Design Process
December 8, 2016Design Terminology e = Strain δl = change in length of a body, mm l = original length of a... View Article
Categories for 1st Year Maths 2
Centre of Gravity and Moment of Inertia
December 8, 2016The centre of mass of n Point Masses Moment = (Mass) . (Lever arm) $\ov{x} = {∑↙{i=1}↖n m_i x_i}/{∑↙{i=1}↖n m_i}$... View Article
Area, Volume, Mean and Root Mean Square Values
December 8, 2016Representation of area as a double integral Type I: Area enclosed by plane curves expressed in Cartesian co-ordinates Area =... View Article
Multiple Integrals
December 8, 2016Double integration Representation of area as a double integral: $A = lim↙{δx→0} ∑↙{x=a}↖{x=b} y . δx$ Expressed in integral notation... View Article
The Cone and the Cylinder
December 8, 2016Cone with vertex at the origin $ax^2 + b y^2 + c z^2 + 2 fyz + 2 gzx +... View Article
Sphere
December 8, 2016Equations of sphere in different forms (A) Centre and radius form $(x – a)^2 + (y – b)^2 + (z-c)^2... View Article
Co-ordinate System, Plane, Straight Line and Solids of Revolution
December 8, 2016Relations between three coordinate systems Relations between cartesian and spherical polar system of coordinates are x = r sinθ cosϕ... View Article
Curve Tracing and Rectification of Curves
December 8, 2016Rectification of plane curve when its equation is in polar form r=f(θ) 1. r = f(θ) $s = ∫↙{θ_1}↖{θ_2} √{r^2... View Article
Differentiation Under the Integral Sign and Error Functions
December 8, 2016Rule I: Integral with limits (a, b) as constants If I(α) = $∫↙{a}↖b f(x, α) dx, then {dI}/{dα} = ∫↙{a}↖b... View Article
Reduction Formulae, Beta and Gamma Functions
December 8, 2016Reduction formulae for sinusoidal functions 1. To find reduction formula for $∫ sin^n x dx$, n is positive integer ≥... View Article