PMAT 32332: Geometry

Course code  :  PMAT 32332

Title               :  Geometry

Pre-requisites :  PMAT 22293

Learning outcomes:

Upon successful completion of the course students should be able to

• develop an intuitive understanding of the nature of general equation of second degree

• apply transformations and use symmetry to analyze mathematical situations.

• define conic sections and their properties

• explain and use various techniques for calculating tangents, normal, pair of tangents, pole and polar of conic sections

• compute lines, plane, cone, sphere, ellipsoid and hyperboloid in three dimensions

• analyze characteristics and properties of two dimensional and three-dimensional geometric shapes and develop mathematical arguments about geometric relationships

• demonstrate the knowledge of geometry and its applications in the real world.

 Course contents:

Analytical Geometry in Two Dimensions: 

• Pairs of straight lines, General equation of second degree, Translations and rotations of axes, Invariants of transformations.

Conic sections: 

• Classifying general equation of second degree into Parabolas, Ellipses, Hyperbolas, eccentricity. Equation of tangent, Pairs of tangents and chords of contact, Harmonic conjugates, Pole and Polar, Parametric treatment, Degenerate conic, Properties of conic.

Analytical Geometry in Three Dimension: 

• Coordinate system, Direction cosines and direction ratios of a line, Angle between two lines, Parallel lines, Perpendicular lines, Plane and Straight line, Shortest distance between two-non intersecting lines, Skewed lines, General Equation of the second degree, Sphere, Cone, Ellipsoid and hyperboloid, Tangent plane, Normal, Pole and Polar.

 Method of Teaching and Learning : A combination of lectures and tutorial discussions.

 Assessment : Based on tutorials, tests and end of course examination.

 Recommended Reading:

1. Chatterjee, D. (2008). Analytical Geometry, Alpha Science International.

2. Thomas, G.B. & Finney, R.L. (2008). Calculus and Analytic Geometry.

3. Maxwell, E.A. (1962). Elementary Coordinate Geometry, Oxford University press.

4. Jain, P.K. & Ahmad, K. (1994). Analytical Geometry of Two Dimensions, Wiley.

5. Kishan, H. (2006). Coordinate Geometry of Two Dimensions. Atlantic Publishers & Dist.

6. Jain, P.K. (2005). A Textbook of Analytical Geometry of Three Dimensions. New Age International.

7. McCrea, W.H. (2006). Analytical Geometry of Three Dimensions, Dover Publications, INC.