The Big Theorem of Differential Equations: Existence & Uniqueness

Описание: MY DIFFERENTIAL EQUATIONS PLAYLIST: ►   • Ordinary Differential Equations (ODEs)  
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.

♡♡♡SUPPORT THE CHANNEL♡♡♡
►Support on PATREON:   / drtrefor  
►MATH BOOKS I LOVE (affiliate link): https://www.amazon.com/shop/treforbazett
►CURIOSITY BOX: https://www.CuriosityBox.com/DrTrefor use CODE drtrefor for 25% off awesome STEM merch boxes

0:00 Intro
1:37 Ex: Existence Failing
4:10 Ex: Uniqueness Failing
9:15 Existence & Uniqueness Theorem

COURSE PLAYLISTS:
►DISCRETE MATH:    • Discrete Math (Full Course: Sets, Logic, P...  
►LINEAR ALGEBRA:    • Linear Algebra (Full Course)  
►CALCULUS I:    • Calculus I (Limits, Derivative, Integrals)...  
►CALCULUS II:    • Calculus II (Integration Methods, Series, ...  
►MULTIVARIABLE CALCULUS (Calc III):    • Calculus III: Multivariable Calculus (Vect...  
►VECTOR CALCULUS (Calc IV):    • Calculus IV: Vector Calculus (Line Integra...  
►DIFFERENTIAL EQUATIONS:    • Ordinary Differential Equations (ODEs)  
►LAPLACE TRANSFORM:    • Laplace Transforms and Solving ODEs  
►GAME THEORY:    • Game Theory  

OTHER PLAYLISTS:
►Cool Math Series:
   • Cool Math Series  
►Learning Math Series:
   • 5 Tips To Make Math Practice Problems Actu...  
►LaTeX:    • Intro to LaTeX **Full Tutorial**  Part II ...  

SOCIALS:
►X/Twitter: http://X.com/treforbazett
►TikTok:   / drtrefor  
►Instagram (photography based):   / treforphotography