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MAU22E01 Engineering mathematics III

Module Code MAU22E01
Module Title Engineering mathematics III
Semester taught Semester 1
ECTS Credits 5
Module Lecturer Prof. Dmitri Zaitsev
Module Prerequisites MAU11E02 Engineering mathematics II

Assessment Details

  • This module is examined in a 2-hour examination at the end of Semester 1.
  • Continuous assessment contributes 10% towards the overall mark.
  • Re-assessment, if needed, consists of 100% exam.

Contact Hours

11 weeks of teaching with 3 lectures and 1 tutorial per week.

Learning Outcomes

On successful completion of this module, students will be able to

  • Relate linear systems, linear transformations and their matrices.
  • Check whether a system of vectors is linearly independent and/or a basis.
  • Calculate the dimension of a subspace.
  • Calculate the rank and the nullity of a matrix.
  • Construct a basis for the row, column and null spaces of a matrix.
  • Calculate the eigenvalues and the eigenvectors of a square matrix.
  • Apply the Gram-Schmidt process to transform a given basis into an orthogonal basis.
  • Solve ordinary differential equations using general and particular solutions.
  • Calculate the Fourier series of a given function and analyse its behaviour.
  • Apply Fourier series to solve ordinary differential equations.
  • Calculate the Fourier transformation of a given function.

Module Content

  • Euclidean n-space and n-vectors.
  • Linear transformations and their matrices, subspaces, linear combinations of vectors, subspaces spanned by a set of vectors, linear independence of a set of vectors.
  • Basis and dimension, standard basis in n-space, coordinates of vectors relative to a basis.
  • General and particular solutions for a linear system.
  • Row, column and null space of a matrix, finding bases for them using elementary row operations, rank and nullity of a matrix.
  • Inner products, lengths, distances and angles.
  • Orthogonal and orthonormal bases relative to an inner product, orthogonal projections to subspaces, Gram-Schmidt process.
  • Eigenvalues and eigenvectors of square matrices.
  • Fourier series for periodic functions, Euler formulas for the Fourier coefficients, even and odd functions, Fourier cosine and Fourier sine series, Fourier integral and Fourier transform.

Recommended Reading

  • Advanced engineering mathematics by Erwin Kreyszig.
  • Elementary linear algebra with applications by Anton and Rorres.