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School of Mathematics

# 1R2 Course Materials

### Available Resources

Introductory Notice

## Handouts

Any relevant handouts will be placed here.

## Example Sheets

Example Sheets will be place here.

• Example Sheet 6 and solutions
• Example Sheet 7 and solutions
• Example Sheet 8 and solutions
• Example Sheet 9 and solutions
• Example Sheet 10 (revised version) and solutions
• Example Sheet 11 and solutions
• ## Coursework

Coursework Tests for 1R2 are 9 am in the Sackville/G11 computer cluster on the following dates. Retests are one week later

Complex Numbers
Monday week 4 (Retest Monday week 5)
Complex Numbers, Hyperbolic Functions and Matrices
Monday week 6 (Retest Monday week 7)
Matrices, Integration
Monday week 8 (Retest Monday week 9)
Differential Equations
Monday week 10 (Retest Monday week 12)

Students scoring less than 7/10 in a test are invited to the retest. At the retest, marks can be increased by a maximum of 4 to a maximum of 7.

Coursework Tests for 1R2 are 9 am in the Computer Cluster in Sackville/G11 on the above dates. Retests are one week later. These tests involve the student interacting with the computer. Week 3 will nivolve a practice session. At this session, students should follow the link to http://mathvle.eps.manchester.ac.uk

These arrangements are similar to those for 1R1 .

## HELM Modules

Complex Numbers
Complex arithmetic
Argand diagrams and polar form
Exponential form
Hyperbolic Functions
The hyperbolic function
Matrices
Introduction to matrices
Matrix multiplication
Determinants
The inverse of a matrix
Solution of Equations
(Context - Using matrices and determinants to solve equations)
Cramer's rule for solving simultaneous equations
Solving simultaneous equations using the inverse matrix
Gauss elimination
Further Integration/ODEs
Integration by substitution
Modelling with differential equations
First Order ODEs
Second Order ODEs
Applications of differential equations (context material)
Further/Partial differentiation
Functions of several variables
Partial derivatives
Stationary points
Errors and percentage change

### Formula Tables

Download, print and get used to looking up information in these Formula Tables. Your lecturer will be able to confirm if these tables will be provided in exams.

## Past exam papers

Download and print exam papers from previous years. Be aware that the syllabus may have changed, making some questions no longer relevant to the course you are taking. The number of questions may also have changed.

• Solutions
• 2009
• 2008
• 2004
• (no other solutions will be provided)