Overview

1. Algebraic and Transcendental Equations Overview: This section introduces methods for solving algebraic and transcendental equations. 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 Overview: Focuses on solving systems of linear equations and eigenvalue problems. 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 Overview: Explains interpolation techniques for estimating unknown values. 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 Overview: Covers techniques for differentiation and integration of tabulated functions. 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 Overview: Methods for solving ODEs numerically. 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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