Harvard Multivariable Calculus
@math21a
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Harvard Multivariable Calculus Tweets. Also for the Summer course. And Math 22
Harvard University Cambridge
Joined August 2009
Welcome to Math S 21a of Summer 2021. A welcome video: The website is here:.
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Welcome to Math S 21a, Summer 2020. The course website is here: Video parts are here:.Tomorrow, is the first class. I'm excited. You will also see Anna, Elliot, Travis, Michael and Jesus who teach with me this summer.
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Welcome to Harvard Mulltivariable 2019! .The website is On Wednesday, September 4th, in Science Center B, there is the intro meeting for the course. Bright and early at 8:15 AM.
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Multivariable Summer School is going to an end. Have a great rest of the summer and keep in touch! .The following picture was taken before the final exam. Last push!
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Welcome to the Harvard Summer School Math S 21a course! .The course website is here: .First class is on Tuesday morning bright and early at 8:30 AM in Hall E. See you then in the Red Room. (RedRum, RedRum . )
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Clairaut counter example animation:.The functions which are given in polar coordinates r<sup>2</sup> sin(2t) or r<sup>2</sup> sin(4t) appear to be similar, but while for the first, the Clairaut theorem holds, the second one is the standard counter example.
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This semester, I teach Math 22a, which is new in the calculus mix this semester. The website is : 22a should have the same workload than 21a. What is different?: A) Early links between linear algebra and calculus B) more mathematical C) introduces proofs.
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In the final exam:.(PDF).we had a Lagrange problem with some l<sup>4</sup> curve. It is an exciting problem to understand such convex billiards. One currently does not know how to prove that the Kolmogorov-Sinai entropy is positive.
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Some of the Mathematica projects of the Math S 21a Harvard Summer.school class. As usual in the summer (covering in 6 weeks all multivariable), there was little time for this project. But the class did nevertheless did produce some nice things: Enjoy.
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Mathematica code proving the equivalence of two formulas for the curve curvature: . r[t_]:={x[t],y[t],z[t]}; s[t_]:=Sqrt[r'[t].r'[t]]; T[t_]:=r'[t]/s[t]; K1[t_]:= Sqrt[T'[t].T'[t]]/s[t]; v[t_]:=Cross[r'[t],r''[t]]; K2[t_]:= Sqrt[v[t].v[t]]/s[t]^3; FullSimplify[K1[t]^2==K2[t]^2].
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Welcome to Harvard Math S 21a! The course site is on:.On the handouts page, you find the handouts from the first week:.like a summary of all lectures:.or some relation between discrete and continuum calculus.
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In the Archimedes Revenge problem (see problem 13 in.,.a gift card was promised for students who can solve it. There has.been one student of that class Runze Li, who solved it correctly until December 31th 2017:. Congratulations!
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A selection of Mathematica projects done this semester: .great job, students of Math 21a, Fall 2017 !.More exhibits:
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The sculpture has appeared in our final exam. It is a death star, neutralized by a cone! The artist has called it life force II. May the force be with us! .
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Some class submissions of the optional tangent art problem in HW 14. Only a small sample.
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Given two lines r(t) = P + t v and s(t) = Q + t w. Is the midpoint (P+Q)/2 equidistant from the lines?(TF20 problem).
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A large resolution rendering from an illustration used for the first midterm. It was rendered in Mathematica using a NASA model of Cassini.
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Become a good friend of the conic cat featuring a parabola, a circle (a special ellipse), a hyperbola and a singular conic, the whiskers !
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Check out the exhibit page of this summer. This is the end of the course.
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Archimedes Revenge: verify that the volume of the solid x^2+y^2-z^2<1, y^2+z^2-x^2<1, z^2+x^2-y^2<1 is log(256). See
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