JNTU
JNTU B.Tech II MATHEMATICS-II Previous Question Paper (April/May - 2023 - R15)
Note: i) Question paper consists of Part A, Part B. ii) Part A is compulsory, which carries 25 marks. In Part A, Answer all questions. iii) In Part B, Answer any one question from each unit. Each question carries 10 marks and may have a, b as sub questions.
Part A
Define a scalar point function and give an example.
Answer
A scalar point function is a function that assigns a unique scalar value to every point in a given region of space. For example, the temperature distribution in a room, defined by
State Green's theorem in a plane.
Answer
Green's theorem states that if C is a simple closed curve in the xy-plane enclosing a region R, and M and N are functions of x and y having continuous partial derivatives in R, then:
Write the Dirichlet’s conditions for a Fourier series.
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Define Fourier sine and cosine integrals.
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Define finite backward differences.
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Write the normal equations in fitting a straight line.
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Explain Regula falsi method.
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Describe LU decomposition method in brief.
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Write the Simpson’s 1/3rd rule.
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Explain Taylor’s series method.
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Part B
Find the directional derivative of
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For any closed surface S, prove that
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Evaluate div F and curl F, where
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Find the Fourier series in (-π, π) for the function f(x) = -x for -π < x < 0 and sin x for 0 < x < π. Hence deduce the sum of the series 1/(1.3) - 1/(3.5) + 1/(5.7) ...
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Find the Fourier transform of f(x) = a2 - x2 for |x| < a and 0 for |x| > a, and hence show that
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Using Newton’s forward or backward interpolation formula and the table of values: x: 1.1, 1.3, 1.5, 1.7, 1.9; f(x): 0.21, 0.69, 1.25, 1.89, 2.61. Obtain the value of f(x) when x = 1.2 and x = 1.8.
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By the method of least squares, find the second degree parabola that best fits the following data: X: 1, 2, 3, 4; Y: 14, 27, 40, 55.
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Find real root of the equation x3 = ex by Bisection method.
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Find a real root of 10x + x = 1.2 using Newton-Raphson method.
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Solve the following system of equations using Gauss Seidel iterative method: 28x + 4y - z = 32; x + 3y + 10z = 24; 2x + 17y + 4z = 35.
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Compute ∫0π sin x dx using Trapezoidal rule, and compare with exact value.
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Using Runge-Kutta method of order 4, solve dy/dx = (y2 - x2) / (y2 + x2) with y(0) = 1 at x = 0.2, 0.4.
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