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Massachusetts Institute of Technology
Multivariable Calculus 1: Vectors and Derivatives
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The first part of 18.02x (Multivariable Calculus) is open at the moment, not for certificate, but the autograder works. The second part starts next month
Unit 1: Functions of two variables Graphing functions and slicing Level curves Partial derivatives Tangent planes Linear approximation Unit 2: Geometry of derivatives Vectors Dot products Gradients Vector fields Directional derivatives Unit 3: Optimization Critical points Second derivative test Constrained optimization Lagrange multipliers Least squares approximation Unit 4: Matrices Systems of equations Matrix algebra Undetermined and overdetermined systems Linear functions as matrix maps Unit 5: Curves Parametric curves in 2 and 3 dimensions Chain rule Vectors and derivatives in three dimensions and higher
⬐ drhodesWhy is vector calculus important to programmers? It may not be to some, but for others it definitely is. For games? Some fluency with vectors in three dimensions goes a long ways. ∇ Multivariable calculus opens doors to upper level engineering, statistics, physics, finance, machine learning theory, it's all over the place.
For people who didn't have a great experience with their own university studies and for current students who may have had a less than stellar introduction over a covid semester, this is a great opportunity to really learn it. If you have single variable differential and integral calculus under your belt, my suggestion is to sign up for this class and give it 100%. The course is free to audit, but if you can afford it then give them your money! They'll be incentivized to make more of these excellent courses and besides, they deserve it.
This is an important time for online learning. The hype over MOOCs has died down and the dedicated remaining educators are still at it, learning from our participation. It's not perfect yet, but even today some of the courses are way better than their brick and mortar counterparts. I think this will be true for 18.02x.