Module Identifier MA10110  
Academic Year 2000/2001  
Co-ordinator Dr V C Mavron  
Semester Semester 1  
Other staff Professor T N Phillips  
Pre-Requisite A-level Mathematics or equivalent.  
Course delivery Lecture   20 x 1 hour lectures  
  Seminars / Tutorials   6 x 1 hour tutorials  
  Workshop   2 x 1 hour workshops (including test)  
Assessment Exam   2 Hours (written examination)   75%  
  Continuous assessment     25%  
  Resit assessment   2 Hours (written examination)   100%  

General description
This module introduces some of the fundamental notions of geometry - points, lines, curves, planes and surfaces - analytically, in the language of coordinate geometry. Conics are classified in terms of their equations and geometric properties. The concepts of tangent and normal are developed. There are brief introductions to protective geometry and to vector methods.

To develop geometric intuition and the ability to view geometric problems analytically and vice versa.

Learning outcomes
On completion of this module, a student should be able to:

1. COORDINATE GEOMETRY IN THE REAL PLANE: The straight line. Conics - particular forms and the general form. Identification of centres, foci and major and minor axes. Cases of degeneracy. Changes of axes. The general equation of the tangent. Families of lines and conics. Parametric plane curves. Tangents and the use of derivatives.
2. INTRODUCTION TO VECTOR METHODS: Unit vectors. Scalar products, angles and orthogonality. Position vectors. Centroids and orthocentres. Vector equations of lines and planes.
3. GEOMETRY IN REAL 3-SPACE: Cartesian coordinates. Equations of lines and planes. The normal. Curves, their tangents and other special direction. Surfaces and their tangent planes. Polar coordinates.

Reading Lists
** Recommended Text
R L Finney and G B Thomas. (1994) Calculus. 2nd. Addison-Wesley