Posted inMechanics of Marine Machines
Kinematic Inversion
Every mechanism has moving members which move relative to each other about the joints connecting…
Posted inMathematics for Marine Engineering
Methods of Integration
Integration is not as easy as differentiation. This is first due to its nature. Finding…
Posted inMathematics for Marine Engineering
Cartesian Coordinates
Using Cartesian Coordinates we mark a point on a graph by how far along and how far up it is: They…
Posted inMathematics for Marine Engineering
Integral Calculus
Gottfried Wilhelm Leibnitz (1646-1716) and Sir Isaac Newton (1643-1727) independently discovered calculus in the mid-17th…
Posted inMathematics for Marine Engineering
Lagrange Multipliers
In the previous section we optimized (i.e. found the absolute extrema) a function on a region…
Posted inMathematics for Marine Engineering
Finding Maxima and Minima using Derivatives
Where is a function at a high or low point? Calculus can help! A maximum…
Posted inMathematics for Marine Engineering
Examples on Chain Rule (Differentiation Rules)
Examples on Chain Rule Example 10.8 Find Fâ˛(x) if F (x) = â[x2 +1] Solution Take u = g(x) = x2 + 1 and f (u)…
Posted inMathematics for Marine Engineering
Euler’s Homogeneous Function Theorem
Let be a homogeneous function of order so that (1) Then define and . Then (2)(3)(4) Let , then (5) This can…
Posted inMathematics for Marine Engineering
Homogeneous Functions
To be Homogeneous a function must pass this test: f(zx,zy) = znf(x,y) In other words Homogeneous is when…