Multivariable Calculus & Matrices - MAT00014C
Module summary
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.
Related modules
Additional information
Pre-requisite modules:
- Foundations & Calculus
Post-requisite modules
- All modules, specifically Linear Algebra and Vector & Complex Calculus.
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Semester 2 2025-26 |
Module aims
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.
Module learning outcomes
At the end of this module students will be able to
-
Solve a variety of second-order differential equations
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Write functions in terms of sums of other functions, i.e. construct Fourier- and Taylor-expansions
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Differentiate and integrate functions of more than one variable
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Perform algebraic operations with matrices
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Use matrices to solve linear equations
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Use a Computer Algebra System to solve problems in both multivariable calculus and matrix algebra.
Module content
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Second-order ODEs
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Functions of multiple variables and partial derivatives
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Taylor and Fourier series
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Double integrals
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Extrema of functions of more than one variable
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Matrices, eigenvalues, eigenvectors, diagonalisation, and their applications to solving systems of linear equations
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Determinants and inverses of matrices
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Real symmetric matrices
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80 |
| Essay/coursework | 20 |
Special assessment rules
None
Additional assessment information
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
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 80 |
| Essay/coursework | 20 |
Module feedback
Current Department policy on feedback is available in the student handbook. Coursework and examinations will be marked and returned in accordance with this policy
Indicative reading
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.