Mechanical & Aerospace Engineering
How a machine, a bridge, an engine and an aircraft stand up, move, heat up and stay under control.
For: anyone starting the degree, anyone who works next to engineers, anyone who has wondered why a beam bends.
Year 1 · The language
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01ReadInteractiveQuiz10 min
Calculus I: Slopes, Totals and the Bridge Between Them
Every rate and every total in engineering is a derivative or an integral.
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02ReadInteractiveQuiz10 min
Physics I: Mechanics — Three Ways to Keep the Books
Forces, energy and momentum: the three ways engineers account for motion.
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03ReadInteractiveQuiz13 min
Linear Algebra: Machines That Move Space
Real structures have hundreds of unknowns; matrices solve them all at once.
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04ReadInteractiveQuiz11 min
Programming Fundamentals: Instructions, State and Taking Things Apart
Engineers model in code (MATLAB, Python) long before they build in metal.
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05ReadInteractiveQuiz12 min
Engineering Drawing & CAD: The Contract Between Designer and Maker
A drawing is a contract: what you draw is what gets made.
Year 2 · Forces and matter
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06ReadInteractiveQuiz10 min
Multivariable Calculus: Calculus on a Landscape
Stress, flow and heat vary across a part, so the maths has to vary in 3D too.
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07ReadInteractiveQuiz11 min
Differential Equations: Laws Written as Rates
Almost every physical law an engineer uses is written as a differential equation.
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08ReadInteractiveQuiz11 min
Statics: Why Things Stand Still
Nothing that stands still has unbalanced forces; that one rule designs bridges.
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09ReadInteractiveQuiz12 min
Mechanics of Materials: Why Things Bend, Buckle and Break
Why beams bend, columns buckle and parts crack, and how to size them so they don't.
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10ReadInteractiveQuiz11 min
Dynamics: Why a Hoop Loses the Race
Moving things: rotation, momentum, and why a spinning wheel resists turning.
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11ReadInteractiveQuiz14 min
Materials Science & Manufacturing: Why Things Are Made of What They Are
Steel, aluminium, polymers, composites: why each part is made of what it's made of.
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12ReadInteractiveQuiz10 min
Physics II: Electricity & Magnetism — Charge, Fields and Light
Motors, sensors and actuators run on electromagnetism.
Year 3 · Energy and fluids
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13ReadInteractiveQuiz13 min
Thermodynamics: Why Every Engine Pays a Heat Tax
Energy is conserved and always degrades; every engine lives inside those two laws.
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14ReadInteractiveQuiz13 min
Fluid Mechanics: Why Air and Water Push Back
Air and water push, drag and lift; the Navier–Stokes equations are the rulebook.
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15ReadInteractiveQuiz12 min
Heat Transfer: Three Roads for Heat
Conduction, convection, radiation: how heat escapes, and how to make it.
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16ReadInteractiveQuiz12 min
Vibrations: Everything Is a Spring and a Mass
Everything vibrates; resonance is how small pushes break big things.
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17ReadInteractiveQuiz12 min
Probability & Statistics: Reasoning with Uncertainty
Tolerances, test data and failure rates are statistics.
Year 4 · Putting it together
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18ReadInteractiveQuiz13 min
Machine Design: The Parts Every Machine Is Built From
Shafts, gears, bearings, bolts: the parts every machine is built from.
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19ReadInteractiveQuiz11 min
Control Systems: How Machines Hold a Setpoint
Feedback is how a machine holds a speed, a heading or a temperature on its own.
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20ReadInteractiveQuiz13 min
Propulsion: Throwing Mass Backwards
Jets and rockets: pushing mass backwards to go forwards.
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21ReadInteractiveQuiz14 min
Systems Engineering & the Capstone: Many Parts, One Product
A product is many subsystems agreeing with each other; that's the capstone.
MIT OpenCourseWare's Mechanical Engineering and Aeronautics & Astronautics course lists, free, with problem sets; then the textbooks named at the end of each subject.
Computer Science
How computers compute, what can and can't be computed, and how to build software that works.