Numerical methods games數值方法互動遊戲

Interactive 3D and step-by-step games from a university course in numerical analysis for engineers. Each game turns one topic of the course into something you can move, break and fix: bracket a root, steer Newton's method on a robot arm, deflate a polynomial, choose pivots in Gauss elimination. They run in your browser, need no account, and record nothing.

Games · 遊戲

Week 3 · Chapra & Canale, Chapter 5 and Section 6.1

Root-Finding Game: Bracketing and Fixed-Point Iteration求根遊戲：包夾法與固定點迭代

Fourteen short modules walk through the bracketing methods (the graphical method, incremental search, bisection, false position and modified false position) and fixed-point iteration, starting from a parachutist's drag-coefficient problem. Step through each idea on a live graph, then answer a quick check. It is a 2D, step-by-step lesson.

Graphical method · Incremental search · Bisection · Number of iterations · Approximate error · False position · Modified false position · Fixed-point iteration · Convergence and divergence · Choosing a method

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Week 4 · Chapra & Canale, Chapter 6

Root Challenge 3D: Newton–Raphson, Secant and Modified Newton3D 求根挑戰：牛頓法、割線法與修正牛頓法

Nine engineering problems, each in four variants: pin fin length, buckling of a strut, snap-through of a shallow arch, friction factor in a pipe, a servo arm, a robot arm, springback compensation, thermal runaway and an implicit dislocation-density update. Run Newton–Raphson, the secant method or modified Newton one step at a time, watch the 3D model and the graph, then choose one answer.

Newton–Raphson · Secant method · Modified Newton for multiple roots · Newton's method for 2 × 2 systems · Convergence and approximate error

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Week 5 · Chapra & Canale, Chapter 7

Polynomial Root Challenge 3D: Horner, Müller and Bairstow3D 多項式求根挑戰：Horner、Müller 與 Bairstow

Six challenges on the roots of polynomials: Root landscape (the surface |p(z)| over the complex plane, with Newton–Raphson and Horner's rule), Deflation order, Müller's parabola, Bairstow dials, Poles and vibration, and Wilkinson wobble. Each is scored out of 100 with stars; practice is free play.

Newton–Raphson with Horner's rule · Synthetic division and deflation · Müller's method · Bairstow's method · Complex roots · Conditioning of roots

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Week 6 · Chapra & Canale, Chapter 9

Gauss Elimination Challenge 3D: Pivoting and Conditioning3D 高斯消去挑戰：選主元與條件數

Six challenges: Where the planes meet (three planes in 3D, steer the solution onto a target), Row operations (forward elimination and back substitution), Pivot duel (pivoting on a 3-digit machine), Shaky planes (conditioning and scaling), Flop budget (operation counts) and Hanging team (setting up and solving 3 × 3 systems). Each is scored out of 100 with stars.

Three planes in 3D · Forward elimination and back substitution · Partial pivoting · Ill-conditioning and scaling · Operation counts · Setting up 3 × 3 systems

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