MIT 18.03: Differential Equations
18.03 is MIT's differential equations course — first and second order ODEs, Laplace transforms, Fourier series, and linear systems — required by most engineering and science majors and among the most-used math courses on OpenCourseWare, where Arthur Mattuck's lectures are a classic.
Fennie is independent and not affiliated with MIT. This is an unofficial study guide.
Build my 18.03 study planWhat makes it hard
The course is a toolbox course, and the failure mode is collecting tools without knowing which one a problem wants: solution methods multiply week after week, and exams hand you equations stripped of the unit headings that told you which technique applies. The Fourier and Laplace units also quietly assume your integration technique is still sharp.
What you'll cover
- • First-order equations and modeling
- • Second-order linear equations and oscillations
- • Laplace transforms
- • Fourier series
- • Systems of ODEs and matrix methods
- • Stability and the phase plane
The 18.03 study guide
How to study for MIT 18.03, step by step.
- 1
Build a method-selection chart as you go
For every technique, record what form of equation it serves and the telltale signs. Exams strip away the unit headings — the chart you built is the skill they're testing.
- 2
Tie every equation to a physical picture
Springs, circuits, and mixing tanks aren't decorations; damping ratios and resonance make sense as physics first. Students who keep the models attached remember the math an order of magnitude better.
- 3
Re-sharpen integration before Laplace and Fourier
Both units are integration-heavy in ways lecture doesn't pause for. A week of integral practice before they arrive prevents the math from failing underneath the new ideas.
- 4
Work the OCW exams after honest attempts
18.03's OCW versions post exams with solutions. Take them timed and study the solutions only afterward — the technique-selection misses are the most instructive ones.
- 5
Keep the toolbox organized with Fennie
Upload the 18.03 syllabus or your OCW plan and Fennie's Daily Plan rotates older methods through review while new ones arrive, with technique-selection quizzes generated from the actual course materials. Free to start.
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How Fennie helps with 18.03
Fennie's Daily Plans rotate 18.03's growing toolbox through review so week-two methods are still sharp when week-ten exams need them. Chat through which technique an equation wants and why, and drill selection-focused practice questions — the skill exams test once the unit headings disappear.
FAQ
Is 18.03 hard?
It's more breadth than depth — many methods, each learnable, with technique selection as the exam skill. Students who organize the toolbox as they go find it steady work.
Can I self-study 18.03 on OCW?
Yes — it's one of OCW's most complete math courses, with Mattuck's lectures, notes, psets, and exams with solutions. Plan 10–14 weeks for a full pass.
Do I need 18.03 for engineering at MIT?
Most Course 2, 6, 8, 10, and 16 pathways require it or a close equivalent — it's the standard math course after 18.02 for engineers.
Pass 18.03 with a plan, not a cram
Upload your 18.03 materials and Fennie generates a Daily Plan paced to your deadline — plus chat, flashcards, and quizzes built from the actual course content.
Get started freeMore MIT courses
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