|Module Title||COORDINATE GEOMETRY|
|Co-ordinator||Dr V C Mavron|
|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%|
|Resit assessment||2 Hours (written examination)||100%|
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.
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.
** Recommended Text
R L Finney and G B Thomas. (1994) Calculus. 2nd. Addison-Wesley