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Geometry and Motion

Course Information

The timetable:

Week 1: Monday, 17:00-18:00 at L3; Friday, 11:00-12:00 at MS.02; Friday, 14:00-15:00 at MS.02

Weeks 2-10: Wednesday, 11:00-12:00 at L3; Friday, 11:00-12:00 at MS.02; Friday, 14:00-15:00 at MS.02

Assignments:

Weekly assignments will be published here every Monday during term 2. They are due back the following Thursday before 14:00. Assignment 10 is not for credit.

Assessment:

85% of the credit comes from the exam, 15% - from assignments. Eight best assignments out of nine are counted towards the final mark. All exam questions are composed out of assignment questions from sections A and B.


Lecture Notes

Please bring a printout of the notes to every lecture

Table of contents Week1 Week2 Week3 Week4

Week5 Week6 Week7 Week8 Week9 Week10




Assignments

Assignment 1 Assignment 2 Assignment 3 Assignment 4 Assignment 5

Assignment 6 Assignment 7 Assignment 8 Assignment 9 Assignment 10 (Assignment 10 is not for credit)



Professor Dwight Barkley's very helpful videos

Week 1

Working with Parametrisations I Working with Parametrisations II Working with Parametrisations: Parabolas

Working with Parametrisations: Spirals I Working with Parametrisations: Spirals II

Working with Parametrisations: Polar Coordinates

Working with Parametrisations: the Helix Working with Parametrisations: Cone Spiral

Working with Parametrisations: Sketching Working with Parametrisations: Curves in multiple segments


Week 2

Particle motion: Circular motion I Particle motion: Circular motion II Particle motion: Sinusoidal motion

Particle motion: Helix Arc length: Basic computation  Arc length: The hypocycloid

Reparametrising by arc length: the Helix


Week 3

Differential geometry of the Parabola I Differential geometry of the Parabola II

Differential geometry of the Helix I Differential geometry of the Helix II

Alternative curvature formula


Week 4

Practicing the Partial Derivative I  Practicing the Partial Derivative II

Practicing the Chain Rule Practicing the Directional Derivative

Practicing Higher Derivatives and PDEs



Week 5

Tangent Plane to a Surface I Tangent Plane to a Surface II

Differentials


Week 6

Practising Multiple Integrals I Practising Multiple Integrals II

Practising Multiple Integrals III: Volume  Practising Multiple Integrals IV: Type I

Type I or Type II domains   Interchanging order of integration


Week 7

Spherical Coordinates  Area and Volume Elements in Special Coordinates

Integration in Polar Coordinates I Integration in Polar Coordinates II

Integration in Cylindrical Coordinates Integration in Spherical Coordinates


Week 8

Linear Coordinate Transformations Nonlinear Coordinate Transformations

Polar Coordinates Integration by Transformation


Week 9

Tangent Plane and Normal to a Surface Tangents Planes II

Parametrising Surfaces Surface Integrals I

Surface Integrals II  Flux Integrals



Extra materials

Impossibiility theorems for elementary integration (by Brian Conrad)