Advanced Mathematics encompasses the most intricate and profound concepts in the field of math, forming the backbone of higher studies and research. With Moogle Math’s Advanced Mathematics Solver, you can tackle complex topics such as topology, abstract algebra, advanced calculus, and functional analysis with precision and clarity.
group_operations(group={e, a, b}, operation="multiplication")is_open_set(topology={{}, {1}, {1, 2}}, set={1})evaluate_integral(function="e^(-x^2)", limits={0, infinity})Linear Programming
Example: Solve a linear optimization problem.
Input: linear_programming(objective="maximize", constraints={x+y<=5, x>=0, y>=0})
Fourier Analysis
Example: Find the Fourier series representation of f(x)=x2f(x) = x^2 on [−π,π][- \pi, \pi].
Input: fourier_series(function="x^2", interval={-pi, pi})
To get the best results from Moogle, follow these tips
Example: Simplify the matrix exponential \(e^{At}\) for \(A = \begin{bmatrix} 1 & 0 \\ 0 & -1 \end{bmatrix}\).
Input: matrix_exponential(matrix=[[1, 0], [0, -1]])
Example: Solve the partial differential equation \(\frac{\partial u}{\partial t} = \alpha \frac{\partial^2 u}{\partial x^2}\).
Input: pde_solver(equation="du/dt = alpha * d2u/dx2")
Input: function_norm(function="f(x)=sin(x)", space="L2", interval=[0, pi])
Example: Compute the Ricci tensor for a given metric.
Input: ricci_tensor(metric=[[1, 0], [0, -1]])