Differential Equations : Formulation and solution of differential equations of the forms.
1) dy / dx = ƒ(x).g(y)
2) dy / dx = ƒ(y/x)
3) dy / dx = (ax+by) / (cx+dy)
4) dy / dx = (a1x+b1y+c1 ) / (a2x+b2y+c2 ), (a1/a2 = b1/b2)
5) dy / dx + p(x)y = Q(x)
6) d²y / dx² + p1dy/dx + p2y = 0 with p1 and p2 constants.
7) d²y/dx² = ƒ(x)
Ellipse and Hyperbola : Reduction to standard form of general equation of second degree when xy term is absent. Conjugate hyperbola. Simple properties. Parametric equations. Location of a point with respect to a conic.
Straight line : Slope of a line. Equation of lines in different forms, angle between two lines. Condition of perpendicularity and parallelism of two lines. Distance of a point from a line. Distance between two parallel lines.
Co-ordinate Geometry
Trigonometry
Trigonometric ratios, compound angles, multiple and submultiple angles, general solution of trigonometric equations. Properties of triangles, inverse trigonometric functions. Co-ordinate geometry of two dimensions
Probability : Classical definition, addition rule, conditional probability and Bayes’ theorem, independence, multiplication rule.
