# 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)