Advanced calculators for matrices, vectors, complex numbers, quadratics, polynomials, systems of equations, sequences, and numerical calculus.
Perform matrix addition, subtraction, multiplication, transpose, determinant, inverse, and rank calculations up to 3x3/4x4.
Calculate vector addition, dot product, cross product, magnitude, unit vector normalization, and angle between vectors.
Perform complex number arithmetic (a + bi) including addition, multiplication, division, magnitude, argument, and conjugate.
Solve quadratic equations (ax² + bx + c = 0) with real or complex roots, discriminant, and parabola vertex coordinates.
Evaluate, add, subtract, multiply polynomials and compute symbolic derivatives for algebraic expressions.
Solve systems of 2x2 and 3x3 linear equations using Cramer's rule with system determinant analysis.
Calculate nth term, sum of n terms, common difference, and common ratio for arithmetic and geometric progressions.
Compute n!, nPr permutations, and nCr combinations with step-by-step mathematical explanations.
Approximate definite integrals using the Trapezoidal Rule and Simpson's 1/3 Rule with subinterval steps.
Approximate first and second derivatives using Forward, Backward, and Central Finite Difference methods.