Mathematics for the Sciences I - MAT00007C

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  • Department: Mathematics
  • Credit value: 20 credits
  • Credit level: C
  • Academic year of delivery: 2022-23

Module will run

Occurrence Teaching period
A Autumn Term 2022-23

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

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