# 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.