MATH 127
Vector Analysis, Matrix and Coordinate Geometry
Geometry (Two Dimensions)
Transformation of coordinates, axes and its uses, pair of straight
lines, homogeneous equations of second degree, angle between
the pair of straight lines, pair of lines joining the origin to the point
of intersection of two given curves, equation of conics and its
reduction to standard forms, circles, system of circles, coaxial
circles and limiting points, parabola, ellipse and hyperbole
(Cartesian and polar coordinates).
Geometry (Three Dimensions)
System of coordinates, direction cosines, projections, equation of
planes, straight lines and spheres.
Reference Books
1. The Elements of Coordinate Geometry by S. L. Loney.
2. An Elementary Treatise on Coordinate Geometry of Three Dimensions by Robert J.T. Bell.
3. Handouts.
Vector Analysis Multiplication of vectors by scalars. scalar and vector product of two vectors
and their geometrical interpretation, triple products and multiple products, differentiation
and integration of vectors along with elementary applications, vector geometry, definition of
line, surface and volume integrals. gradient, divergence and curl of point functions. Green’s
theorem, Gauss's theorem, Stoke's theorem and their applications.
Matrix: Definition of matrix, different types of matrices, algebra of matrices. adjoint and
inverse of a matrix, elementary transformations of matrices, matrix, polynomials, Cay- lay-
Hamilton theory with uses of rank and nullity, normal and canonical forms, solution of linear
equations, definition and properties of vector space, subspaces, basis and dimension, linear
dependence and independence of vectors.
Reference Books
1. Vector Analysis - Seymour Lipschutz. Dermis Spellman and Murray R.Spiegel, Schaum's outlines
2. Vector Analysis - M. D. Raisinghania
3. Linear Algebra by Rahman
4. Linear algebra by Howard Anton
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