Numerical Analysis for Engineers

Lectures in this MOOC (64)

Covers numerical integration using quadrature formulas to approximate integrals of continuous functions over intervals.

Explores the resolution of one-dimensional boundary problems with different cord models and highlights the distinction from other types of problems.

Covers methods to solve linear systems with a finite number of operations.

Covers the concept of weights in a quadrature formula used for approximation and provides a theorem for calculating the weights.

Summarizes methods for resolving linear systems, including Gaussian elimination and LU decomposition.

Introduces a model problem and discusses the Finite Difference Method.

Covers the fixed-point method with an example and its convergence criteria.

Covers the numerical resolution of differential equations, focusing on first-order equations and Euler diagrams.

Covers the fixed point method for finding x bar = g(x bar) and demonstrates convergence and divergence of sequences.

Covers error division and schemes for solving differential equations.

Discusses numerical differentiation, error analysis, and finite difference formulas.

Explores the inefficiencies of the incorrect method for polynomial interpolation.

Focuses on the convergence and linearity of the fixed-point method.

Explores the accuracy of central finite difference formulas for derivatives.

Explores fixed point methods for function solutions and non-linear systems.

Covers numerical integration using rectangle and trapezoid formulas, with decreasing error as step size decreases.

Analyzes the error in numerical derivatives using finite difference formulas.

Covers the basics of numerically approximating integrals over intervals and changing variables.

Explains the construction and benefits of Gauss formulas for numerical integration.

Covers four finite difference formulas for approximating derivatives, including progressive, retrograde, and centered formulas.

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