Numerical Definition and 775 Threads

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. T

    Intro to analysis, intro to real analysis I, numerical analysis

    Hello, Is there a difference from these courses, or are they the same course with different names? I need to know which one to choose for the upcoming semester... Intro to Analysis, Intro to Real Analysis I, and Numerical Analysis Thank you, Tracie
  2. P

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  3. P

    I Numerical Integration twice (acceleration to displacement)

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  4. Alexanddros81

    Simple Pendulum motion - Numerical Integration

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  5. F

    I Derivative and Numerical approach

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  6. F

    A Numerical solution of Hamiltonian systems

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  7. S

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  8. Pushoam

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  9. Pushoam

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  10. M

    Numerical Nonlinear Lifting Line Theory in MA

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  11. awholenumber

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  12. C

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  13. Jamison Lahman

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  14. S

    Python Numerical integration in Python (throwing a ball)

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  15. E

    B Numerically Solving GRT Problems - Textbook/Article Recommendation

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  16. hilbert2

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  17. Ian Baughman

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  18. M

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  19. Conclaude

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  20. T

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  21. DeathbyGreen

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  22. A

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  23. S

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  24. D

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  25. I

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  26. T

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  30. S

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  31. Telemachus

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  32. P

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  33. vmr101

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  34. N

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  35. M

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  36. Elvis 123456789

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  37. E

    I Decomposing a Function for Numerical Integration

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  38. D

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  39. N

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  40. F

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  41. MidgetDwarf

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  42. user123897

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  43. awholenumber

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  44. awholenumber

    I Few more numerical methods question....?

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  45. awholenumber

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  46. Samia qureshi

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  47. Johnny_Sparx

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  48. T

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  49. Themis

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  50. davidbenari

    I Numerical integration of PDEs: How do you satisfy boundary conditions

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