The Big Theorem of Differential Equations: Existence & Uniqueness
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The theory of differential equations works because of a class of theorems called existence and uniqueness theorems. They tell us, given an initial value problem, when that IVP has a solution, and if a solution exists, then it also tells us it is unique. We will focus on the Picard or Picard-Lindelof existence and uniqueness theorem which applies to first order differential equation. A key focus will be on the domain on which a unique solution is guaranteed to exist.
0:00 Intro
1:37 Ex: Existence Failing
4:10 Ex: Uniqueness Failing
9:15 Existence & Uniqueness Theorem
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Видео The Big Theorem of Differential Equations: Existence & Uniqueness канала Dr. Trefor Bazett
Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs
The theory of differential equations works because of a class of theorems called existence and uniqueness theorems. They tell us, given an initial value problem, when that IVP has a solution, and if a solution exists, then it also tells us it is unique. We will focus on the Picard or Picard-Lindelof existence and uniqueness theorem which applies to first order differential equation. A key focus will be on the domain on which a unique solution is guaranteed to exist.
0:00 Intro
1:37 Ex: Existence Failing
4:10 Ex: Uniqueness Failing
9:15 Existence & Uniqueness Theorem
OTHER COURSE PLAYLISTS:
►DISCRETE MATH: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxersk8fUxiUMSIx0DBqsKZS
►LINEAR ALGEBRA: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfUl0tcqPNTJsb7R6BqSLo6
►CALCULUS I: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfT9RMcReZ4WcoVILP4k6-m
► CALCULUS II: https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc4ySKTIW19TLrT91Ik9M4n
►MULTIVARIABLE CALCULUS (Calc III): https://www.youtube.com/playlist?list=PLHXZ9OQGMqxc_CvEy7xBKRQr6I214QJcd
►VECTOR CALCULUS (Calc IV) https://www.youtube.com/playlist?list=PLHXZ9OQGMqxfW0GMqeUE1bLKaYor6kbHa
►LAPLACE TRANSFORM: https://www.youtube.com/watch?v=xeeM3TT4Zgg&list=PLHXZ9OQGMqxcJXnLr08cyNaup4RDsbAl1
OTHER PLAYLISTS:
► Learning Math Series
https://www.youtube.com/watch?v=LPH2lqis3D0&list=PLHXZ9OQGMqxfSkRtlL5KPq6JqMNTh_MBw
►Cool Math Series:
https://www.youtube.com/playlist?list=PLHXZ9OQGMqxelE_9RzwJ-cqfUtaFBpiho
BECOME A MEMBER:
►Join: https://www.youtube.com/channel/UC9rTsvTxJnx1DNrDA3Rqa6A/join
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): http://twitter.com/treforbazett
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Видео The Big Theorem of Differential Equations: Existence & Uniqueness канала Dr. Trefor Bazett
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