Tuesday 10am Salmon Lecture Theatre: Aideen Griffin

Tuesday 10am M21 Museum Building: Francisco Garcia Abad

Wednesday 9am 1.20 Lloyd Building: Francisco Garcia Abad

Thursday 9am Salmon Lecture Theatre: Aideen Griffin

Thursday 9am Drawing Office Museum Building: Francisco Garcia Abad

Rough hand-written Lecture Notes can be found here, here, here and here for applications to ODE

Problem Sheets in PDF: Sheet 1 Sheet 2 Sheet 3 Sheet 4 Sheet 5 Sheet 6 Sheet 7 Sheet 8 Sheet 9

Most solutions to the exercises are very similar to those older ones that can be found here, here and here and here. Solutions to the last two exercises from 2015 are here.

**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 (see Example 7 in Chapter 6.3). Eigenvalues and Eigenvectors of Square Matrices.

**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.

Calculus for Beginners and Artists by Daniel Kleitman

Multivariable Calculus Online by Jeff Knisley

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

An Interactive Guide To The Fourier Transform by Better Explained

Intuitive Understanding Of Eulerâ€™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

2E01 2017 by Dmitri Zaitsev with Problem Sheets and Solutions.

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.

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