Lectures are listed in reverse chronological order. Week 15 apr27.pdf 6+ global Gauss-Bonnet Theorem apr25.pdf 6+ local Gauss-Bonnet Theorem Week 14 apr22.pdf 5+ geodesics and isometries of hyperbolic space apr20.pdf 5+ geodesics and isometries of hyperbolic space apr18.pdf 5 Studying the intrinsic DE's for geodesics Week 13 apr15.pdf 5 Geodesics! apr13.pdf 4.6-4.8 Gauss curvature from WE representation. Conjugate surfaces. apr11.pdf 4.6-4.8 Reconstructing X(u,v) from Phi(u,v) by complex antidifferentiation. Week 12 apr8.pdf 4.6-4.8 computing the triple composition St(U(X(u,v))) for conformally parameterized minimal surfaces; we're continuing the notes below. Also, see the directory minimalsurfaces minimal.pdf 4.6-4.8 old undergraduate colloquium notes on minimal surfaces apr6.pdf 4.6-4.8 supplements to the minimal surface notes (above) apr4.pdf 4.3 Two minimal surface theorems to accompany our soap bubbles Week 11 apr1.pdf 4.4 Ros' proof of Alexandrov's sphere theorem for compact constant mean curvature surfaces. mar30.pdf 4.4 the first variation of area computation, and why H=0 surfaces are called minimal. mar28.pdf 4.1-4.4 balloon science, corrected Week 10 mar25.pdf 4.1-4.3 pressure, surface tension, and mean curvature mar23.pdf 3.4-3.5 Finishing Liebmann, and starting the study of constant mean curvature. mar21.pdf 3.4-3.5 Liebmann's amazing theorem that compact surfaces with constant Gauss curvature must be spheres. Also, more Christoffel fun. Week 9 mar11.pdf 3.4 computation with indices and the summation convention mar9.pdf 3.4 isometric surfaces and Gauss' Theorem Egregium mar7.pdf 3.3 surfaces of revolution with constant K Week 8 mar2.pdf 3.5   totally umiblic surfaces are parts of spheres or planes feb28.pdf 1.1-3.3 review for midterm; also, using inverse function theorem to prove local graph property Week 7 feb25.pdf 2.4, 3.3 normal curvature, lines of curvature, surfaces of revolution feb23.pdf 2.4 normal curvature Week 6 feb18.pdf 3.1-3.3 calculating the matrix for the shape operator, K, H. feb16.pdf 2.3 Mean and Gauss curvature, the shape operator, and the tangential hessian feb14.pdf 2.2-2.3 Relationship between the shape operator and the Hessian of the function parametrizing the surface about its tangent plane Week 5 feb11.pdf linalg: matrix of a linear transformation, self-adjoint operators, the spectral theorem; background we apply to the shape operator. feb9.pdf 2.2 the shape operator feb7.pdf 2.2 the unit normal and orientability, directional derivatives. Week 4 feb4.pdf 2.1-2.2 Surfaces!! : local patches, atlas, differentiable surfaces and maps between them. The tangent space. feb2.pdf extra: the one and only fundamental theorem of calculus jan31 No notes - we spent the day working on homework in the computer lab. Week 3 jan28.pdf 1.6: isoperimetric inequality, but not the book's proof. jan26.pdf 1.4, 1.7: integrating the Frenet system, for space curves and for plane curves. Calculations without p.b.a.l. Maple documents from today: pdf and maple worksheet for integrating the Frenet System in space: frenetsystem.pdf frenetsystem.mws planar curves with prescribed planar curvature: planefrenet.pdf planefrenet.mws computing curvature and torsion for arbitrary parametric curves, with computer algebra: curtor.pdf curtor.mws jan24.pdf 1.3: Frenet system and E! theorem for curves of prescribed curvature and torsion Week 2 jan21.pdf extra: Kepler's and Newton's Laws jan19.pdf 1.2-1.3 arclength, straight lines minimize length, acceleration decomposition Week 1 jan14.pdf 1.1-1.3 review of dot and cross product, universal product rule for differentiation. jan12.pdf 1.1 curves jan10.pdf intro A global curvature theorem for curves, and one for surfaces |