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    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
    Popular

    Journey Overview

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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

    Content
    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

    Content
    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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