The Theory of Higher Order Differential Equations
57.5 هزار بار بازدید -
3 سال پیش
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MY DIFFERENTIAL EQUATIONS PLAYLIST: ►
MY DIFFERENTIAL EQUATIONS PLAYLIST: ►Ordinary Differential Equations (ODEs)
Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs
Previously in my ODE Playlist we've talked about the theory of 1st order or 2nd order differential equations. Now we turn to the more general nth order ODE, specifically focusing on linear homogeneous ODEs. A lot of the theory is the same, but we have a few complications to deal with. Firstly, we have a new Existence and Uniqueness theorem for linear ODEs. Next, we have the principle of superposition which allows us to take linear combinations of solutions and deduce new solutions. Finally we describe the method to find the general solution to an nth order ODE and use the Wronskian to verify linear independence of the fundamental set of solutions:
0:00 Linear nth order ODEs
1:52 Existence & Uniqueness
3:20 Superposition
5:00 General Solution
7:02 The Method
OTHER COURSE PLAYLISTS:
►DISCRETE MATH: Discrete Math (Full Course: Sets, Log...
►LINEAR ALGEBRA: Linear Algebra (Full Course)
►CALCULUS I: Calculus I (Limits, Derivative, Integ...
► CALCULUS II: Calculus II (Integration Methods, Ser...
►MULTIVARIABLE CALCULUS (Calc III): Calculus III: Multivariable Calculus ...
►VECTOR CALCULUS (Calc IV) Calculus IV: Vector Calculus (Line In...
►LAPLACE TRANSFORM: How to solve ODEs with infinite serie...
OTHER PLAYLISTS:
► Learning Math Series
5 Tips To Make Math Practice Problems...
►Cool Math Series:
Cool Math Series
BECOME A MEMBER:
►Join: @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): Twitter: treforbazett
►Instagram (photography based): Instagram: treforphotography
Open Source (i.e free) ODE Textbook: ►http://web.uvic.ca/~tbazett/diffyqs
Previously in my ODE Playlist we've talked about the theory of 1st order or 2nd order differential equations. Now we turn to the more general nth order ODE, specifically focusing on linear homogeneous ODEs. A lot of the theory is the same, but we have a few complications to deal with. Firstly, we have a new Existence and Uniqueness theorem for linear ODEs. Next, we have the principle of superposition which allows us to take linear combinations of solutions and deduce new solutions. Finally we describe the method to find the general solution to an nth order ODE and use the Wronskian to verify linear independence of the fundamental set of solutions:
0:00 Linear nth order ODEs
1:52 Existence & Uniqueness
3:20 Superposition
5:00 General Solution
7:02 The Method
OTHER COURSE PLAYLISTS:
►DISCRETE MATH: Discrete Math (Full Course: Sets, Log...
►LINEAR ALGEBRA: Linear Algebra (Full Course)
►CALCULUS I: Calculus I (Limits, Derivative, Integ...
► CALCULUS II: Calculus II (Integration Methods, Ser...
►MULTIVARIABLE CALCULUS (Calc III): Calculus III: Multivariable Calculus ...
►VECTOR CALCULUS (Calc IV) Calculus IV: Vector Calculus (Line In...
►LAPLACE TRANSFORM: How to solve ODEs with infinite serie...
OTHER PLAYLISTS:
► Learning Math Series
5 Tips To Make Math Practice Problems...
►Cool Math Series:
Cool Math Series
BECOME A MEMBER:
►Join: @drtrefor
MATH BOOKS & MERCH I LOVE:
► My Amazon Affiliate Shop: https://www.amazon.com/shop/treforbazett
SOCIALS:
►Twitter (math based): Twitter: treforbazett
►Instagram (photography based): Instagram: treforphotography
3 سال پیش
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