Functions
Differentiation
Complex numbers
Vectors
Integration
Matrices
Differential equations
Laplace Transforms
This module is a 15-credit, year-long module which covers the mathematics you will need for the first year of your degree.
Twice a week, you will go through the following cycle of events:
The module is assessed by:
The videos and online tests only cover basic material, so in order to pass the course, you will have to engage fully with the problem sheets, the exercises, and past papers.
Here is a page of links to the official course information, including syllabus information.
There are some full-class lectures scheduled as below. Everyone should attend all of these lectures.
These will be held on Mondays in weeks 1, 3 and 4, at 5pm in Hicks LT1.
These will be held on Mondays in weeks 1 and 8, at 12pm in Diamond LT1.
Here are the notes for the lectures that have taken place.
| Semester 1 | Semester 2 | |
|---|---|---|
| Week 1 | Notes | Notes |
| Week 3 | Notes | |
| Week 4 | Notes | Notes |
There is a reading week for the course in Week 7 of Semester 1. There will be no lectures or problem classes in this week, and you should use it to catch up on all the material from the course so far.
| Semester 1 | |
|---|---|
| Notes | Exercises |
| Functions | Exercises and worked solutions |
| Differentiation | Exercises and worked solutions |
| Maclaurin series and l'Hopital's Rule | Exercises and worked solutions |
| Partial Differentiation | Exercises and worked solutions |
| Complex Numbers | Exercises 1 and
worked solutions Exercises 2 and worked solutions |
| Vectors | Exercises and worked solutions |
| Semester 2 | |
| Integration, Matrices, Differential equations | Exercises and worked solutions |
The video lectures and online tests are accessed at the link below.
Note: The login details are not the same as for your University email account. You will need to enter your details and click 'Send Password' to receive the password via email.
Videos and tests are normally released in Semester 2 at the following times:
If it doesn't work, try using a different browser, or failing that a different computer or device altogether. Make sure Javascript is enabled! Please don't leave the tests until close to the deadline: it is unlikely that you will be able to get any technical help late in the evenings.
For revision purposes, the playlists for the completed sections so far are below.
| Functions |
Differentiation |
Complex numbers |
Vectors |
| Integration |
Matrices |
Differential equations |
Laplace Transforms |
The problem class groups with rooms are shown on the documents below. Each student attends two problem classes per week.
If you don't think you're on the list, email mas-engineering@shef.ac.uk.
The worksheets used by the tutors in the problem classes are available below.
| Semester 1 | |
|---|---|
| Week 1 | Curve Sketching |
| Domain and Range | |
| Week 2 | Trigonometry and Binomial Expansions |
| Inverse Functions | |
| Week 3 | Hyperbolic Functions |
| Differentiation | |
| Week 5 | Differentiation Rules |
| Inverse Function Rule | |
| Week 6 | Parametric, Implicit |
| Maclaurin Series | |
| Week 7 | l'Hopital |
| Partial Differentiation | |
| Week 8 | Partial Second Derivatives |
| Complex Numbers | |
| Week 9 | Argand Diagram |
| Euler's Relation | |
| Week 10 | De Moivre |
| Vectors | |
| Week 11 | Scalar Product |
| Vector Product | |
| Week 12 | Vector Differentiation |
| Semester 2 | |
| Week 1 | Revision |
| Integration by Inspection | |
| Week 2 | Integration by Substitution |
| Integration by Parts | |
| Week 3 | Further Integrals |
| Definite Integration | |
| Week 4 | Improper Integrals |
| Matrices | |
| Week 5 | Matrix Multiplication |
| Determinants | |
| Week 6 | More Determinants |
| More Inverses | |
| Week 7 | Systems of Equations |
| Gaussian Elimination | |
| Week 8 | Eigenvectors |
| Differential Equations | |
| Week 9 | Integrating Factors |
| Second Order Linear | |
| Week 10 | Particular Integrals |
| Laplace Transforms | |
| Week 11 | Laplace and Differential Equations |
| Revision | |
Some questions have stars next to them: these questions are usually a little harder, and usually contain material that's not examinable. However, doing them might still be good preparation for the exams!
There is an email address for getting support, mas-engineering@shef.ac.uk. This is usually the best way of getting help with non-mathematical problems, including problems with the videos and online tests.
You will receive a response as quickly as possible. This e-mail is checked only between 8:30am and 4pm from Monday to Friday, and you will not receive a response outside these times. It may take longer to receive a response at peak times, particularly at the start of term. Please include your module code (MAS161) in the title of any emails you send.
The discussion board is a forum for students to use to ask and answer (anonymously, if preferred) questions on the material for the course. The board lies in MOLE, so log-in with your usual username and password when asked.
This is usually the best way of getting help with mathematical problems.
There are past papers, with solutions, for the previous two years' exams below. According to departmental policy, we will not be providing solutions for other exams. However, you can find past papers from further back on the past exams page on the School of Mathematics and Statistics webpage.
Here are some other possibly-useful exam-related things:
The resit, for those students who need it, will take place in August, and will follow the same model as the Semester 2 exam (three hours, twelve short and eight long questions; your online test scores will still count).
Below are things related to material covered in the course which may be of interest to you.