Applied Mathematics

100 marks · 3 hours · 3 questions

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Applied Mathematics · all years Q. 1 · Find the directional derivative of…Q. 3 · A system of forces acts…Q. 8 · The Trapezoidal rule applied to…With this paper← 2018 2020 →

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Q. 1

(a)Find the directional derivative of f ( x , y , z ) = $f(x, y, z) = xy^2 + yz^2$ at the point $(2,-1, 1 )$ in the direction of the vector $i+2j+2k$ ?
(b)Evaluate $\oint_C (xy+y^2)dx+x^2dy$ where c is bounded by the line y = x y = x y = x and the curve y = $y = x^2$ Part (b):

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Q. 3

(a)A system of forces acts on a plate in the form of an equilateral triangle of side 2 a 2a 2 a .
(b)If a particle P move with a velocity V given by $V^2 = n^2 (ax^2 + 2bx + c)$ .

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Q. 8

(a)The Trapezoidal rule applied to $\int_0^2 f(x)dx$ gives the value 4, and the Simpson's rule gives value 2, what is the value of $f(1)$ ?
(b)Find the first two derivatives at x = 1.1 x=1.1 x = 1.1 and x = 1 x =1 x = 1 from the following data table.

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The 2019 CSS Applied Mathematics paper set by the FPSC. Question wording only; questions marked “Not yet checked” have not been compared with the official paper yet.

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