\\\\(
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Week 5, Short Day: Particular Surfaces in Space
Today we continue our work with plane and surface integrals. Apart from graphs of functions of two variables, we will today also consider surfaces of revolution. You will learn methods for the parametrization of such surfaces, and you will train on the computation of the corresponding Jacobians and integrals in the exercises.
Today’s Key Concepts
Surface that is the graph of a function of two variables. Surface of revolution. Profile curve/directrix.
Preparation and Syllabus
Today’s content cover eNote 24 Line and Plane Integrals, Section 24.2, and subjects from eNote 25 Surface and Volume Integrals, Section 25.1.
Maple Ressources
Today’s Maple demo is 28_SurfaceParametrizations .
Activity Program
- 13.00 – 14.00: $\,$Lecture (aud. 42, b. 303A) (link to streaming)
- 14.00 – 16.00: $\,$Group exercises in the study areas (b. 302, bottom floor)
- 16.00 – 17.00: $\,$Weekly Test trial.
Group Exercises
- Integration by Parts and Substitution with Two Variables
- Plane Integral with Parametrization
- Graph Surface, Parametrization and Integration
- Surface of Revolution
- Graph Surface
Weekly Test
For all Weekly Tests, the following applies:
- The test is an on-location test, meaning it can only be accessed in the study area.
- No electronic aids are allowed (except for your own notes on e.g. a tablet).
- The test can be accessed in the the Möbius quiz system via a link on DTU Learn in the module for 01006 (in the top menu click “Möbius”).
- Your solutions to the test questions must be typed into Möbius without in-between calculations or steps. The result is automatically evaluated by Möbius.
- To ensure a smooth experience use the Firefox or Chrome browser, and disable any add-blocker.
- Use a DTU network.
- You may discuss the test questions with fellow students in your study group, but you have your own version of the test with scrambled numbers that you yourself must solve and enter into Möbius.
- During the final hour on Fridays you have one attempt. Passing this attempt will grant you 1 bonus point. From Friday at 18:00 until Wednesday at 18:00 the test is reopened for repeated attempts. Passing during this phase will grant you ½ bonus point.