Course: Engineering Mathematics - Numerical Analysis

In numerical analysis, Newton's method (also known as the Newton–Raphson method), named after Isaac Newton and Joseph Raphson, is a method for finding successively better approximations to the roots (or zeroes) of a real-valued function.  

In numerical analysis, the secant method is a root-finding algorithm that uses a succession of roots of secant lines to better approximate a root of a function f. The secant method can be thought of as a finite-difference approximation of Newton's method.  

The bisection method in mathematics is a root-finding methodthat repeatedly bisects an interval and then selects a subinterval in which a root must lie for further processing. .... The method is also called the interval halving method, the binary searchmethod, or the dichotomy method.  

In mathematics, and more specifically in numerical analysis, the trapezoidal rule (also known as the trapezoid rule or trapezium rule) is a technique for approximating the definite integral. . The trapezoidal rule works by approximating the region under the graph of the function as a trapezoid and calculating its area. 

Use multiple-segment Simpson's 1/3 rule of integration to solve integrals, and derive the true error formula for multiple-segment Simpson's 1/3 rule. The trapezoidal rule was based on approximating the integrand by a first order polynomial, and then integrating the polynomial over interval of integration.