Numerical analysis

High school (ages 12+)
Mathematics & Numbers

Name:

Date:

Step 1 · Read the article

Open the article and read it at the level above. Then answer the questions below in your own words.

https://smallwhale.org/articles/numerical-analysis

Write what each word means, using the article.

Do not copy the article. Write two things you learned, the way you would explain them to a friend.

Answers below are taken from the article’s stored facts, so they match what the student read.

1. How big is Numerical analysis?Solving linear systems, root finding, integration, and differential equations
2. What is the field of study?Mathematics and computer science focused on approximate solutions
3. What is the core objective?To design and analyze algorithms for quantitative problems
4. Why do we need numerical analysis instead of exact math?Many real problems are too hard to solve exactly, so numerical analysis gives algorithms that get close enough in a few steps.
5. How do computers find the roots of equations?They use root-finding algorithms like the bisection method, Newton-Raphson, and secant method to locate where a function equals zero.

Algorithm: A finite, well-defined sequence of computational steps to solve a problem.
Convergence: The property of a sequence of approximations getting closer to the true solution.
Error Analysis: The study of how errors in computation affect the accuracy of the final result.
Finite Element Method (FEM): A numerical technique for finding approximate solutions to boundary value problems for differential equations.