# Mathematics for the Sciences II - MAT00008C

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• Department: Mathematics
• Module co-ordinator: Prof. Reidun Twarock
• Credit value: 20 credits
• Credit level: C
• Academic year of delivery: 2017-18

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## Module will run

Occurrence Teaching cycle
A Spring Term 2017-18 to Summer Term 2017-18

## 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, linear independence [4]
• Trace, Determinant, Inverse, multiplicativity of the determinant [4]
• Eigenvectors, diagonalization, symmetric and Hermitian matrices, quadratic forms. [6]
• Multiple integration, order of integration, integration in polar/spherical coordinates [4]
• Critical points, 2nd derivative test in 1 and 2 dimensions, Lagrange multipliers [6]
• Limits and convergence, l’Hopital’s rule, limits at infinity, improper integrals. [4]
• The gradient and its geometric significance, directional derivatives [3]
• Conservative vector fields, line integrals, fundamental theorem of line integrals [3]
• Divergence and curl [3]
• Surface and volume integrals [4]
• Independent random variables, discrete and continuous probability distributions, probabilities for unions and intersections, the Gamma distribution. [3]
• Random variables, probability distributions, variance, binomial distribution, Poisson distribution, normal distribution, central limit theorem, error propagation [5]

## 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.