Module MAU22E01: Engineering Mathematics III

See also School of Engineering MAU22E01 page and School of Mathematics MAU22E01 page

School of Mathematics, Trinity College

Lecturer Dmitri Zaitsev

Requirements/prerequisites: MAU11E01, MAU11E02
Number of lectures per week: 3 + 1 tutorial (tutorials starting week 2)
Duration: 11 weeks

The Annual Exam will have 6 questions. Credit will be given for the best 5 questions. Assignments count 10% and Final Exam 90%. Supplemental Exam counts 100%. Examination material is within the scope of the problem sheets.

Organization and Content:

For up-to date information, please see the module page MAU22E01-A-SEM101-202021 ENGINEERING MATHEMATICS III on TCD Blackboard.


To be posted regularly to Blackboard as videos with slides, starting from the first week (of Sept 28). I'll be sending respective announcements through Blackboard at the beginning.


Weekly live online, starting the week of Oct 5-9, via Microsoft Teams through channels set for each group: Groups 1/2/3: Wednesday at 1pm, Groups 4/5: Friday at 12pm, Group 6 (MSISS): Wednesday at 11am.


Problem sheets will be posted in advance for each tutorial. Only some of the sheets will be marked (not the first sheet), to ease the burden of the online submission and marking, and contribute for 10% of your total mark. It is important to be able to do all the problems, including unmarked ones, to ensure you are prepared for the exam.

Public Discussion Forum on Gitlab:

An alternative to our Discussion Board on Blackboard. Please join to ask questions, give feedback or help others if you know answers. Unlike many other forums, here you can type mathematics formulas in Latex, and that feature will make it more convenient for us to give a better answer by including properly looking mathematical formulas. Gitlab is an important discussion/collaboration tool (not only for coding projects) that we are using as a forum. Also beneficial for strengthening TCD Graduate Attributes.

Module outline:

Linear Algebra: Chapters 3-6 (11th and 10th edition) or 3-7 (9th edition) in Anton-Rorres' book "Elementary Linear Algebra (with applications)". Euclidean n-Space and n-Vectors, Operations with them. 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 Nullspace of a Matrix. Finding Bases for them using Elementary Row Operations. Rank and Nullity of a Matrix. Inner Products, Lengths, Distances and Angles relative to them. Orthogonal and Orthonormal Bases relative to an Inner Product. Orthogonal projections to Subspaces. Gram-Schmidt Process. Eigenvalues, Eigenvectors and Diagonalization of Square Matrices. Applications to Systems of Ordinary Differential Equations.

Fourier Analysis: Chapter 11 (in 10th ed.) in Kreyszig' book "Advanced Engineering Mathematics". Fourier Series for periodic functions. Euler Formulas for the Fourier Coefficients. Even and Odd Functions. Fourier Cosine and Fourier Sine Series for them. Fourier Integral and Fourier Transform.

Lecture Notes:

To appear, feel free to check the old rough hand-written Lecture Notes (not essential for understanding the material): here, here, here and here for applications to ODE

Links to explore to deepen your knowledge:

Calculus for Beginners and Artists by Daniel Kleitman
Multivariable Calculus Online by Jeff Knisley
Linear Algebra:
Importance of Linear algebra in Engineering Design Methodology by Mysore Narayanan (PDF file)
Linear Algebra Toolkit by Przemyslaw Bogacki
Java applet introducing 3-vectors by Maths Online
Matrix Algebra Tutorials by S.O.S. MATHematics
A Linear Algebra book by Jim Hefferon
An Intuitive Guide to Linear Algebra by Better Explained
The beauty I see in algebra by Margot Gerritsen at TEDxStanford
Vector algebra by Math Insight.
Fourier Theory:
An Interactive Guide To The Fourier Transform by Better Explained
Intuitive Understanding Of Euler’s Formula by Better Explained
Beautiful Fourier series visualisation with d3.js
Beautiful WebGL water simulation by Evan Wallace and the author's article about it
How should mathematics be taught to non-mathematicians? by Timothy Gowers (1998 Fields Medal)
Why Do We Learn Math? by Better Explained
The Crowdsourced Guide to Learning maintained by the online learning platform FutureLearn

Past 2E1/2E2 web pages:

2E01 2019 by Dmitri Zaitsev with Problem Sheets.
2E01 2018 by Dmitri Zaitsev with Problem Sheets and Solutions.
2E01 2017 by Dmitri Zaitsev with Problem Sheets.
2E01 2016 by Dmitri Zaitsev with Problem Sheets.
2E02 2015 by Dmitri Zaitsev with Problem Sheets.
2E02 2014 by Dmitri Zaitsev with Problem Sheets.
2E02 2013 by Dmitri Zaitsev with Problem Sheets.
2E02 2012 by Dmitri Zaitsev with Problem Sheets.
2E02 2011 by Dmitri Zaitsev with Problem Sheets.
2E02 2010 by Dmitri Zaitsev with Problem Sheets.
2E2 2008-09 by Dmitri Zaitsev with Problem Sheets and some Solutions.
2E2 2007-08 by Dmitri Zaitsev with Problem Sheets and some Solutions.
2E1 2006-07 Part I by Richard Timoney and Part II by Dmitri Zaitsev with Problem Sheets and some Solutions.
2E1 2005-06 by Dmitri Zaitsev with Problem Sheets and some Solutions.
2E1 2004-05 by Dmitri Zaitsev with Problem Sheets and some Solutions.
2E1 2003-04 by Fermin Viniegra with many interesting links.

Past examinations:

TCD examination papers (2012 - present)
TCD examination papers (1998 - 2012)
School of Mathematics examination papers (1992 - 2000)

For Scholarship exam related problems see also years 2009 and 2008 papers.

Student Counselling Service


I will appreciate any (also critical) suggestions that you may have for the module. Let me know your opinion, what can/should be improved, avoided etc. and I'll try my best to take it into account.