• To make the students familiarize with Mathematical Modeling of physical systems using differential equations advanced techniques of integration, tracing of curve, multiple integrals and their applications. The aim is to equip them with the techniques to understand advanced level mathematics and its applications that would enhance thinking power, useful in their disciplines.

The students will be able to 

C008.1:- learn the effective mathematical tools for solutions of first order differential equations.

C008.2:- apply mathematical tools to model physical processes such as Newton’s law of cooling, electrical circuit, rectilinear motion, mass spring systems, heat transfer etc.  

C008.3:- learn advanced integration techniques such as Reduction formulae, Beta functions, Gamma functions, Differentiation under integral sign and Error functions needed in evaluating multiple integrals and their applications. 

C008.4:- trace the curve for a given equation and measure arc length of various curves. 

C008.5:- learn the concepts of solid geometry using equations of sphere, cone and cylinder in a comprehensive manner. 

C008.6:- learn the evaluation of multiple integrals and its application to find area bounded by curves, volume bounded by surfaces, Center of gravity and Moment of inertia. 

Exact differential equations, Equations reducible to exact form,Linear differential equations, Equations reducible to linear form,Bernoulli's equation.

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.

Reduction formulae,Beta and Gamma functions,Differentiation under integral sign,Error function.

Tracing of curves,Cartesian curves,Polar curves,Parametric curves,Rectification of curves.

Cartesian coordinate system,Spherical polar coordinate system,Cylindrical coordinate system,Sphere,Cone,Cylinder.

Double and triple integrations,Applications to find:- Area, Volume, Mass, Center of gravity, Moment of inertia.