E-CodeTI-89 Titanium math programs
14 checked math programs for the TI-89 Titanium. Each one runs in E-Code's virtual calculator in your browser, and you can put it on your own calculator.
The programs
- Quadratic roots, exact when possible: Solves ax²+bx+c=0 and keeps rational roots exact (1/2, not .5); reports no real roots or a double root.
- Linear system, exact answers: Solves 2 to 4 linear equations by Gauss-Jordan in exact arithmetic, so the answers stay fractions like 1/3; reports no solution or infinitely many (with the rank).
- Fraction calculator: exact, mixed, decimal: Add, subtract, multiply or divide two fractions exactly (pick the operation from a pop-up): the result in lowest terms, its numerator and denominator, as a mixed number, as a decimal, and the least common denominator.
- Prime factorization and divisors: Factors a whole number into primes as a string like 2^3*3^2*5, and gives the number of divisors, the sum of divisors, and whether it is prime.
- LU decomposition with pivoting (exact): Factor a 2×2 to 4×4 matrix as PA = LU with partial pivoting, in exact fractions: the row order P, every row of L and U, and the determinant.
- Matrix inverse, exact: Inverse of a 2×2 to 4×4 matrix by Gauss-Jordan on [A | I] in exact fractions, row by row, or SINGULAR when there is none.
- Newton's method on a typed function: Type f(x) as text and a starting guess: every Newton iterate is shown, then the root, f(root) and the number of steps; reports a flat spot or no convergence.
- Trapezoid and Simpson vs nInt: Type f(x), the limits and an even number of panels: the trapezoid and Simpson estimates, the calculator's nInt value, and each rule's error.
- ODE: Euler vs RK4 table: Type dy/dx = f(x,y), the starting point, the end x and up to 20 steps: a table of the RK4 solution, then Euler and RK4 at the end side by side.
- Series partial sums, exact: Type the term a(k) as text and the range of k: the exact partial sum (a fraction when the terms are rational), its decimal value, and the ratio |a(n+1)/a(n)| as a hint for convergence.
- Matrix inverse from a typed matrix: Type a square matrix like [[4,7][2,6]]: its determinant and the exact inverse row by row, or SINGULAR when there is none.
- LU decomposition of a typed matrix: Type a square matrix: PA = LU with partial pivoting — the row order, L and U row by row in exact fractions, and the determinant.
- Linear system Ax = b from a typed matrix: Type the coefficient matrix (any shape) and the right-hand side: rref decides — the unique solution in exact fractions, INFINITELY MANY with the rank, or NO SOLUTION.
- Cramer's rule with every determinant: Type a square coefficient matrix and the right side: D, each Dᵢ (column i replaced by the right side) and xᵢ = Dᵢ/D, all exact.