Co-ordinate Geometry of Two Dimensions
Translation and rotation of axes, Identification of conics with their properties.
Co-ordinate Geometry of Three Dimensions
Cartesian, Cylindrical polar and Spherical polar coordinates, Distance of two points, Section formula, Projection, Direction cosines and direction ratios, Angle between two lines, Distance of a point from a line, Planes: different forms of the equation of a plane, Distance of a point from a plane, Equations of bisector of planes, Straight line: different forms of equations of straight line, Angle between a line and plane, Coplanar lines, Shortest distance between two lines, Sphere: general equation of the sphere, Tangent plane, Angle of intersection of two spheres, Cone: equation with vertex at origin, Standard equations of central conicoid.
Ordinary Differential Equations
Order and degree of ordinary differential equations, Formation of differential equations, Solutions of first order first degree differential equations by various methods, Solutions of general linear equations of second and higher orders with constant coefficients, Solution of linear homogeneous equations.
Partial Differential Equations (PDE)
Linear PDE with constant coefficients, Solution by separation of variables.
Solution of differential equations in series by the method of Frobenius, Bessel’s and Legendre’s differential equations and their solutions.