Numerical Analysis Description

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MATH 272


BS Physics





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This course provides a fundamental introduction to numerical analysis suitable for undergraduate students in Physics / Electronics, and engineering. It is assumed that the reader is familiar with calculus and has taken a structured programming course. MatLab programs are the vehicle for presenting the underlying numerical algorithms. COURSE DESCRIPTION Ch. 1 : Number representation (4H) Binary system Octal system Converting between systems Applications Ch. 2: Solutions of Equations in one variable f(x) =0 (8H) Bracketing Methods for locating a Root Initial Approximation and Convergence Criteria The Bisection Algorithm Fixed-Point iteration Newton-Raphson Method Lagrange Method Method of False Position (or Regular Falsi) Ch 3: Interpolation and polynomial Approximation (6 H) Introduction to interpolation Lagrange Approximation Newton Polynomials Aitken algorithm La formule Barycentrique Error Analysis Ch 4: Numerical Integration (6 H) Introduction to Quadrature The Rectangle Rule TheTrapezoidal Rule Gauss-Legendre integration The Simpson’s Rule Errors of Integration Applications Ch 5: Approximation Theory (6 H) Introduction Discrete Least-Squares Approximation Orthogonal Polynomials and Least-Squares Approximation Rational function and Approximation Trigonometric Polynomial Approximation Spline interpolation Curve Fitting Applications Ch 6: Solution of Differential Equations (6 H) Introduction to Differential Equations Elementary Theory of Initial-value problem Euler’s Method Higher-order Taylor Methods Runge-Kutta method Applications Ch 7: Solution of Linear Systems A.X = B (8 H) Introduction to vector and Matrix Upper (Lower) triangular Systems Gaussian Elimination and Pivoting Triangular Factorization (L.U, L.LT) Gauss-Jordan Method Gauss-Siedel (iterative Method) Ch. 8 : Lab Work: Matlab (4 H) Introduction to MatLab Solutions of Equations in one variable f(x) =0 Numerical Integration Solution of Differential Equations Approximations and errors