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I have a numerical analysis course, Course content is as follows can anyone recommend me a good book or several books which covers these areas. If the book gives an intuitive idea it would be better.

Solving system of linear equations

  • Direct Methods

• Algebraic Process • Gaussian Elimination • Gauss-Jordan Elimination • Matrix-Factorization (Triangularization)

  • Iterative Methods

• Gauss-Jacobi Method • Gauss-Seidel Method • Convergence of Relaxation

Interpolation Methods

•Linear Interpolation •Newton’s Divided Difference Formula (Polynomial Approximations) •Newton’s Forward Difference Interpolation •Cubic Spline Interpolation

Solving ODE

•Method of Starting the solution (Taylor (power) series approach) •Picard’s Method of Successive Approximations •Euler’s Method •Improved Euler’s Method •Modified Euler’s Method •Runge-KuttaMethod •Predictor-Corrector Method

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    $\begingroup$ Store and Bulirsch is another good book to be aware of. $\endgroup$ – littleO Dec 11 '18 at 2:55
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Numerical Analysis by Richard L. Burden and J. Douglas Faires covers all the topics you have mentioned and it's a good book with proper explanations.

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