maths.free › Numerical Methods
Numerical Methods
Root finding, approximation, numerical integration and error.
មេរៀន
newton's method on x^2 - 2 from 1
Core
Numerical integration: trapezoid and Simpson
Approximating an integral from sampled values, with error bounds.
integrate e^(-x^2) dx from 0 to 1
Core
Interpolation and Taylor approximation
Fitting polynomials through points, and approximating functions near a centre.
taylor series of e^x
Core
Floating point and error
Why 0.1 + 0.2 ≠ 0.3 on a computer, and how error propagates.
0.1 + 0.2
Most equations have no closed form; numerical methods find answers to as many decimals as you like and, crucially, tell you how wrong they might be. Every iteration here is shown as a step.
មេរៀនបន្ថែម
Finding roots
Integration and interpolation
Linear systems and ODEs
Error
មេរៀនមួយចំនួននេះត្រូវបានកែប្រែពីអត្ថបទបើកចំហ ៖ Wikipedia. ទំព័រមេរៀននីមួយៗមានឈ្មោះប្រភព និងអាជ្ញាបណ្ណរបស់វា ។
និមិត្តសញ្ញាដែលបានប្រើនៅទីនេះ
ចុចនិមិត្តសញ្ញាណាមួយសម្រាប់ការកំណត់ពេញលេញ រូបភាព និងតួអក្សរនីមួយៗមានន័យអ្វី ។
សំណួរដែលមនុស្សសួរ
Why not just solve exactly?
Most equations have no closed-form solution at all, and many that do are unusable in practice. A numerical method delivers as many correct digits as you need, and a good one tells you how many that is.
Why can Newton's method fail?
If it starts where the tangent is nearly flat it shoots far away; near a repeated root it slows to a crawl; and with several roots it may land on the wrong one. A bracketing method like bisection is slower but cannot fail.
វាយវា ឬគូរវានៅលើទំព័រកម្មវិធីដោះស្រាយ ៖ ជំហាននីមួយៗ រូបភាព ចម្លើយដែលលាក់រហូតដល់អ្នកសួរ ។ ដោះស្រាយ →
សាខាផ្សេងទៀត
＋ Arithmetic𝑥 Algebra△ Geometry∿ Trigonometryƒ Precalculusσ Statistics & Probability⊢ Discrete Math & Logic∫ Calculus⊞ Linear Algebraℕ Number Theoryẏ Differential Equations∇ Multivariable Calculusε Real Analysis⋔ Combinatorics & Graph Theory∈ Set Theory & Logic𝔾 Abstract Algebra𝑃 Probability Theoryℂ Complex Analysis◎ Topologyμ Measure Theory‖·‖ Functional Analysisκ Differential Geometryπ₁ Algebraic Topology→ Category Theory∂ Partial Differential Equations≋ Fluid Dynamics∞ Frontiers