Numerical approximation methods from "summary" of Second Year Calculus by DAVID BRESSOUD
Numerical approximation methods are important techniques used to solve mathematical problems that cannot be solved analytically. They involve breaking the problem into smaller simpler parts and imposing a set of conditions to approximate an answer.- Numerical approximation methods are used to solve problems where there is either no exact solution or the exact solution can be very difficult to find mathematically. These methods allow us to approximate our solutions as close to reality as possible.
- One common numerical approximation method is using interpolation of several points to fill in a graph or set of data. This means that you only estimate values on a graph or set of data; the process does not involve calculating an equation for the function.
- You can also use Monte Carlo simulation as a numerical approximation method, which provides statistical results by randomly generating points and speed up the calculation process. The points created are then tested against certain criteria and makes changes and corrections accordingly.
- Numerical integration techniques are also useful when integrating complicated expressions. We replace our integrals with a suitable mathematical expression, or alternatively we get around it by constructing rectangles at each point of the given area.
