Engineering mathematics - I

Differential Calculus Curve tracing, Curvature of Cartesian curves, Curvature of parametric and polar curves. Integral Calculus Rectification of standard curves, Areas bounded by standard curves, Volumes and surfaces of revolution of curves, Centre of gravity and moment of inertia of simple bodies by integral calculus and of composite areas by the principle of moments, Applications of integral calculus to find centre of pressure, Mean and root mean square values. Partial Derivatives Function of two or more variables, Partial differentiation, Homogeneous functions and Euler's theorem, Composite functions, Total derivatives, Derivative of implicit function, Change of variables, Jacobianes. Applications of Partial Differentiation Tangent and normal to a surface; Taylor's and Maclaurin's series for a function of two variables, Errors and approximations, Maxima and minima of function of several variables, Lagrange s method of undetermined multipliers. Solid Geometry Sphere, Cylinder, Cone, Standard conicoids (Ellipsoid, Paraboloid and Hyperboloid).Multiple Integral Double and triple integration, Change of order of integration, Change of variable, Application of double integration to find areas. Application of double and triple integration to find volumes, Beta and Gamma functions. Infinite Series Convergence and divergence of series, Tests of convergence : Comparison test, Integral test, Ratio test, Rabee's test, Logarithmic test, Cauchy's root test. Convergence and Absolute convergence of alternating series, Power series and Uniform convergence. Complex Numbers De-Moivre's theorem and applications, Exponential and logarithmic complex functions, Circular and hyperbolic functions of complex variables, Real and imaginary parts of inverse functions, Summation of trigonometric series.