Syllabus
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Course Code: MT-402 Course Name: Numerical Analysis |
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| MODULE NO / UNIT | COURSE SYLLABUS CONTENTS OF MODULE | NOTES |
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| 1 | Round-off error and computer arithmetic, Local and global truncation errors, Algorithms and convergence. Numerical methods for solving algebraic and transcendental Equations: Bisection method, false position method, fixed point iteration method, Newton-Raphson method and secant method. Newton’s iterative method for finding pth root of a number. | |
| 2 | Numerical methods for solving simultaneous linear equations: Gauss-elimination method, Gauss-Jordan method, Triangularization method (LU decomposition method). Crout’s method, Cholesky Decomposition method. Iterative method; Jacobi’s method, Gauss-Seidal method, relaxation method. | |
| 3 | Finite Differences operators and their relations. Interpolation with equal intervals: Gregory-Newton forward and backward difference interpolations. Interpolation with unequal intervals: Newton’s divided difference formulae, Lagrange’s Interpolation formulae. Central Differences: Gauss forward and Gauss’s backward interpolation formulae. Sterling formula, Bessel’s formula. Piecewise linear interpolation, Cubic spline interpolation. Numerical Differentiation: First and second derivative of a function using interpolation formulae. |
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| 4 | Numerical Integration: Newton-Cote’s Quadrature formula, Trapezoidal rule, Simpson’s one- third and three-eighth rule, Chebychev formula, Gauss Quadrature formula. Numerical solution of ordinary differential equations: Single step methods- Picard’s method. Taylor’s series method, Euler’s method, Runge-Kutta Methods. Multiple step methods; Predictor-corrector method, Modified Euler’s method, Milne-Simpson’s method. |
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