MATH-251(d): Numerical analysis

Lectures in this course (29)

Explores direct methods for solving linear equations and the impact of errors on solutions and matrix properties.

Explores direct and iterative methods for solving linear equations, emphasizing symmetric matrices and computational cost.

Covers iterative methods for solving linear equations and analyzing convergence, including error control and positive definite matrices.

Introduces iterative methods for solving linear equations and discusses the gradient method for minimizing errors.

Explores gradient and conjugate gradient methods for solving linear systems efficiently.

Explores the Cauchy problem and Euler methods for numerical solutions in ODEs.

Covers the Crank-Nicolson and Heun's methods, discussing uniqueness of solutions and truncation errors in numerical methods.

Covers error analysis, stability, and adaptive time stepping in numerical methods, including convergence order and equilibrium points.

Covers Runge-Kutta and multi-step methods in Chapter 6, including high-order methods and MATLAB examples.

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