Calendar: 1951-1952 Page 198

SYLLABUSES OF COURSES 199 MATHEMATICS Pure and Applied PART Revision of dynamics vector and scalar quantities angular motion easy cases of impulsive forces rotation of rigid bodies about fixed point relation of torque and angular acceleration moment of momentum angular kinetic energy first and second moments of area and moments of inertia radius of gyration units-C and ft lb sec systems and conversions between these Differentiation and integration of algebraic trigonometric exponen- tial logarithmic and hyperbolic functions Maxima and minima of single variable Technique of integration including change of variable use of identi- ties and partial fractions Integration by parts Definite integrals including applications to arcs areas volumes first and second moments Formation and solution of simple first order differential equations Taylor's and Maclaurin's series and other simple methods of expansion Approximate graphical and numerical solution of equations Simple geometrical properties of the circle parabola ellipse and hyperbola Complex numbers and de Moivre's theorem Radius of curvature Introduction to the catenary PART II Partial differentiation Maxima and minima of functions of several independent variables Multiple integrals Change of independent variables Vector algebra and analysis Line surface and volume integrals Differential equations including first and second order equations integrable by quadratures linear differential equations with constant coefficients equations reducible to these and simultaneous linear equations with constant coefficients Orthogonal systems of curves particularly coaxal circles and confocal conies Pole and polar Use of inversion Simple partial differential equations The Poisson and Laplace Equations Spherical Trigonometry Fourier Series and numerical harmonic analysis Use of determinants Three dimensional co-ordinate geometry of straight lines planes and simple surfaces with their tangent planes and normals