Mathematics for Marine Engineering

Methods of Integration

Integration is not as easy as differentiation. This is first due to…

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August 6, 2021

Integral Calculus

Gottfried Wilhelm Leibnitz (1646-1716) and Sir Isaac Newton (1643-1727) independently discovered calculus…

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August 6, 2021

Lagrange Multipliers

In the previous section we optimized (i.e. found the absolute extrema) a function…

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August 6, 2021

Finding Maxima and Minima using Derivatives

Where is a function at a high or low point? Calculus can…

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August 6, 2021

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)…

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August 6, 2021

Euler’s Homogeneous Function Theorem

Let  be a homogeneous function of order  so that (1) Then define  and . Then (2)(3)(4) Let , then…

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August 6, 2021

Homogeneous Functions

To be Homogeneous a function must pass this test: f(zx,zy) = znf(x,y) In other…

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August 6, 2021

Higher-Order Partial Derivatives

Fred has mastered differentiating when a function has only one variable. Somehow,…

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August 6, 2021

Geometry of partial derivatives

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August 6, 2021

Partial Derivatives

Now that we have the brief discussion on limits out of the…

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August 6, 2021