MIT 18.03: Differential Equations
18.03 is MIT's differential equations course, covering first and second order ODEs, Laplace transforms, Fourier series, and linear systems. It's 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.
What 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.
Today
Today's 18.03 plan
What a Fennie Daily Plan looks like for 18.03. Yours is built from your own syllabus and adapts every day to your deadlines and progress.
First plan free, no card required. Fennie is independent and unaffiliated with your school.
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.
More MIT courses
18.01: Single Variable Calculus
18.01 is MIT's single-variable calculus GIR, covering limits, differentiation, integration, and infinite series, required of every MIT student without prior credit. The OCW version, including David Jerison's lectures, has taught calculus to millions of self-learners.
18.02: Multivariable Calculus
18.02 is MIT's multivariable calculus GIR: vectors, partial derivatives, multiple integrals, and vector calculus through Green's, Stokes', and the divergence theorems. It's required for every MIT student and is among the most-viewed math courses on OpenCourseWare.
18.06: Linear Algebra
18.06 is MIT's linear algebra course, made world-famous by Gilbert Strang, whose OCW lectures are arguably the most beloved math course recordings ever published. It covers systems of equations, vector spaces, orthogonality, determinants, eigenvalues, and the SVD with Strang's signature intuition-first style.
18.05: Introduction to Probability and Statistics
18.05 is MIT's introduction to probability and statistics: probability models, random variables, Bayesian and frequentist inference, and regression, taught in a celebrated flipped, problem-centered format whose complete materials on OCW make it one of the most recommended statistics self-study courses anywhere.