Multivariable Calculus: Math 202 , Spring 2000
hypercube in mathematica
can create your own view of the hypercube by copying this mathematica file.
The pictures have no perspective. Rather, they show the image
of the hypercube under your choice of a linear map from R^4 to R^2,
which preserves the y and z axes.
(Mac only) Download "Geometry games".
Note 1 Quadratic functions,
Taylor approximation, Critical points, Second derivative test, Least squares
Pictures for Note 1
Exam 1 review, Exam
Note 2 Line
integrals in the plane, vector fields, work integrals, conservative vector
fields and independence of path
Solutions to exercises in Note 2
Extra exercises for Note 2
Pictures: Vector Fields with no flow and
no flux around closed curves
Double integrals, Area, Average, Center of Mass
Solutions to exercises in Note 3
Gaussian Integral, Factorial function, Beta integral, Volumes of Spheres
Solutions to exercises in Note 4
Green's Theorem, Two-dimensional Curl, Fundamental Theorem of Calculus,
Divergence of a Vector field, Cauchy-Riemann equations, Most Interesting
Vector Field, Jacobian,
Linear mappings, Regions bounded by graphs.
Solutions to exercises in Note 5
exercises for Notes 3,4,5
Exam 2 solutions
Line integrals in three dimensions, three dimensional curl, parametrized
surfaces, surface integrals, flux integrals, Stokes theorem, triple integrals,
Extra Problems for Note 6
Final Exam (with solutions)