Differential Equations and Dynamical Systems
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Model and analyze change: ODEs, phase portraits, and stability made approachable.
10 content steps
4 quizzes
~210 minutes
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Journey Steps
Preview
1
Content Step 1
Content
What is an ODE? Initial value problems
2
Content Step 2
Content
Separable and linear first‑order equations
3
Content Step 3
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Exact equations and integrating factors
4
Quiz 4
Quiz
Checkpoint Quiz
5
Content Step 5
Content
Second‑order linear ODEs with constant coefficients
6
Content Step 6
Content
Undetermined coefficients and variation of parameters
7
Content Step 7
Content
Laplace transforms (concepts and uses)
8
Quiz 8
Quiz
Checkpoint Quiz
9
Content Step 9
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Systems of ODEs and eigen‑methods
10
Content Step 10
Content
Nonlinear systems and phase portraits
11
Content Step 11
Content
Stability and limit cycles (overview)
12
Quiz 12
Quiz
Checkpoint Quiz
13
Content Step 13
Content
Applications in physics, biology, and engineering
14
Quiz 14
Quiz
Checkpoint Quiz
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