Engineering Mathematics III

Module code: MAU22E01 · Semester: 1

Resources

• Module descriptor (Maths Department)

Questions by Year

0 of 13 done · tick papers and add notes as you go

• 2025/26
• 2024/25
• 2023/24
• 2022/23
• 2021/22
• 2020/21
• 2019/20
• 2017/18 (old code MA2E01)
• 2016/17 (old code MA2E01)
• 2015/16 (old code MA2E01)
• 2014/15 (old code MA2E01)
• 2013/14 (old code MA2E01)
• 2012/13 (old code MA2E01)

Papers open on tcd.ie (sign in to TCD first).

Topics

• Euclidean n-space, linear transformations and their matrices LO1
• Subspaces, span, linear independence, basis and dimension LO2–3
• Row, column and null spaces; rank and nullity LO4–5
• General and particular solutions of linear systems LO1, LO8
• Inner products, orthogonal projections, Gram-Schmidt LO7
• Eigenvalues and eigenvectors LO6
• Fourier series: Euler formulas, even and odd functions, half-range series LO9–10
• Fourier integral and Fourier transform LO11

Learning outcomes

1. Relate linear systems, linear transformations and matrices
2. Check linear independence and whether vectors form a basis
3. Find the dimension of a subspace
4. Find the rank and nullity of a matrix
5. Find bases for the row, column and null spaces
6. Find eigenvalues and eigenvectors
7. Orthogonalise a basis with Gram-Schmidt
8. Solve ODEs with general and particular solutions
9. Find and analyse Fourier series
10. Use Fourier series to solve ODEs
11. Find Fourier transforms

Summarised from the module descriptor, checked November 2026.