Introductory Numerical Methods (GDCO0072)

Numerical methods for undergrads in STEM courses (usually Engineering, Statistics, Physics, and Mathematics).

Resources

Books
Made in Brazil
  • Cálculo Numérico, by Neide Bertoldi
    • Notas: didática mediana, mas bastante completo e robusto; agrega perfis analítico e aplicado; atende múltiplas graduações.
  • Cálculo Numérico: Aspectos Teóricos e Computacionais, by Ruggiero and Lopes
    • Notas: boa didática; voltado a perfis analíticos; inclinado à Matemática.
  • Fundamentos de Calculo Numérico, by A.A. Dornelles Filho
    • Notas: didática boa; cobertura geral de um curso semestral.
  • Portal REAMAT - Cálculo Numérico @UFRGS
    • Notas: livro colaborativo aberto; interessante
Classical
  • Numerical Methods for Scientists and Engineers, by R. W. Hamming
  • Numerical Mathematics and Computing, by W. Cheney and D. Kincaid
  • Numerical Recipes
  • Numerical Methods, by G. Dahlquist and A. Bjorck
Numerical Analysis
  • Fundamentals of Engineering Numerical Analysis, by Parviz Moin
  • Numerical Analysis, by Timothy Sauer @George Mason Univ.
  • Numerical Analysis, by Burden and Faires.
  • An Introduction to Numerical Methods and Analysis, by James F. Epperson
  • Numerical Analysis: Mathematics of Scientific Computing, by D. Kincaid and W. Cheney
  • Elementary Numerical Analysis, by K. Atkinson and W. Han
Numerical Linear Algebra
  • Applied Numerical Linear Algebra, by J. W. Demmel
  • Linear Algebra and its Applications, by G. Strang
  • Matrix Computations, by G. H. Golub and C. F. Van Loan
  • Numerical Matrix Analysis: Linear Systems and Least Squares, by I. C. F. Ipsen
Engineering
  • Numerical Methods for Engineers, by R. P. Canale and S. C. Chapra
  • Numerical Methods for Engineers and Scientists, by A. Gilat and V. Subramanian
  • Numerical Methods in Engineering with Python 3, by J. Kiusalaas @PennState
  • Elementary Mechanics Using Python, by A.M-Sorenssen
  • Numerical Methods for Engineers, by D. V. Griffiths, ‎and I. M. Smith
Computing
Movies

List of movies talking about mathematics, computing, theorems, and geniuses. Contents directly related to numerical methods are made explicit below.

  • “Adventures of a Mathematician” (2020) (O Matemático). This movie is an account of how the mathematician Stanislaw Ulam, the physicist Edward Teller, and other scientists began to develop the hydrogen bomb at Los Alamos, USA, in the post-war 1950s. Ulam is the inventor of the Monte-Carlo numerical method and a pioneer with John Von Neumann to the advent of the computer. In a few scenes, Ulam teaches random variables and probability distributions. A summary of “The Super” (the hydrogen bomb) can be read here.

  • “The Current War” (2017) (A Batalha das Correntes). The dramatic race between Thomas Edison and George Westinghouse (involving Nikola Tesla) to determine who would provide power to the modern world.

  • “Hidden Figures” (2016) (Estrelas Além do Tempo). In this movie, Taraji Hanson performs Katherine Johnson, a former NASA’s human computer, that uses the Euler’s method to compute the John Glenn capsule’s back-to-Earth trajectory.

  • “The Man Who Knew Infinity” (2015) (O Homem que Via o Infinito). The overcoming story of the life and academic career of the mathematician Srinivasa Ramanujan after leaving India for England. Ramanujan struggled to present a new theorem-proof to the famous G. H. Hardy and elite scientists at Cambridge, which led him to get his Ph.D. title.

  • “The Theory of Everything” (2014) (A Teoria de Tudo). The story of Stephen Hawkins.

  • “The Imitation Game” (2014) (O Jogo da Imitação). On cryptography, this movie is the story of Alan Turing and his friends trying to crack the German “Enigma” code during World War 2.

  • “A Beautiful Mind” (2001) (Uma Mente Brilhante). In this movie, Russell Crowe performs John Nash, Nobel in Economics during his Ph.D. trial at Princeton. Nash’s thesis was related to Game Theory, where fixed-point theorems are applied.

  • “Good Will Hunting” (1997) (Gênio Indomável). The story of Will Hunting, a janitor at MIT with remarkable mathematical skills helped by a psychologist due to his lack of life purpose.

Videos
  • Computer Architecture Course, by Orlando J. Hernandez
    • Especially, chapter 3 covers computer arithmetics, binary numbers, and overflow/underflow issues.
Papers
Libraries
  • Netlib: online repository for numerical libraries.
  • Eigen: C++ template library for linear algebra (matrices, vectors, numerical solvers), and related algorithms.
  • Boost: multi-purpose C++-based libraries. Lots of math specializations.
  • CGAL: efficient and reliable geometric algorithms in the form of a C++ library. It provides data structures and algorithms for triangulations, Voronoi diagrams, surface and volume mesh generation, and so on.
  • meshio: universal mesh in/out conversion tool.
  • TetGen: A Quality Tetrahedral Mesh Generator and a 3D Delaunay Triangulator.
  • Triangle: A Two-Dimensional Quality Mesh Generator and Delaunay Triangulator.
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