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# Multivariable Calculus & Matrices - MAT00014C

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• Department: Mathematics
• Module co-ordinator: Dr. Zaq Coelho
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2024-25
• See module specification for other years: 2023-24

## 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

• None

### Prohibited combinations

• None

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 2024-25

## 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

1. Solve a variety of second-order differential equations

2. Write functions in terms of sums of other functions, i.e. construct Fourier- and Taylor-expansions

3. Differentiate and integrate functions of more than one variable

4. Perform algebraic operations with matrices

5. Use matrices to solve linear equations

6. Use a Computer Algebra System to solve problems in both multivariable calculus and matrix algebra.

## Module content

• 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

## Assessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Multivariable Calculus & Matrices
2 hours 70
Essay/coursework
Computer coursework : Multivariable Calculus & Matrices - Computational exercises
2 hours 20
Essay/coursework
Written coursework : Multivariable Calculus & Matrices
N/A 10

### Special assessment rules

None

If a student has a failing module mark, only failed components need be reassessed.

NB the 10% written coursework is merged with the exam, so if a student fails the module they resit the exam for 80%. If they have passed the 20% computer-based coursework they may keep that mark, or they may choose to resit it.

Note:

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

### Reassessment

Task Length % of module mark
Closed/in-person Exam (Centrally scheduled)
Closed exam : Multivariable Calculus & Matrices
2 hours 80
Essay/coursework
Essay : Multivariable Calculus & Matrices
N/A 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