School of Mathematics, Trinity College

Course 2E02 - Mathematics for SF Engineering, MSISS and MEMS 2010 (click for more information)

(SF Engineers & MSISS & MEMS)

Lecturer Dmitri Zaitsev

The exam will have 6 questions. Credit will be given for the best 5 questions.

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

There will be no new sheets.

Every problem in the calculus of variations has a solution, provided the word solution is suitably understood. -- David Hilbert

Course outline:

Linear Algebra (Chapters 4-7 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). Best Approximation by the Least Squares method. Eigenvalues and Eigenvectors of Square Matrices.

Fourier Analysis (Chapter 10 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.

Helpful links.
Calculus for Beginners and Artists by Daniel Kleitman.
Multivariable Calculus Online by Jeff Knisley
Taylor's formula, linear and quadratic approximations by Eric A. Carlen
Linear Algebra:
Working with Vectors (A Self-Help Workbook for Science and Engineering Students by Jenny Olive)
Java applet introducing 3-vectors by Maths Online
Matrix Algebra Tutorials by S.O.S. MATHematics
A Linear Algebra book by Jim Hefferon (PDF file)
Importance of Linear algebra in Engineering Design Methodology by Mysore Narayanan (PDF file)

Old 2E1/2E2 web pages.
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.

For exam-related problems look in TCD past examination papers and Mathematics department examination papers.

Student Counselling Service

I will appreciate any (also critical) suggestions that you may have for the next term. Let me know your opinion, what can/should be improved, avoided etc. and I will do my best to follow them. Please use the feedback form from where you can also send anonymous messages.