Real numbers, inequalities and intervals; function, domain and range; basic co-ordinate geometry; polar co-ordinates; mathematical induction; binomial theorem; combination of functions; symmetry in functions and graphs; inverse functions; complex numbers - real and imaginary form; geometry of complex numbers; limits; on-sided limits - continuity; derivatives; Leibniz's formula; differentials; differentiation of inverse trigonometric functions; implicit differentiation; parametrically defined curves and parametric differentiation; the exponential function; the logarithmic function; hyperbolic functions; inverse hyperbolic functions; properties and applications of differentiability; functions of two variables; limits of continuity of functions of two real variables; partial differentiation; the total differential; the chain rule; change of variable in partial differentiation; antidifferentiation (integration); integration by substitution; some useful standard forms; integration by parts; partial fractions and integration of rational functions; the definite integral; the fundamental theorem of integral calculus and the evaluation of definite integrals; improper integrals; numerical integration; geometrical applications of definite integrals; centre of mass of a plane lamina (centroid); applications of integration to the hydrostatic pressure on a plate; moments of inertia; sequences; infinite numerical series; power series; Taylor and Maclaurin series; Taylor's theorem for functions of two variables - stationery points and their identification; Fourier series; determinants; matrices - equality, addition, subtraction, scaling and transposition; matrix multiplication; the inverse matrix; solution of a system of linear equations - Gaussian elimination; the Gauss-Seidel iterative method; the algebraic eigenvalue problem; scalars, vectors and vector addition; vectors in component form; the straight line; the scalar product (dot product); the plane; the vector product (cross product); applications of the vector product; differentiation and integration of vectors; dynamics of a particle and the motion of a particle in a plane; scalar and vector fields and the gradient of a scalar function; ordinary differential equations - order and degree, initial an boundary conditions; first order differential equations solvable by separation of variables; the method of isoclines and Euler's methods; homogeneous and near homogeneous equations; exact differential equations; the first order linear differential equation. (Part Contents)
