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# Mathematics for the Sciences I - MAT00007C

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• Department: Mathematics
• Module co-ordinator: Dr. Konstantin Ilin
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2021-22

## Module will run

Occurrence Teaching cycle
A Autumn Term 2021-22

## Module aims

To consolidate and broaden A-level mathematics

To provide a solid and secure mathematical foundation for relevant modules in other departments.

To provide the foundation for Mathematics for the Sciences II and thence for higher level Mathematics and Physics modules to be taken at stages 2 and above.

## Module learning outcomes

At the end of the module you should be able to demonstrate competence in essential topics of

• algebra
• differential calculus
• integral calculus
• differential equations
• Fourier series

## Module content

• Differentiation, Integration, substitution and parts, definite integrals
• Partial derivatives, higher order partial derivatives, linear approximation, the chain rule, implicit differentiation
• Limits of series, geometric series, Taylor series
• Complex numbers, the complex plane, the complex exponential function, roots of unity
• Exponential and hyperbolic functions
• Vectors, norm, scalar product, vector product, triple product, parametric lines, vector-valued functions, speed, and arc length
• Matrix addition and multiplication, transpose and trace (arbitrary dimensions), determinant and inverse for 2x2 matrices
• Groups and permutations
• Differential equations, solution of 1st order separable and linear ODEs
• Second order linear ODEs (homogeneous and inhomogeneous), resonance
• The wave and heat equations, Fourier series, complex exponential series, Fourier transform

## Assessment

Task Length % of module mark
Online Exam
Mathematics for the Sciences I
N/A 100

None

### Reassessment

Task Length % of module mark
Online Exam
Mathematics for the Sciences I
N/A 100

## Module feedback

Current Department policy on feedback is available in the undergraduate student handbook. Coursework and examinations will be marked and returned in accordance with this policy.

Mathematical Methods for Physics and Engineering, KF Riley, MP Hobson and SJ Bence, Cambridge University Press

The information on this page is indicative of the module that is currently on offer. The University is constantly exploring ways to enhance and improve its degree programmes and therefore reserves the right to make variations to the content and method of delivery of modules, and to discontinue modules, if such action is reasonably considered to be necessary by the University. Where appropriate, the University will notify and consult with affected students in advance about any changes that are required in line with the University's policy on the Approval of Modifications to Existing Taught Programmes of Study.