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:
Links to homework assignments can be found below. Assignments 1-9 are due back the on Thursdays of weeks 2-10 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
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
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)
Integration by substitution (from Wikipedia)