PMAT 32632: Geometry

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Course code  :  PMAT 32632

Title               :  Geometry

Pre-requisites :  PMAT 22583

 

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
  • define conic sections and their properties
  • explain and use various techniques for calculating tangents, normals pair of tangents, pole and polar of conic sections
  • compute lines, plane, cone, sphere, ellipsoid and hyperboloid in three dimension
  • choose appropriate mathematical functions to model physical phenomena

 Course contents:

Analytical Geometry in Two Dimensions: Pairs of straight lines, General equation of second degree, Translations and rotations of axes,

Conic sections: Parabolas, Ellipses, Hyperbolas, Classifying conic sections by eccentricity.  Equations  of tangents, Pairs of tangents and chords of contact, Harmonic conjugates, Pole and Polar, Invariance, Reduction to standard forms of conic, Parametric treatment, Degenerate conic, Properties of conic, Matrix methods.

Polar equations of straight lines, circles and conics.

Analytical Geometry in Three Dimension: Vector Equations of a line, plane and sphere, Cone ellipsoid and hyperboloid. Tangent plane, Normal, Pole and Polar, Ruled surfaces, General Equation of the second degree.

 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. and 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.
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