Dr. Sarah's Differential Geometry (in-class items, video slides...) - Spring 2024

The best way to contact me is during office hours or on the ASULearn need help forum, as I usually check the posts daily, even on weekends.
  • 4140 Syllabus and Grading Policies
  • 5535 Syllabus and Grading Policies
  • What is Due When?
    Date ▢ work is due at the beginning of class

    Final Activities and Project

    6 May - Mon ▢ 2-4:30 is our assigned time at finals
    final project

    1 May - Wed ▢ prepare to share final project idea or title during class and complete any items that remain open
    class: share final project idea or title during class
    29 Apr - Mon ▢ anonymous course survey
    ▢ course evaluations
    ▢ re-engage 14
    class: during class, work on the final project or optional revisions. I'll be there to help, but you can work from elsewhere if you prefer.

    Geometry of Spacetime and Relativity

    24 Apr - Wed ▢ general relativity and the field equations interactive video slides   interactions
    ▢ read relativity article
    class: relativity and concluding activities
    22 Apr - Mon ▢ Project 3: research, investigate and present a metric form
    (optional) Wormholes.mw
    ▢ re-engage 13
    class: presentations

    17 Apr - Wed ▢ begin final project
    class: during class, work on project 3 or the final project. I'll be there to help, but you can work from elsewhere if you prefer.
    15 Apr - Mon ▢ read pp. 416-430
    ▢ wormhole metric and relativity interactive video slides   Maple   interactions
    ▢ re-engage 12
    class: curvatures and Christoffel symbols of modified Brenton universe and final project recording ideas

    10 Apr - Wed ▢ read How to Create Your Own Universe in Three Easy Steps by Lawrence Brenton
    ▢ Minkowski spacetime and Christoffel computations interactive video slides   interactions
    ▢ choice of metric form for project 3
    class: spacetime and metric form research
    8 Apr - Mon ▢ read pp. 397-416
    ▢ geodesic equations, tensors, and spacetime interactive video slides   Maple   interactions
    class: M.C. Escher Regular Division of the Plane VI (1957),   curvatures and Christoffel symbols of the Poincare upper-half plane surface

    Theory of Surfaces

    3 Apr - Wed ▢ prepare for the in-class surfaces assessment and complete any items that remain open
    ▢ re-engage 11
    class: surfaces assessment
    1 Apr - Mon ▢ read pp. 226-235
    ▢ surfaces not embedded interactive video slides   Maple   interactions
    ▢ begin surfaces assessment guide
    ▢ re-engage 10
    class: surfaces not embedded and preparing for in-class surfaces assessment, Daina Taimina

    27 Mar - Wed ▢ Project 2: research, investigate and present a surface, Maple, graduate problems are on ASULearn
    class: presentations
    25 Mar - Mon ▢ read pp. 275-277, 289-292
    ▢ Gauss-Bonnet interactive video slides  interactions
    ▢ re-engage 9
    class: Gauss-Bonnet on a round donut

    20 Mar - Wed ▢ read p. 164
    ▢ surface area interactive video slides   Maple 1   Maple 2  interactions
    class: surface area and curvature matching activity
    18 Mar - Mon ▢ read pp. 88-91, 91-96, 107-108, 111-114, 123-124
    ▢ second fundamental form and Gauss's Theorema Egregium interactive video slides  interactions
    ▢ re-engage 8
    class: π-day, Gaussian and mean curvature, spherical pi

    6 Mar - Wed ▢ read pp. 83-87
    ▢ shape operator interactive video slides   Maple  interactions
    class: shape operator: mystery surface, round donut, and Catalan surface
    4 Mar - Mon ▢ read surfaces article
    ▢ first fundamental form interactive video slides   Maple  interactions
    ▢ choose surface for Project 2
    ▢ re-engage 8
    class: first fundamental form: flat and round donuts

    28 Feb - Wed ▢ read pp. 70-76, 212
    ▢ speed of a geodesic interactive video slides   Maple  interactions
    class: holey donuts
    26 Feb - Mon ▢ read pp. 67-68, 77-82, 209
    ▢ coordinates and geodesic curvature interactive video slides   Maple  interactions
    ▢ re-engage 6
    class: sphere and spherical coordinates, Maple

    21 Feb - Wed ▢ surfaces, geodesics and coverings interactive video slides   Maple  interactions
    ▢ read pp. 247-250
    class: geodesics on cones cones

    Geometry of Curves

    19 Feb - Mon ▢ prepare for the in-class curves assessment and complete any items that remain open
    class: curves assessment

    14 Feb - Wed ▢ read 1.5 pp. 34-35
    ▢ curvature and torsion applications 2 interactive video slides   Maple  interactions
    ▢ begin curves assessment guide
    class: strake, mystery curve and preparing for in-class curves assessment, slide
    12 Feb - Mon ▢ Project 1: research, investigate and present a curve, Maple, graduate problems are on ASULearn
    ▢ re-engage 4
    class: presentations

    7 Feb - Wed ▢ read 1.3 pp. 21-25
    ▢ curvature and torsion applications 1 interactive video slides  interactions
    class: curvature, torsion, the Darboux vector and the fundamental theorem of space curves
    5 Feb - Mon ▢ read How Flies Fly
    ▢ read 1.3 pp. 19-20
    ▢ TNB 2 interactive video slides   Maple  interactions
    ▢ re-engage 3
    class: Rucker, TNB frame, curves matching, and spherical epitrochoid,   Maple,   slides,

    31 Jan - Wed ▢ read 1.3 pp. 17-19
    ▢ TNB 1 interactive video slides   Maple  interactions
    ▢ choice of curve for project 1
    ▢ graduate students: begin working on the additional graduate problems
    class: curve of Archytas, cycloid, helical spiral,   Maple
    29 Jan - Mon ▢ read 1.2 pp. 14-17
    ▢ arc length, tangent, and physical attributes interactive video slides   Maple  interactions
    ▢ practice submitting PDF of by-hand and Maple work
    ▢ re-engage 2
    class: arc length, T, velocity, speed, acceleration, jerk,   slides,   project 1 Maple

    24 Jan - Wed ▢ read 1.1 pp. 8-14
    ▢ tractrix interactive video slides   Maple  interactions
    ▢ add ASULearn profile pic or avatar
    ▢ update Zoom and add a profile pic or avatar
    ▢ send me a posting in the need help forum
    ▢ read the syllabus
    class: comparing and contrasting curves, project 1 Maple
    22 Jan Mon ▢ course intro interative video slides  interactions
    ▢ read curves article
    ▢ read 1.1 pp. 1-7
    ▢ lines and Maple intro interactive video slides   Maple  interactions
    ▢ download or access Maple and open the program
    class: curvature   slides  

    17 Jan - Wed ▢ obtain rental book from the bookstore
    class: in-class and between classes,   2130 review and handout
    (optional) Paul's Online Notes: Calc III