Applied Numerical Methods - Amaleswari, P.; Krishna Veni, B.; Bharath Kumar, P.
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1. Algebraic and Transcendental Equations 1. Overview: This section introduces methods for solving algebraic and transcendental equations. 2. Key Topics: * Iteration, Secant, Newton-Raphson, and Regula-Falsi Methods: Methods for iterative solutions. * Error Analysis: Discusses errors in numerical calculations. * Bisection Method: A root-finding method for continuous functions. 2. System of Linear Equations and Eigenvalue Problems 3. Overview: Focuses on solving systems of linear equations and eigenvalue problems. 4. Key Topics: * Solving Linear Equations: Gauss-Seidel iteration and…mehr

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1. Algebraic and Transcendental Equations 1. Overview: This section introduces methods for solving algebraic and transcendental equations. 2. Key Topics: * Iteration, Secant, Newton-Raphson, and Regula-Falsi Methods: Methods for iterative solutions. * Error Analysis: Discusses errors in numerical calculations. * Bisection Method: A root-finding method for continuous functions. 2. System of Linear Equations and Eigenvalue Problems 3. Overview: Focuses on solving systems of linear equations and eigenvalue problems. 4. Key Topics: * Solving Linear Equations: Gauss-Seidel iteration and LU-Decomposition. * Special Matrices: Tridiagonal systems and the Thomas algorithm. * Eigenvalue/Eigenvector Computation: Jacobi and Power methods for eigenvalues. 3. Interpolation 5. Overview: Explains interpolation techniques for estimating unknown values. 6. Key Topics: * Newton's Interpolation: Forward and backward interpolation formulas. * Other Formulas: Central difference, Lagrange, and divided difference formulas. * Spline Interpolation: Linear and cubic spline methods. 4. Numerical Differentiation and Integration 7. Overview: Covers techniques for differentiation and integration of tabulated functions. 8. Key Topics: * Numerical Differentiation: Derivatives from discrete data. * Numerical Integration: Newton-Cotes, Romberg's method, and Gaussian integer methods. 5. Numerical Solution of Ordinary Differential Equations 9. Overview: Methods for solving ODEs numerically. 10. Key Topics: * Runge-Kutta Methods: For initial value problems. * Predictor-Corrector Methods: Including Adams-Bashforth-Moulton. * Gaussian Quadrature: For integral approximation within ODE solutions.
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