2BA1: the second half-year


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Course Content

The purpose of this course is to give an overview of some important ideas and techniques in mathematics. We will discuss ordinary differential equations, Fourier analysis, quaternions.
  • Ordinary differential equations. Examples.
  • Homogeneous equations with constant coefficients. Operator notation and its applications.
  • Inhomogeneous equations with constant coefficients.
  • Numerical methods of solving ordinary differential equations.
  • Integral inner product. Orthogonality of trigonometric functions.
  • Fourier series. Applications of Fourier series. Euler's formula for the sum of inverse squares.
  • Discrete Fourier transform. Application to multiplication of large integers.
  • Quaternions, vectors in 3-space, and rotations.
  • Basics of number theory. Number theory and cryptography.


There will be two home assignments during the second half of the year. You can find some lecture notes related to this course on the course web page maintained by David Wilkins.

Homework due March 5 [PS] [PDF]
Homework due May 2 [PS] [PDF]

Tutorial, February 20 [PS] [PDF]
Tutorial, April 4 [PS] [PDF]
Tutorial, April 18 [PS] [PDF]

Lecture notes for the second half-year (draft) [PS] [PDF]
For lecture notes for the 6th/7th week (vectors, quaternions and rotations), refer to lecture notes of Dr.David Wilkins:
Vectors (pdf file), Quaternions and rotations (pdf file).

Check timetables to find out the examination date.

You might be interested in looking at past exam papers. They are accessible here.