Sam Collingbourne

Coordinate systems (cylindrical, spherical, polar), vector spaces, continuity, limits, and differentiation for vector-valued and multivariable functions, equation of and approximation using the tangent plane, directional derivatives and the gradient, Lagrange multipliers and optimization, finding maxima and minima for multivariable functions, iterated integrals and normal domains, changing coordinates for multivariable functions -- integrating in polar, cylindrical, and spherical coordinates. Line integrals: Stokes', Green's, and the Divergence theorem.

The fundamentals of modern mathematics - analysis.

How to teach myself an extremely difficult topic as Calculus III.

vectors, lines in vector form, planes in vector form vector-valued functions, multivariable functions, limits of multivariable functions and vector-valued functions derivatives and integration of vector valued functions partial derivatives, finding extreme for multivariable functions, lagrange multipliers, differentiability and continuity of multivariable functions double and triple integrals, line integrals, surface integrals, vector fields and vector calculus green's theorem, fubini's theorem, stoke's theorem, some epsilon delta proofs

real analysis: properties of reals, sequences, series, metric spaces, compactness, continuity, differentiation, integration, function spaces

Vectors, dot/cross product, IR^3, parametric curves, conic sections, level curves, quadric surfaces, tangent planes, linear approx, differentiability, functions of several variables, limits, continuity, directional derivatives, gradient vector, max/min, larange multipliers, complex numbers

Cartesian/polar/cylindrical/spherical coordinate systems, scalar and dot products with vectors, computing cross products, finding equations of lines, planes including tangent lines and planes, parametric curves, quadrics and conics, partial derivatives and their applications, linear approximations and differentiability, the chain rule as it applies to multivariable functions, gradient vectors and directional derivatives, determining the maxima and minima of multivariable functions, Lagrange multipliers, integration of multivariable functions, Fubini's theorem, using change of variables to integrate multivariable functions, vector fields and determining their curl and divergence, line and surface integrals, Green's theorem, Stokes' theorem, and Divergence theorem.

recommend because it's one of the most important topics in mathematics, but I'm not sure if I'd recommend it for people who want fun and easy classes!

I learned all about multivariable functions, and I learned how to collaborate well with the other people in my class and how to properly utilize office hours.

Basics of vectors, vector lines and vector planes Study of functions of multiple variables including differentiation, limits, differentiability, maxima and minima, optimization through Lagrange multipliers Complex numbers