Mathematics for the Sciences II - MAT00008C
- Department: Mathematics
- Credit value: 20 credits
- Credit level: C
- Academic year of delivery: 2022-23
Related modules
Module will run
| Occurrence | Teaching period |
|---|---|
| A | Spring Term 2022-23 to Summer Term 2022-23 |
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
Indicative assessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 100 |
Special assessment rules
None
Indicative reassessment
| Task | % of module mark |
|---|---|
| Closed/in-person Exam (Centrally scheduled) | 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.
Indicative reading
Mathematical Methods for Physics and Engineering, KF Riley, MP Hobson and SJ Bence, Cambridge University Press