MTH381
Question: Let \\(f(x,y)=x^2-3xy+6y)\\) find \\(f(2,3)\\)\n
Answer: 4
Question: Evaluate \\(\\int_{-1}^{1}\\int_{0}^{z}\\int_{x-z}^{x+z}(x+y+z)dzdxdy\\)
Answer: \\(0\\)
Question: Let f(x) be a single real valued function in the interval a\\leqslant x\\leqslant b, the line integral is define as:
Answer: \\(\\int_{a}^{b}f(x)dx\\)
Question: A line integral of a vector function F® over a curve C is defined by
Answer: \\(\\int_{C}F(r)dr\\)
Question: Evaluate \\(\\int_{0}^{1}\\int_{0}^{1}(x^2+y^2)dydx\\)
Answer: \\frac{2}{3}
Question: Find the Jacobian of \\(u=x^2+y^2, v=2xy\\)\n\n
Answer: \\(4(x^2+y^2)\\)
Question: The Harmonic function \\(\\triangledown^2f=0\\) is called the ….
Answer: Laplace equation
Question: In queestion one u is called the ….?
Answer: dependent variable
Question: Let \\(u=f(x,y)\\) then the variables x and y are called…:\n
Answer: independent variables
Question: Find the Jacobian \\(\\frac{\\partial(u,v)}{\\partial(x,y)}\\) of the following \\(\\frac{\\partial(u,v)}{\\partial(x,y)} \\(u = x+\\frac{y^2}{x}, v=\\frac{y^2}{x}\\)\n\n
Answer: \\(\\frac{2y}{x}\\)
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