What is Numerical: Definition and 772 Discussions

Numerical analysis is the study of algorithms that use numerical approximation (as opposed to symbolic manipulations) for the problems of mathematical analysis (as distinguished from discrete mathematics). Numerical analysis naturally finds application in all fields of engineering and the physical sciences, but in the 21st century also the life sciences, social sciences, medicine, business and even the arts have adopted elements of scientific computations. The growth in computing power has revolutionized the use of realistic mathematical models in science and engineering, and subtle numerical analysis is required to implement these detailed models of the world. For example, ordinary differential equations appear in celestial mechanics (predicting the motions of planets, stars and galaxies); numerical linear algebra is important for data analysis; stochastic differential equations and Markov chains are essential in simulating living cells for medicine and biology.
Before the advent of modern computers, numerical methods often depended on hand interpolation formulas applied to data from large printed tables. Since the mid 20th century, computers calculate the required functions instead, but many of the same formulas nevertheless continue to be used as part of the software algorithms.The numerical point of view goes back to the earliest mathematical writings. A tablet from the Yale Babylonian Collection (YBC 7289), gives a sexagesimal numerical approximation of the square root of 2, the length of the diagonal in a unit square.
Numerical analysis continues this long tradition: rather than exact symbolic answers, which can only be applied to real-world measurements by translation into digits, it gives approximate solutions within specified error bounds.

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  1. C

    Any recommendations for a book on advanced numerical methods?

    I'm looking for a good book on numerical methods. I know most of the basic algorithms but one that delves more into things like adaptive quadrature and that type of thing is what I'm looking for. Any texts people could recommend?
  2. G

    Calculating Velocity Change for Hohmann Transfer Orbit

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  3. franciobr

    Numerical integration - Techniques to remove singularities

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  4. Hercuflea

    Numerical analysis vs functional analysis vs statistics for engineerin

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  5. P

    Numerical methods for nonlinear PDEs in large domains

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  6. G

    MHB How can I optimize numerical approximation with fewer samples?

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  7. Y

    Heat Capacity Numerical Problem

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  8. sankalpmittal

    Yet another numerical on friction

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  9. S

    Analysis of Image superimposing using numerical analysis

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  10. S

    MHB Analysis of Image superimposing using numerical analysis

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  11. K

    Numerical floating point addition

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  12. jbrussell93

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  13. M

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  14. M

    Numerical stability of stiff problem

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  15. S

    Numerical Integration of 2nd Order DE

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  16. Somefantastik

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  17. Albert1

    MHB Numerical Integration: Find x to 3 Decimal Points

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  18. maistral

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  19. I like Serena

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  20. Q

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  21. S

    Taking Numerical Analysis next semester. How should I prepare?

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  22. E

    MATLAB Is a Basic Understanding of Matlab Enough for Applied Numerical Methods?

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  23. P

    How to start knowledge build-up for becoming a numerical modeler?

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  24. D

    Numerical differentiation with change of variable

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  25. S

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  26. F

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  27. T

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  28. R

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  29. D

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  30. A

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  31. H

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  32. B

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  33. S

    Numerical problem on vector algebra - components of vectors

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  34. F

    Modes and numerical aperture of a fiber optic cable

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  35. H

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  36. N

    Find Numerical Value Of Transverse Modulus

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  37. H

    Numerical Integration - Problem

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  38. S

    Solving a Transcendental Equation Using a Numerical or Graphical Method

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  39. M

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  40. N

    Applications of Calculus and Numerical Methods

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  41. F

    Coupled PDE System - Numerical Solution

    All, As part of my research I came up with a boundary value problem where I need to solve the following system of coupled PDE: 1- a1 * f,xx + a2 * f,yy + a3 * g,xx + a4 * g,yy - a5 * f - a6 * g = 0 2- b1 * f,xx + b2 * f,yy + b3 * g,xx + b4 * g,yy - b5 * f - b6 * g = 0 Where, ai's...
  42. bcrowell

    Numerical method for finding charge density on a conductor

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  43. G

    Error in numerical approximation of an integration

    Homework Statement a,b\in R, a<b, n\in N\\ h=\frac{b-a}{n} , x_i = a+ih , i=0..n \\ f\in C^1[a,b] we approximate the integral of f in a,b with Q_n(f) = h\left[f(x_1) + f(x_1) + ... + f(x_n)\right] Find the error R_n(f) = \int_a^bf(x)dx - Q_n(f), as function of the first derivative of f...
  44. A

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  45. Hepth

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  46. M

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  47. N

    A question about numerical series

    suppose an>0, \sumandiverges then what can we say about \sum an/1+nan I think it divergent, but I'm not sure。
  48. D

    Need help with numerical lifting line method

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  49. M

    Numerical Solution to System of Non-linear Equations

    Homework Statement I am having problems solving this system of non-linear equations in Matlab and Mathematica. a,b,c,d,e,f are all independent variables. In Matlab I use fsolve() and get one solution, in Mathematica I use NSolve[] and get another totally different solution. Mathematica...
  50. S

    [Paper choice] Numerical Mathematics or Analog Electronics and Circuit Analysis.

    I am a physics major and have to make a choice between either of these two papers. The numerical mathematics is at the equivalent to US senior level and the electronics paper is equivalent to US junior level. I'm quite interested in biophysics and/or medical physics for grad school but I'm not...
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