- Department: Mathematics
- Credit value: 20 credits
- Credit level: C
- Academic year of delivery: 2024-25
- See module specification for other years: 2023-24
This module will develop the basic tools necessary to study higher level mathematics, including Taylor and Fourier series, matrices and their applications, multivariate functions and their derivatives, and double integrals.
Pre-requisite modules
Co-requisite modules
- None
Prohibited combinations
- None
Pre-requisite modules:
Post-requisite modules
Occurrence | Teaching period |
---|---|
A | Semester 2 2024-25 |
Following on from Foundations & Calculus, the basic tools necessary to study higher level mathematics will continue to be developed, including Taylor and Fourier series, matrices and their applications, multivariate functions and their derivatives, and double integrals. Students will develop their understanding through lectures, self study, small group teaching and computer labs. The lectures will be supplemented by a free open source textbook that will be used to support the lectures and computer sessions using a symbolic algebra package which will give students the tools to carry out calculations and also to self-check results.
At the end of this module students will be able to
Solve a variety of second-order differential equations
Write functions in terms of sums of other functions, i.e. construct Fourier- and Taylor-expansions
Differentiate and integrate functions of more than one variable
Perform algebraic operations with matrices
Use matrices to solve linear equations
Use a Computer Algebra System to solve problems in both multivariable calculus and matrix algebra.
Second-order ODEs
Functions of multiple variables and partial derivatives
Taylor and Fourier series
Double integrals
Extrema of functions of more than one variable
Matrices, eigenvalues, eigenvectors, diagonalisation, and their applications to solving systems of linear equations
Determinants and inverses of matrices
Real symmetric matrices
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 80 |
Essay/coursework | 20 |
None
If a student has a failing module mark, only failed components need be reassessed.
Note:
The assessed coursework component mark will be calculated from a written coureswork and computer exercises, weighted 1:1 respectively.
Due to the pedagogical desire to provide speedy feedback in seminars, extensions to the written coursework and computer exercises are not possible.
To mitigate for exceptional circumstances, the written coursework grade will be the best 4 out of the 5 assignments. If more than one assignment is affected by exceptional circumstances, an ECA claim must be submitted (with evidence).
Similarly, the computational grade will be the best 4 out of the 5 exercises. If more than one exercise is affected by exceptional circumstances, an ECA claim must be submitted (with evidence).
For extreme exceptional circumstances cases, the 10% coursework component can be discounted, with the exam mark making up 80% of the module
Task | % of module mark |
---|---|
Closed/in-person Exam (Centrally scheduled) | 80 |
Essay/coursework | 20 |
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy
There are many excellent textbooks. For calculus, this course will be based around
https://lyryx.com/calculus-early-transcendentals/
which is a free open source calculus textbook.