Numerical Methods & Scientific Computing

Numerical Methods & Scientific Computing#

Table of Contents#

Resources#

Kovalev, Leonid. Numerical Methods with Programming.

Moler, Cleve. Numerical Computing with MATLAB.

YouTube Channels

  • [Y] wenshenpsu

YouTube Videos

  • [Y] Mr P Solver. (08 Nov 2022). “How to: Monte Carlo Simulation in Python (Introduction)”. YouTube.

  • [Y] Mr P Solver. (12 Oct 2021). “Curve Fitting in Python (2022)”. YouTube.

  • [Y] Mr P Solver. (27 Sep 2021). “How To Interpolate Data In Python”. YouTube.

Dot Physics

  • [ y ] 06-16-2023. “Python Code from Scratch: Convert Decimal to Hexadecimal”.

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Texts#

  • [ h ] Ascher, Uri M. & Chen Greif. A First Course in Numerical Methods.

  • [ h ][ g ] Driscoll, Tobin A. & Richard J. Braun. Fundamentals of Numerical Computation.

  • Hager, Georg & Gerhard Wellein. (2010). Introduction to High Performance Computing for Scientists and Engineers. CRC Press. Heath, Michael T. (2018). Scientific Computing: An Introductory Survey, 2nd Ed. Learning Modules.

  • [ h ] Kong, Qingkai; Timmy Siauw; & Alexandre Bayen. (2020). Python Programming and Numerical Methods: A Guide for Engineers and Scientists. Academic Press.

  • Shen, Wen. (2019). An Introduction to Numerical Computation. 2nd Ed. World Scientific.

    • [ y ] CMPSC/MATH 451

    • [ y ] Numerical Computation spring 2015

  • Stewart, G. W. (1996). Afternotes on Numerical Analysis.

Terms#

  • [ w ] Approximation Error

  • [ w ] Binary Number

  • [ w ] BCD Binary-Coded Decimal

  • [ w ] Bit

  • [ w ] Catastrophic Cancellation

  • [ w ] Computer Number Format

  • [ w ] Divided Differences

  • [ w ] Decimal Representation

  • [ w ] Double-Precision Floating Point

  • [ w ] Exponent Bias

  • [ w ] Fast Multipole Method (FMM)

  • [ w ] Find First Set

  • [ w ] Finite Difference

  • [ w ] Finite Element Method (FEM)

  • [ w ] Fixed-Point Arithmetic

  • [ w ] Floating-Point Arithmetic

  • [ w ] Floating-Point Operations per Second (FLOPS)

  • [ w ] Floating-Point Unit (FPU)

  • [ w ] Huffman Coding

  • [ w ] IEEE 754

  • [ w ] Interpolation

  • [ w ] Lagrange Polynomial

  • [ w ] Linear Approximation

  • [ w ] Loss of Significance

  • [ w ] Machine Epsilon

  • [ w ] Method of Complements

  • [ w ] N-Body Simulation

  • [ w ] Newton Polynomial

  • [ w ] Newton’s Method

  • [ w ] Number

  • [ w ] Numeral System

  • [ w ] Numerical Analysis

  • [ w ] Numerical Differentiation

  • [ w ] Numerical Integration

  • [ w ] Numerical Methods for Ordinary Differential Equations

  • [ w ] Numerical Methods for Partial Differential Equations

  • [ w ] Numerical Stability

  • [ w ] Offset Binary

  • [ w ] Ones’ Complement

  • [ w ] Polynomial Interpolation

  • [ w ] Positional Notation

  • [ w ] Radix

  • [ w ] Reflected Binary Code (RBC)

  • [ w ] Relative Error

  • [ w ] Roundoff Error

  • [ w ] Runge’s Phenomenon

  • [ w ] Scientific Computing

  • [ w ] Sign Bit

  • [ w ] Sign-Magnitude Representation

  • [ w ] Signed Number Representation

  • [ w ] Signedness

  • [ w ] Significand

  • [ w ] Significant Digits

  • [ w ] Significant Figures

  • [ w ] Single-Precision Floating-Point

  • [ w ] Spline

  • [ w ] Spline Interpolation

  • [ w ] Sterbenz Lemma

  • [ w ] Trigonometric Interpolation

  • [ w ] Truncation

  • [ w ] Twos Complement

  • [ w ] Unit of Least Precision

  • [ w ] Variable-Length Code

  • [ w ] Verlet Integration

  • [ w ] Verlet List

Contents