16/03/2022, 08:58 GitHub –
Imperial-MATH50003/MATH50003NumericalAnalysis: Notes and course material
for MATH50003 Numerical Analysis https://github.com/Imperial-MATH50003/MATH50003NumericalAnalysis 1/6 Imperial-MATH50003 / MATH50003NumericalAnalysis Public Notes and course material for MATH50003 Numerical Analysis MIT License 27 stars 77 forks Code Issues 5 Pull requests 4 Actions Projects Wiki Security Insights View code MATH50003NumericalAnalysis Notes and course material for MATH50003 Numerical Analysis Lecturer: Dr Sheehan Olver Problem Classes: 2–4pm Thursdays, Huxley 340–342 Overview lecture: 10–11am Fridays, Clore Q&A: 9:50–10:30 Mondays, 10:40–11:20 Tuesdays on Teams Course notes Background material 1. Introduction to Julia: we introduce the basic features of the Julia language. 2. Asymptotics and Computational Cost: we review Big-O, little-o and asymptotic to notation, and their usage in describing computational cost. Part I: Computing with numbers Star Notifications main Go to file dlfivefifty … 16 hours ago README.md 16/03/2022,
08:58 GitHub – Imperial-MATH50003/MATH50003NumericalAnalysis: Notes and
course material for MATH50003 Numerical Analysis https://github.com/Imperial-MATH50003/MATH50003NumericalAnalysis 2/6 1. Numbers: we discuss how computers represent integers and real numbers, as well as their arithmetic operations. 2. Differentiation: we discuss ways of approximating derivatives, including automatic differentiation, which is essential to machine learning. Part II: Computing with matrices 1. Structured Matrices: we discuss types of structured matrices (permutations, orthogonal matrices, triangular, banded). 2. Decompositions: we discuss algorithms for computing matrix decompositions (QR and PLU decompositions) and their use in solving linear systems. 3. Singular values and condition numbers: we discuss vector and matrix norms, and condition numbers for matrices, and the singular value decomposition. 4. Differential Equations: we discuss the numerical solution of linear differential equations, including both time-dependent ordinary differential equations and boundary value problems, by reduction to linear systems. Part III: Computing with functions 1. Fourier series: we discuss Fourier series and their usage in numerical computations via the fast Fourier transform. 2. Orthogonal Polynomials: we discuss orthogonal polynomials—polynomials orthogonal with respect to a prescribed weight. 3. Interpolation and Gaussian quadrature: we discuss polynomial interpolation, Gaussian quadrature, and expansions in orthogonal polynomials. Assessment 1. Practice computer-based exam (Solutions) 2. Computer-based exam (released on Blackboard): 18 March 2022, 3–5pm (1 hour exam, 1 hour upload/download) 3. Practice final exam (pen-and-paper, not for credit): Summer Term (TBC) 4. Final exam (pen-and-paper): Summer Term (TBC) Problem sheets 1. Week 1 (Solutions): Binary representation, integers, floating point numbers, and interval arithmetic 2. Week 2 (Solutions): Finite-differences, dual numbers, and Newton iteration 3. Week 3 (Solutions): dense, triangular, banded, permutation, rotation and reflection matrices 4. Week 4 (Solutions): least squares, QR and PLU decompositions
