Engineering Mathematics - Ii

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, Mass and Spring systems, 1-Dimensional Conduction of Heat. Chemical problems.Solid Geometry Cartesian, Spherical Polar and Cylindrical Coordinate System, Relation between Coordinate System Sphere, Cone and Cylinder, Solids of Revolution.Fourier Series (FS)Definition, Dirichlet's conditions, Full Range FS, Half Range FS Harmonic Analysis and Application to Problems in Engineering.Integral Calculus : Reduction formulae for Trigonometric functions. Beta and Gamma functions.Integral Calculus :Differentiation Under the Integral Sign (DUIS). Error functions.Curve Tracing : Tracing of Cartesian, Polar and Parametric Curves. Rectification of Curves.Multiple Integrals and their ApplicationsDouble and Triple integrations and its applications to Areas, Volumes, Mean and Root Mean Square values, Mass, Center of gravity and Moment of Inertia.