First Year Engineering Mathematics.

This page contains resources for the first year, lent term, course in engineering mathematics. It covers convolution, Fourier series and an overview of probability.

• Course notes
• Files for use with the examples papers
• Sample exam questions (2011) relating to Section 10 of the notes on Statistics
• Convolution demo by Prof Erik Cheever, Department of Engineering, Swarthmore College, Pennsylvania
• Fourier series demo (and others), by Center for Signal and Image Processing (CSIP), Georgia Institute of Technology.
• 1A Maths 2001, Paper 4, Question 6 (adapted).
• Answer to 1A Maths 2001, Paper 4, Question 6 (adapted).
• 1A Maths 1997, Paper 4, Question 9.
• Answer to 1A Maths 1997, Paper 4, Question 9.
• Matlab demo of solution to 1A Maths 1997, Paper 4, Question 9.
• Experimental video of the 2008 lectures. Beware that there are some differences between the 2008 lectures and the 2009/10 lectures. There are a small number of corrections, a couple of extra slides giving motivating examples and the Fourier series notation has been changed to maintain consistency with the new Maths data book that was issued in Ocober 2008.

Videos of the 2009 lectures

These lectures are substantially the same as those that are being given in Lent 2010. In 2010 there are small corrections and updates to slides number 16, 20, 24, 25, 42, 60, 76, 112, 119 and 142 but otherwise the notes are identical to the 2009 version.

• Lecture 1 Linear systems, superposition, step function, step response, delta function and impulse response.
• Lecture 2 Finding the impulse response from a differential equation and convolution.
• Lecture 3 Alternative form of the convolution integral, causal systems, convolution in space and spatially varying impulse responses.
• Lecture 4 Fourier series for part of a function of length 2π. Odd and even functions and the conditions for various Fourier coefficients to be zero.
• Lecture 5 General range Fourier series. Three ways of finding a Fourier series: direct, integrating impulses and using the maths data book.
• Lecture 6 Fourier series rate of convergence. Building the series with a period longer than the thing you want to model to improve convergence or reduce the number of integrals that you need to evaluate.
• Lecture 7 Complex Fourier series. Converting between the complex series and the sin/cos series.
• Lecture 8 Worked examples of questions on convolution and Fourier series.
• Lecture 9 Introduction to the probability topics covered in the teach-yourself booklet.

The same videos are also available, in a variety of formats, from the University's streaming media service.

Lecture 8: Worked Tripos Question Examples, Wednesday 3rd March 2010.

Lecture 9, Section 10 of the handout: Statistics, Wednesday 16th March 2011.

Updated: Feb 2009