Calculus

Enter a function f(x) and interval bounds [a, b] to compute the secant line slope with step-by-step MathJax formulas and a visual graph.

Enter P(x), Q(x), exponent n, and initial conditions to linearize the Bernoulli equation, find a closed-form solution, and plot the slope field.

Calculate linear, circular, and continuous convolution of signals and functions with interactive visualizations, detailed step-by-step solutions, and comprehensive mathematical analysis.

Calculate the curl of any 2D or 3D vector field with a step-by-step determinant expansion. Enter the component functions, get the symbolic curl, evaluate it at a point, spot irrotational fields and view a vorticity overlay.

Enter y=f(x) or a parametric curve and a point to get curvature, the radius of curvature and the osculating circle, with derivative steps.

Calculate derivatives instantly with step-by-step solutions. Supports single-variable, partial, implicit, and directional derivatives with interactive visualizations.

Enter a first-order ODE and an x-y window to plot the slope field, add up to 8 solution curves and see the equilibrium nullclines.

Enter a multivariable function, a point and a direction to get the directional derivative and gradient, with steps. The maximum equals the gradient's magnitude.

Calculate the divergence of any 2D or 3D vector field with step-by-step partial derivatives. Enter the component functions, get the symbolic divergence, evaluate it at a point, identify sources and sinks, and view a heat map.

Enter a function, integration variables, and optional limits to compute double integrals with step-by-step solutions and 3D surface plots.

Solve any first-order ODE numerically with Euler's method. See the iteration table, the Euler polygon drawn on the slope field, and a convergence comparison at h, h/2 and h/4, with optional error analysis against a closed form.

Enter real or complex samples and a sample rate to compute discrete FFT magnitude, phase, frequency bins, and dominant peaks.

Enter dy/dx = f(x, y), initial values, and an x range to solve the differential equation and generate a slope field with a solution curve.

Enter a periodic function and its interval to calculate Fourier coefficients a0, an, and bn. Up to 20 terms are computed at once.

Calculate the gradient vector of a multivariable function. Enter f(x, y) or f(x, y, z) to get every partial derivative, evaluate the gradient at a point, read its magnitude and direction, and view a 2D gradient field.

Compute derivatives of implicit functions F(x,y)=0 with detailed step-by-step solutions. Supports polynomials, trigonometric, exponential, and logarithmic functions up to 5th order derivatives.

Enter an integrand and bounds, including infinity. Evaluate Type I and Type II improper integrals and see whether they converge, with steps.

Calculate the exact sum of convergent infinite series including geometric, telescoping, p-series, and well-known special series. Get step-by-step convergence proofs with animated partial sum visualizations.

Calculate the instantaneous rate of change of any function at a point using the limit definition. Get step-by-step solutions with MathJax formulas, an interactive tangent line graph and a convergence table as h approaches zero.

Calculate definite and indefinite integrals with detailed step-by-step solutions, interactive function visualization, and comprehensive explanations for calculus students and professionals.

Compute the inverse Laplace transform of F(s) to find f(t). Get step-by-step solutions, visualizations, and understand the transformation from frequency domain to time domain.

Enter a numerator, a denominator, and the point, including infinity. Evaluate 0/0 or infinity-over-infinity forms by differentiating, with steps.

Enter a function of t. See its Laplace transform with steps and both the time-domain and s-domain pictures.

Calculate limits of mathematical functions with detailed step-by-step solutions. Supports one-sided limits, indeterminate forms, and L'Hospital's Rule.

Calculate line integrals of scalar and vector fields along parametric curves in 2D and 3D. Enter the field, parametric equations and bounds for symbolic results with step-by-step solutions, arc length and a curve visualization.

Compute the Maclaurin series expansion of common functions at x = 0. Get the nth-order polynomial terms, a Lagrange remainder estimate, the radius of convergence and an animated graph of partial sums converging to the function.

Find roots of equations with the Newton-Raphson method. Enter any function and an initial guess to see step-by-step iterations with tangent line approximations, convergence analysis and a graph tracing the path to the root.

Enter a function and the interval. Compare Gauss-Legendre, Romberg, and adaptive Simpson results, with error and evaluation counts.

Find the maximum and minimum values of any function using the first and second derivative tests. Get critical points, intervals of increase and decrease, concavity analysis, inflection points and an interactive graph with worked steps.

Enter a multivariable function and specify variables and derivative orders, such as x:2,y:1. Get the partial derivative with steps and applied rules.

Find the power series representation of a function centred at any point. Compute Taylor and Maclaurin coefficients, determine the radius and interval of convergence with endpoint analysis, and watch partial sums converge.

Determine the radius and interval of convergence for power series using the Ratio Test or Root Test, with step-by-step solutions, convergence visualization, and endpoint analysis.

Pick a setup such as a sliding ladder, filling cone, expanding sphere, or balloon, and enter the known rates. Get the related rate with steps.

Approximate definite integrals using Riemann sums with left endpoint, right endpoint, midpoint, trapezoidal, and Simpson's rule. View animated rectangle visualizations, step-by-step solutions, and convergence analysis.

Enter an equation, initial conditions, and a step size. See each k1-to-k4 step and a solution table, for at most 1000 steps.

Enter coefficients, forcing expression, initial values, and x range to find the closed-form ODE solution, damping classification, and phase-plane plot.

Test whether an infinite series converges using the Ratio, Root, Integral, Comparison, Limit Comparison, Alternating Series and p-Series tests, with step-by-step solutions and animated partial sum graphs.

Approximate definite integrals with Simpson's 1/3 rule, 3/8 rule and the composite rule. Includes an interactive parabolic visualization, error estimation, convergence analysis, method comparison and step-by-step solutions.

Compute derivatives of any single-variable function with step-by-step solutions, differentiation rule identification, interactive graph, and critical point analysis.

Evaluate surface integrals of scalar fields and flux integrals of vector fields over parametric surfaces. Choose a preset - sphere, cylinder, cone, paraboloid or torus - or enter your own, with normal vectors and a 3D visualization.

Calculate the surface area of a solid of revolution. Enter any function f(x), set integration bounds and axis of rotation, and get step-by-step solutions with interactive 3D visualizations using the disk and shell surface area formulas.

Enter differential equations or matrix coefficients to classify equilibrium points, compute eigenvalues step by step, and generate trajectory phase portraits.

Calculate the Taylor series expansion of any function around a point with step-by-step derivative calculations, interactive comparison graph, and educational explanations.

Approximate an integral from a function with bounds and subintervals, or from x and y data. Review worked steps and individual trapezoid areas.

Compute triple integrals with detailed step-by-step solutions and 3D visualization. Supports definite and indefinite integrals with symbolic computation.

Calculate the volume of a solid of revolution using the disk, washer, and shell methods. Enter your function, bounds, and axis of rotation to get step-by-step solutions with interactive 3D visualizations.

Calculate the Wronskian determinant of a set of functions to test linear independence. See the full matrix with derivatives, a step-by-step determinant expansion, and a verdict on whether the functions form a fundamental set.

Compute one-sided Z-transforms and causal inverse Z-transforms. Enter a sequence formula, finite sample list, or rational X(z) to get the transform, ROC, poles and zeros, sample table, and visual z-plane analysis.