Co-ordinate geometry of two dimensions:
Change of axes, transformation of co-ordinates, simplification of equations of curves, General equation of second degree, Straight line, Circle, Parabola, Ellipse, Hyperbola.
Co-ordinate geometry of three dimensions:
Systems of co-ordinate, distance of two points, Section formula, projection, direction cosines, Equations of planes and lines, sphere, Cone, Central conicoid.
Addition and multiplication of vectors, Application to geometry and mechanics, triple product and multiple products, linear dependencies and independence of vectors, Definition of line, surface, and volume integrals, Vector spaces.
Differentiation of vectors with application, Gradient of a scalar function, Divergence and curl of a vector function, Physical significance of gradient, divergence and curl, Vector integration, divergence theorem, Stock’s theorem, Green’s Theorem and their application. Curvilinear coordinate.
Complex number system, General functions of complex variable limits and continuity of function of complex variable and related theorems, Complex differentiation and the Canchy Riemann equation, Infinite series, Convergence and uniform convergence, Line integral of a complex function, Canchy integral formula, Lionville’s theorem, Taylor’s and Lorenz’s theorem, Singular points, Residue, Chantey’s residue theorem.