E-CodeTI-84 Plus CE math programs
18 checked math programs for the TI-84 Plus CE. Each one runs in E-Code's virtual calculator in your browser, and you can put it on your own calculator.
The programs
- Quadratic formula solver: Prompts for a, b, c and shows both real roots, or reports there are none.
- Circle area and circumference: Prompts for a radius, shows the area and circumference.
- Newton-Raphson root finder: Finds a root of x³-2x-5 using 8 Newton-Raphson iterations from x₀=2.
- Bisection root finder: Solves cos(x)=x by bisection over [0,1] to the Dottie number, ≈0.739.
- Riemann sum area estimator: Approximates the area under x² from 0 to a bound using 1000 rectangles.
- Formula reference card: A flip-through Menu( of the quadratic, slope, and distance formulas.
- Law of Cosines solver: Two sides and the included angle, solved for the third side.
- Numerical integration lab: Type any f(X): compares the trapezoid rule, Simpson's rule (both helper programs) and fnInt( with their errors.
- Linear system solver (n equations): Solves 2 to 6 linear equations in as many unknowns from typed rows {a1,...,an,b}; says NO SOLUTION or INFINITELY MANY (with the rank) instead of failing, and prints the residual as a check.
- Polynomial roots, complex included: Every root, real or complex, of a degree 1-5 polynomial typed as a coefficient list, by Bairstow's quadratic factors (no a+bi mode needed); shows real and imaginary parts and the residual |p(root)|.
- Newton's method with an iteration table: Type any f(X) and a starting guess: prints every Newton iterate in a table (central-difference derivative), then the root to 9 decimals, f(root) and the iteration count; reports a flat spot, divergence or no convergence.
- ODE solver: Euler vs RK4 with a table: Type y'=f(X,Y), the start point, the end X and the number of steps: prints an RK4 table, then Euler vs RK4 at the end, and reruns RK4 with twice the steps for an error estimate.
- Vectors: dot, cross, angle, projection: Type two 2-D or 3-D vectors: lengths, dot product, the angle between them in degrees, the cross product with the parallelogram and triangle areas, and the projection of U onto V.
- Calculus applications: area, arc length, volume, surface: Type f(x) (and g(x) where needed) and the limits: area between curves, arc length, volume of revolution about the x-axis by disks/washers or about the y-axis by shells, and surface area of revolution — Simpson's rule with 200 panels.
- Eigenvalues and eigenvectors (2×2, 3×3): Every eigenvalue of a 2×2 or 3×3 matrix, complex ones included, from the characteristic polynomial, with the trace and determinant, then a unit eigenvector for each real eigenvalue.
- Taylor polynomial: approximation and error: Taylor polynomial of e^x, sin x or cos x about any center, or of ln(1+x) and 1/(1-x) about 0, of any order up to 30: the approximation at x, the true value, the actual error, and the Lagrange error bound where it applies.
- Matrix toolkit: det, inverse, product, power, transpose: Type matrices row by row (up to 4×4): determinant and inverse (or SINGULAR), the product A·B, a power A^k, or the transpose — each result shown row by row as C11=, C12=, …
- LU decomposition with partial pivoting: Factor a 2×2 to 4×4 matrix as PA = LU with partial pivoting: every entry of L and U, the row order P and the determinant.