Introductory Numerical Analysis Assignment help, Introductory Numerical Analysis Online Experts
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Differential equation, integral equation, approximation theory, linear and non linear algebra are some important concept of numerical analysis. For solving engineering problems, numerical analysis uses its tools. These tools are computer graphics, GUI, symbolic mathematical computations. Partial differential equation problem can be solved by the finite element method in a variety of engineering fields including fluid dynamics, heat transfer and stress analysis.
- Floating point arithmetic
- Catastrophic cancellation
- Quadratic equation formula
- Horner's method
- Lagrange interpolation.
- Linear algebra
- Sparse matrices
- Vector norms
- Error bounds
- Matrix norms
- Nonlinear equations
- Bisection method
- Fixed point iteration
- Newton's method
Topics for Introductory Numerical Analysis Assignment help :
- Preliminaries of Computing, Basic concepts: round-off errors, floating point arithmetic, Convergence, Numerical solution of Nonlinear Equations, Bisection method, fixed-point iteration, Newton’s method, Error analysis for Iterative Methods, Computing roots of polynomials, Interpolation and Polynomial Approximation, Lagrange Polynomial, Divided Differences, Hermite Interpolation, Numerical integration and differentiation, Trapezoidal rule, etc.
- Gaussian quadrature and Euler-Maclaurin formula, Applied Linear Algebra, Direct methods for solving linear systems, numerical factorizations, Eigenvalue problems, IVP problems for ODE, Euler’s, Taylor, Runge-Kutta, and multistep methods, Stability
- Numerical linear algebra, Direct methods, Iterative methods, Approximation theory, Least square approximation, Approximating Eigenvalues, Power method, Householder’s method, BVP for ODE, Shooting methods, Course invitation, Evaluation of infinite sums, Numerical integration of functions: Newton-Cotes quadrature , Application to improper integrals, Heuristic convergence analysis of Newton-Cotes quadrature, Numerical integration of ODEs, Reduction of high-order ODEs to first-order form , Euler's method, Numerical integration of ODEs: Beyond Euler's method,Convergence analysis of the improved Euler method ,Runge-Kutta methods.
- Adaptive stepsizing, Pathologies in ODE solvers: Stability, stiffness, and implicit methods , Pathologies in ODEs themselves: non-uniqueness and non-existence , Boundary-value problems; shooting methods , The beam equation, Richardson extrapolation , Numerical differentiation: finite-difference stencils
- Finite-difference approach to boundary-value problems, Computer representation of numbers: fixed- and floating-point arithmetic , Exactly representable numbers and rounding errors , Catastrophic loss of floating-point precision, Computer representation of numbers: Accumulation of rounding errors , Numerical stability of forward and backward recurrence relations for special functions, Numerical root-finding: Sample problems and 1D methods, Convergence of Newton's method, Newton's method in higher dimensions, Monte-Carlo integration, Fourier analysis: The fourfold way, Parseval, Plancherel, and Poisson formulas, Paley-Wiener theorems.
- Convolution, Fourier series, Applications of Fourier analysis, Ewald summation, Rigorous convergence analysis of Newton-Cotes quadrature, Clenshaw-Curtis quadrature , Discrete Fourier transforms, DFT and its uses, Signal processing, arbitrary-precision arithmetic, discrete convolution , PDE solvers, Orthogonal polynomials , Gauss-Legendre quadrature, Applications of Fourier analysis, Modulation, Wireless communications and lock-in amplifiers, Spectral efficiency of telecommunications coding schemes
Complex topics covered by Introductory Numerical Analysis Assignment Online experts :
- Integral equations, Nystrom's method, Numerical linear algebra , dense-direct and sparse-iterative algorithms, PDE solvers, Numerical nonlinear algebra: Resultants and tensor eigenvalues, the bisection method of solving equations, Newton-Raphson method of solving equations, Lagrange polynomial interpolation
- Newton-Cotes quadrature , Gaussian quadrature, Romberg quadrature, Taylor method of solving differential equations , Picard method of solving differential equations , Runga-Kutta method of solving differential equations, adaptive step-size solutions of differential equations
- Richardson extrapolation , queueing theory and simulation , Monte-Carlo integration , splines and curve-fitting methods