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1
What is a DIFFERENTIAL EQUATION?? **Intro to my full ODE course**
2
The Key Definitions of Differential Equations: ODE, order, solution, initial condition, IVP
3
Separation of Variables // Differential Equations
4
Newton's Law of Cooling // Separable ODE Example
5
The Geometric Meaning of Differential Equations // Slope Fields, Integral Curves & Isoclines
6
The Big Theorem of Differential Equations: Existence & Uniqueness
7
Linear Differential Equations & the Method of Integrating Factors
8
The Method of Integrating Factors for Linear 1st Order ODEs **full example**
9
The Bernoulli Equation // Substitutions in Differential Equations
10
Autonomous Equations, Equilibrium Solutions, and Stability
11
The Logistic Growth Differential Equation
12
The Theory of 2nd Order ODEs // Existence & Uniqueness, Superposition, & Linear Independence
13
How to Solve Constant Coefficient Homogeneous Differential Equations
14
Constant Coefficient ODEs: Real & Distinct vs Real & Repeated vs Complex Pair
15
Higher Order Constant Coefficient Differential Equations: y'''+y'=0 and y''''-3y'''+3y''-y'=0
16
Linear Independence of Functions & The Wronskian
17
The Theory of Higher Order Differential Equations
18
Undamped Mechanical Vibrations & Hooke's Law // Simple Harmonic Motion
19
Mechanical Vibrations: Underdamped vs Overdamped vs Critically Damped
20
Undetermined Coefficients: Solving non-homogeneous ODEs
21
Variation of Parameters || How to solve non-homogeneous ODEs
22
How to solve ODEs with infinite series | Intro & Easiest Example: y'=y
23
When can you use Series to solve ODEs? Ordinary vs Singular Points
24
How to use SERIES to solve DIFFERENTIAL EQUATIONS example: Airy's Equation y''-xy=0
Description:
Dive into a comprehensive introduction to Ordinary Differential Equations (ODEs) through this 4.5-hour video playlist. Explore key concepts including the definition of differential equations, separation of variables, Newton's Law of Cooling, and geometric interpretations. Learn about existence and uniqueness theorems, linear differential equations, and integrating factors. Discover techniques for solving various types of ODEs, including autonomous equations, Bernoulli equations, and constant coefficient homogeneous equations. Investigate mechanical vibrations, undetermined coefficients, and variation of parameters. Conclude with an introduction to solving ODEs using infinite series methods, covering ordinary and singular points, as well as specific examples like Airy's Equation.

Ordinary Differential Equations

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#Mathematics #Differential Equations #Ordinary Differential Equations #Separation of Variables #Integrating Factors
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What is a DIFFERENTIAL EQUATION?? **Intro to my full ODE course**