Unit I First Order Ordinary differential Equations : Exact differential equations, Equations reducible to exact form. Linear differential equations, Equations reducible to linear form, Bernoulli’s equation.
Unit II Applications of Differential Equations : Applications of Differential Equations to Orthogonal Trajectories, Newton’s Law of Cooling, Kirchhoff’s Law of Electrical Circuits, Rectilinear Motion, Simple Harmonic Motion, One dimensional Conduction of Heat.
Unit III Integral Calculus : Reduction Formulae, Beta and Gamma functions, Differentiation Under Integral Sign and Error functions.
Unit IV Curve Tracing : Tracing of Curves – Cartesian, Polar and Parametric curves, Rectification of curves.
Unit V Solid Geometry : Cartesian, Spherical polar and Cylindrical coordinate systems, Sphere, Cone and Cylinder.
Unit VI Multiple Integrals and their Applications : Double and Triple integrations, Change of order of integration, Applications to find Area, Volume, Mass, Centre of Gravity and Moment of Inertia.