Ma214 08

Summary

In this lecture, we introduce the notion of order of a fixed point iteration method. We then study orders of various such methods. From the course Applied Linear Algebra at the University of Michigan. We learn the modified Newton-Raphson method and Aitken's Delta-squared method in this lecture. This lecture completes the ... The Newton-Raphson method is discussed in this lecture. We discuss the Secant method and the regula falsi method in this lecture. We begin the theme on ordinary differential equations and discuss Euler's method. This lecture initiates the discussion on Runge-Kutta methods. This lecture introduces the bisection method to find the roots of equations in one variable. We continue studying interpolation by looking at some examples and understanding the error form. We initiate the discussion on numerical integration by discussing the trapezoidal and Simpson's rules. We learn iterative techniques such as the Jacobi and Gauß-Seidel methods to solve systems of linear equations. An explicit application of the error formula for Lagrange interpolation is discussed in the beginning and then we go towards ...