Lectures in course ChE-312: Numerical methods

Covers essential MATLAB functions, variables, loops, and debugging tools.

Explores direct methods for solving linear systems of equations, including Gauss elimination and LU decomposition.

Covers tips on matrix construction and function manipulation using MATLAB.

Introduces root finding using the bisection method for nonlinear equations, illustrated with a three-tanks system example.

Explores the sensitivity of solutions in numerical methods, including linear systems and matrix norms, with an example of deblurring images.

Explores Jacobi, Gauss-Seidel, and SOR iterative methods for solving linear systems efficiently.

Covers the Newton-Raphson method, Jacobian matrix, and iterative schemes for solving nonlinear equations.

Covers open methods, Newton-Raphson, and secant method for iterative solutions in numerical methods.

Explores bisection and Regula Falsi bracketing methods for finding roots.

Covers the implementation of numerical methods in MATLAB for solving chemical problems.

Covers numerical differentiation, forward differences, Taylor's expansion, Big O notation, and error minimization.

Explores backward and central differences for numerical differentiation, analyzing their properties and error analysis.

Covers Richardson extrapolation for numerical differentiation to reduce error.

Covers numerical integration methods, including Newton-Cotes and the Trapezoidal Rule.

Explores Romberg integration to improve numerical integration accuracy through iterative refinement of estimates.

Explains Lagrange interpolation for numerical integration and introduces Simpson's rules.

Covers Newton-Cotes integration, Trapezoid rule, Simpson rules, and numerical quadrature conditioning.

Explores Gauss quadrature for numerical integration, optimizing evaluation points and weights for accurate results.

Covers Ordinary Differential Equations, first-order solutions, and numerical methods for IVP and BVP.

Introduces the Euler Forward Method for ODEs, focusing on error analysis and stability.