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# Mathematics for the Sciences II - MAT00008C

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• Department: Mathematics
• Module co-ordinator: Information currently unavailable
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2018-19

• None

• None

## Module will run

Occurrence Teaching cycle
A Spring Term 2018-19 to Summer Term 2018-19

## 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
University - closed examination
Mathematics for the Sciences II
3 hours 100

None

### Reassessment

Task Length % of module mark
University - closed examination
Mathematics for the Sciences II
3 hours 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.