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# Mathematics for the Sciences II - MAT00008C

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• Department: Mathematics
• Module co-ordinator: Dr. Richard Bingham
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2020-21

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## Module will run

Occurrence Teaching cycle
A Spring Term 2020-21 to Summer Term 2020-21

## Module aims

To provide a solid and secure foundation for for higher level mathematics and physics modules to be taken at stages 2 and above.

## Module learning outcomes

Demonstrate competence in the essential topics of

a) multi-variate calculus,

b) vector calculus,

c) linear algebra,

d) probability

## Module content

• Systems of linear equations, Gaussian elimination (row reduction) linear independence
• Determinant and Inverse in arbitrary dimension, multiplicativity of the determinant
• Eigenvalues and eigenvectors, diagonalization, symmetric and Hermitian matrices, quadratic forms.
• Multiple integration, order of integration, integration in polar/spherical coordinates
• Critical points, 2nd derivative test in 1 and 2 dimensions, Lagrange multipliers
• Limits and convergence, l’Hopital’s rule, limits at infinity, improper integrals.
• The gradient and its geometric significance, directional derivatives
• Conservative vector fields, line integrals, fundamental theorem of line integrals
• Divergence and curl
• Surface and volume integrals
•  Independent random variables, discrete and continuous probability distributions, probabilities for unions and intersections, the Gamma distribution.
• Random    variables, probability    distributions,   variance,   binomial  distribution,    Poisson    distribution, normal distribution, central limit theorem, error propagation

## Assessment

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

None

### Reassessment

Task Length % of module mark
Online Exam
Mathematics for the Sciences II
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.