What you’ll learn

Turn word problems into clear mathematical models
Use the right theorem or method without guessing
Blend analytic techniques with numerical intuition
Check your own work with simple sanity checks and visuals

Curriculum

M1 First-order ODEs & models — 5 lessons

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Direction fields & slope

12m
Locked Intermediate 12 min

Ordinary Differential Equations (ODEs)

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Separable equations

14m
Locked Intermediate 14 min

Ordinary Differential Equations (ODEs)

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Linear first-order (IF method)

16m
Locked Intermediate 16 min

Ordinary Differential Equations (ODEs)

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Exact equations & integrating factors

14m
Locked Intermediate 14 min

Ordinary Differential Equations (ODEs)

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Existence–uniqueness & modeling notes

12m
Locked Intermediate 12 min

Ordinary Differential Equations (ODEs)

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M2 Second-order linear ODEs — 4 lessons

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2nd-order with constant coefficients

16m
Locked Intermediate 16 min

Ordinary Differential Equations (ODEs)

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Undetermined coefficients

16m
Locked Intermediate 16 min

Ordinary Differential Equations (ODEs)

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Variation of parameters

16m
Locked Intermediate 16 min

Ordinary Differential Equations (ODEs)

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Mechanical vibrations & resonance

14m
Locked Intermediate 14 min

Ordinary Differential Equations (ODEs)

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M3 Laplace transforms — 3 lessons

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Laplace transform basics

14m
Locked Intermediate 14 min

Ordinary Differential Equations (ODEs)

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Step & impulse functions

14m
Locked Intermediate 14 min

Ordinary Differential Equations (ODEs)

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Solving IVPs via Laplace

16m
Locked Intermediate 16 min

Ordinary Differential Equations (ODEs)

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M4 Systems & phase plane — 3 lessons

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Systems: matrix form

14m
Locked Intermediate 14 min

Ordinary Differential Equations (ODEs)

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Eigenvalues/eigenvectors

16m
Locked Intermediate 16 min

Ordinary Differential Equations (ODEs)

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Phase plane & stability

16m
Locked Intermediate 16 min

Ordinary Differential Equations (ODEs)

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M5 Numerical methods — 3 lessons

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Euler & improved Euler

12m
Locked Intermediate 12 min

Ordinary Differential Equations (ODEs)

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Runge–Kutta (RK4)

14m
Locked Intermediate 14 min

Ordinary Differential Equations (ODEs)

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Stiffness (brief intro)

12m
Locked Intermediate 12 min

Ordinary Differential Equations (ODEs)

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M6 Applications & projects — 2 lessons

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Modeling mini-project I

12m
Locked Intermediate 12 min

Ordinary Differential Equations (ODEs)

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Modeling mini-project II

12m
Locked Intermediate 12 min

Ordinary Differential Equations (ODEs)

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Projects

Model a real-world system (growth, decay, motion, or heat flow) or dataset
Write a short report comparing analytic and numerical solutions
Create study notes and formula sheets you can reuse in exams

Prerequisites

Prior exposure to high-school algebra and functions
For ODE/PDE: at least Calculus I (or concurrent)
Willingness to pause and re-watch explanations until they click

Who is this for?

Students currently in a university math course who want a second pass
STEM majors building a stronger analysis foundation
Self-taught learners filling in gaps before ML/AI or physics

Outcomes

Less “formula hunting”, more structured problem-solving
A reusable set of notes, diagrams, and checklists
More confidence walking into problem sets and exams

Resources

Tip: Right-click → “Save link as…” if your browser opens the file.

FAQ

Is this beginner-friendly?

Yes. We start from mental models and build up with guided practice and plenty of worked examples.

Will I need extra software?

We stick to free or standard tools. Any optional extras are clearly marked and have alternatives.

Do I get updates?

Yes—lifetime access with updates as the field, tools, and exam expectations evolve.

Ordinary Differential Equations (ODEs)

What you’ll learn

Curriculum

Projects

Prerequisites

Who is this for?

Outcomes

Resources

FAQ

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Ordinary Differential Equations (ODEs)

What you’ll learn

Curriculum

Projects

Prerequisites

Who is this for?

Outcomes

Resources

FAQ

Conversation History

Settings

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