor, thanks for this intro. I already finished Linear algebra(textbook: linear algebra done right) and ODE(MIT 18.03), spearatly. Do i still need to take this course?

[asadbabilbabil]

In library genesis.. free pdf math book.. on internet

[bandulureal]

what if those 2 rabbits had the same sex? 😇

[ivanandresvilla]

someone knows how to download the book for free??