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.
Application of DE : Applications of DE to orthogonal trajectories, Newton's law of cooling, Kirchhoff's law of electrical circuits, Motion under gravity, Rectilinear motion, Simple harmonic motion, One-Dimensional conduction of heat, Chemical problems.
Fourier Series : Definition, Dirichlet's conditions, Full range Fourier Series, Half range Fourier Series, Harmonic analysis and application to problems in engineering.
Integral Calculus : Reduction formulae, Beta and gamma functions.
Integral Calculus : Differentiation under the integral sign, Error functions.
Curve Tracing : Tracing of curves, Cartesian, Polar and parametric curves. Rectification of curves.
Solid Geometry : Cartesian, Spherical polar and cylindrical co-ordinate systems, Sphere, Cone and cylinder.
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.