Unit 1 : Differential Equations (DE)
Definition, Order and Degree of DE , Formation of DE , Solutions of Variable Separable DE, Exact DE, Linear DE and reducible to these types.
Unit 2 : Application of DE
Applications of DE to Orthogonal Trajectories, Newton's Law of Cooling, Kirchoff's Law of Electrical Circuits, Motion under Gravity, Rectilinear Motion , Simple Harmonic Motion, One-dimensional Conduction of Heat, Chemical Problems.
Unit 3 : Fourier Series
Definition, Dirichlet's conditions, Full range Fourier Series, Half Range Fourier Series, Harmonic Analysis and Applications to Problems in Engineering.
Integral Calculus : Reduction formulae , Beta and Gamma functions.
Unit 4 : Integral Calculus and Curve Tracing
Integral Calculus : Differentiation Under the Integral Sign , Error functions.
Curve Tracing : Tracing of Curves, Cartesian, Polar and Parametric Curves, Rectification of Curves
Unit 5 : Solid Geometry
Cartesian, Spherical Polar and Cylindrical Coordinate Systems, Sphere , Cone and Cylinder.
Unit 6 : Multiple Integrals and their Applications
Double and Triple Integrations, Applications to Area , Volume, Mean and Root Mean Square Values, Mass, Centre of Gravity and Moment of Inertia.