--- title: Numerical Analysis description: Numerical analysis is the study of algorithms that use numerical approximation for mathematical analysis problems. Learners will understand how to design, analyze, and implement algorithms to solve continuous mathematical equations computationally. category: mathematics subcategory: numerical-analysis-and-topology difficulty: beginner, intermediate, advanced url: /subject/numerical-analysis --- # Numerical Analysis Numerical analysis is the study of algorithms that use numerical approximation for mathematical analysis problems. Learners will understand how to design, analyze, and implement algorithms to solve continuous mathematical equations computationally. ## Available Resources 3 Books • 2 Courses • 4 Websites ## Websites ### 1. Numerical Recipes Official companion site to Press, Teukolsky, Vetterling and Flannery's Numerical Recipes, giving online access to the third-edition text plus C++ source for interpolation, linear algebra, integration, ODEs, optimisation and statistical routines. **Difficulty:** Beginner | **Price:** Free **Link:** https://numerical.recipes/ **Tags:** numerical-methods, scientific-computing, algorithms, cpp, reference ### 2. Nick Higham's Blog Posts by numerical analyst Nicholas J. Higham of the University of Manchester, including the 'What Is' series of short explainers on matrix concepts, floating-point arithmetic notes, software tips, and advice on mathematical writing. **Difficulty:** Beginner | **Price:** Free **Link:** https://nhigham.com/ **Tags:** numerical-linear-algebra, floating-point, matrix-computations, mathematical-writing, blog ### 3. MIT Numerical Computation Guide Gilbert Strang's course-and-book page for Computational Science and Engineering, collecting chapter material, MATLAB codes, problem sets and 18.085 lecture links covering finite differences, finite elements, Fourier methods and applied linear algebra. **Difficulty:** Beginner | **Price:** Free **Link:** https://math.mit.edu/~gs/computational/index.html **Tags:** numerical-methods, applied-linear-algebra, matlab, finite-elements, scientific-computing ### 4. scicomp.stackexchange.com SciComp Stack Exchange is a Stack Exchange Q&A site for scientific computing, covering numerical analysis, numerical linear algebra, simulations, and related computational methods. It contains questions, answers, and code examples spanning theory, algorithms, and practical implementation in languages such as Python, MATLAB, and C++. **Difficulty:** Intermediate | **Language:** English | **Price:** Free **Link:** https://scicomp.stackexchange.com **Tags:** websites, mathematics-statistics, numerical-analysis-topology ## Courses ### 1. Computational Science and Engineering I (MIT 18.085) **Author:** Gilbert Strang Applied linear algebra for networks, structures and estimation, followed by equilibrium differential equations, Laplace's equation, boundary-value problems, calculus of variations, Fourier series and the discrete Fourier transform. Includes 50 lecture videos, problem sets and exams with solutions, and programming assignments. **Difficulty:** Intermediate | **Price:** Free **Link:** https://ocw.mit.edu/courses/18-085-computational-science-and-engineering-i-fall-2008/ **Tags:** applied-linear-algebra, boundary-value-problems, calculus-of-variations, fourier-analysis, differential-equations ### 2. Numerical Methods for Engineers This course covers the most important numerical methods that an engineer should know, including root finding, matrix algebra, integration and interpolation, ordinary and partial differential equations. We learn how to use MATLAB to solve numerical problems, and access to MATLAB online and the MATLAB grader is given to all students who enroll. We assume students are already familiar with the basics of matrix algebra, differential equations, and vector calculus. They should have a working knowledge of a programming language, and be willing to learn MATLAB. The course contains 74 short lecture videos and MATLAB demonstrations. After each lecture or demonstration, there are problems to solve or programs to write. The course is organized into six weeks, and at the end of each week, there is an assessed quiz and a longer programming project. Download the lecture notes from the link https://www.math.hkust.edu.hk/~machas/numerical-methods-for-engineers.pdf And watch the promotional video from the link https://youtu.be/qFJGMBDfFMY **Difficulty:** Beginner | **Language:** English | **Duration:** 6 weeks of study, 4 hours/week | **Price:** Free **Link:** https://www.coursera.org/learn/numerical-methods-engineers **Tags:** courses, mathematics-statistics, differential-equations ## Books ### 1. An Introduction to Numerical Analysis **Author:** Endre Süli, David F. Mayers Oxford's standard undergraduate text derives and proves the core algorithms: bisection and Newton iteration, Gaussian elimination, polynomial interpolation, orthogonal polynomials, Gaussian quadrature, initial and boundary value problems for ordinary differential equations, and finite elements, with error and stability analysis throughout. **Difficulty:** Advanced | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0521007941?tag=edmonddante07-20 **Tags:** numerical-analysis, interpolation, quadrature, root-finding, ordinary-differential-equations ### 2. Numerical Linear Algebra **Author:** Lloyd N. Trefethen, David Bau III Trefethen and Bau's forty short lectures on matrix computation, starting from the SVD and QR factorisation and building through conditioning, stability, direct solvers, eigenvalue algorithms and iterative methods such as Arnoldi and conjugate gradients. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0898713617?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, numerical-analysis-topology ### 3. Matrix Computations **Author:** Gene H. Golub, Charles F. Van Loan The standard graduate reference on matrix algorithms, presenting block algorithms, error and perturbation analysis for factorisations, least squares, eigenvalue and singular value problems, and Krylov subspace iterations at the level needed to implement them. **Difficulty:** Intermediate | **Language:** English | **Price:** Paid **Link:** https://www.amazon.com/dp/0801854148?tag=edmonddante07-20 **Tags:** books, mathematics-statistics, numerical-analysis-topology --- *This content is part of Dantes.io - Your Treasure Map to Knowledge* *Curated by humans at Dantes.io. Personal study use welcome; republishing this curation requires permission (team@dantes.io).* View this page online: https://dantes.io/subject/numerical-analysis