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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 F′(x) if F (x) = √[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…
Posted inMathematics for Marine Engineering
Higher-Order Partial Derivatives
Fred has mastered differentiating when a function has only one variable. Somehow, he missed the…
Posted inMathematics for Marine Engineering
Partial Derivatives
Now that we have the brief discussion on limits out of the way we can…
Posted inMathematics for Marine Engineering
Limits and Continuity
The concept of the Limits and Continuity is one of the most crucial things to understand…
Posted inMathematics for Marine Engineering
Indeterminate Forms and l’Hospital’s Rule
In this section, we examine a powerful tool for evaluating limits. This tool, known as L’Hôpital’s…
Posted inMathematics for Marine Engineering
Taylor’s Theorem
One of the most important uses of infinite series is the potential for using an…