Calculus

Enter a function f(x) and interval bounds [a, b] in MiniWebtool’s Average Rate of Change Calculator to compute the secant line slope with step-by-step MathJax formulas and a visual graph.

MiniWebtool’s Bernoulli ODE Solver works with equations in Bernoulli form using coefficient expressions P(x), Q(x), and exponent n. Optional initial values define a particular solution for inspection alongside the solution process.

MiniWebtool’s Convolution Calculator combines two sequences or functions using discrete or continuous convolution. Enter the signals and relevant starting indices to inspect the result through worked steps and visualizations.

MiniWebtool’s Curl Calculator differentiates a 2D or 3D vector field to find ∇×F. Enter the components and an optional evaluation point to see symbolic steps, with a rotational-flow visualization for 2D fields.

Inspect how sharply a curve bends with MiniWebtool’s Curvature Calculator. An explicit function or parametric curve and a selected point produce curvature, radius of curvature, derivative steps, and an osculating-circle visualization.

MiniWebtool’s Derivative Calculator differentiates explicit functions, multivariable expressions, or implicit equations. Choose the relevant mode, variables, and order to follow the symbolic steps; a directional mode adds a point and direction for gradient analysis.

See an ODE’s local behavior before solving it analytically in MiniWebtool’s Direction Field / Slope Field Plotter. Enter y′ = f(x, y) to draw tangent segments, then add initial conditions for numerically integrated solution curves.

MiniWebtool’s Directional Derivative Calculator measures a function’s change along a specified direction at a point. It computes the gradient, normalizes the direction vector, and shows their dot product with worked steps and 3D context.

Inspect sources and sinks in MiniWebtool’s Divergence Calculator. Components of a 2D or 3D vector field yield symbolic ∇·F and optional point evaluation, with derivative steps and a 2D flow visualization.

Evaluate an iterated integral in MiniWebtool’s Double Integral Calculator. Enter the function, integration variables, and bounds to follow the two integrations, supported by worked steps and a 3D visualization.

MiniWebtool’s Euler's Method Calculator approximates y′ = f(x, y) from an initial condition. Choose step size and iteration count to inspect the table and slope-field path, with optional step-size comparison and exact-solution error analysis.

MiniWebtool’s Fast Fourier Transform (FFT) Calculator converts real or complex samples into frequency bins. Sample rate, windowing, and padding choices shape magnitude, phase, frequency labels, and peak summaries for interpreting the signal’s spectrum.

MiniWebtool’s First-Order ODE Solver examines dy/dx = f(x, y) and classifies recognizable equation forms. An initial condition supports a numerical solution curve, while a symbolic solution is provided where possible, with a slope field for geometric interpretation.

Break a periodic function into harmonics in MiniWebtool’s Fourier Series Coefficients Calculator. Function, period bounds, and term count determine sine and cosine coefficients for inspecting the series approximation.

Find the direction of steepest increase from a multivariable expression. MiniWebtool’s Gradient Calculator (Multivariable) calculates symbolic partial derivatives and the gradient vector, optionally evaluates them at a point, and draws a gradient field for two-variable functions.

For equations written as F(x,y)=0, MiniWebtool’s Implicit Derivative Calculator differentiates without first isolating y. Follow the chain-rule steps and calculate supported higher derivatives up to fifth order.

Infinite bounds and singularities require limits rather than ordinary endpoint substitution. MiniWebtool’s Improper Integral Calculator evaluates Type I and Type II cases, displaying the convergence result and the steps used to reach it.

Examine whether an infinite series converges and what it sums to. MiniWebtool’s Infinite Series Sum Calculator handles supported series forms, explains the convergence reasoning, and visualizes partial sums approaching the result.

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

For calculus students and professionals, MiniWebtool’s Integral Calculator calculates definite and indefinite integrals with detailed step-by-step solutions, interactive function visualization and comprehensive explanations.

Compute the inverse Laplace transform of F(s) to find f(t) with MiniWebtool’s Inverse Laplace Transform Calculator. Follow step-by-step solutions and visualizations to understand the transformation from frequency domain to time domain.

Evaluate qualifying 0/0 or infinity-over-infinity limits with MiniWebtool’s L'Hôpital's Rule Calculator. Enter numerator, denominator, and approach point to follow the derivative steps used to resolve the indeterminate form.

Transform a time-domain function into the Laplace domain with MiniWebtool’s Laplace Transform Calculator. The symbolic result comes with worked steps and visualizations of the original function and transformed expression.

Investigate a function’s behavior near a point with MiniWebtool’s Limit Calculator. Supported calculations include one-sided limits and indeterminate forms, with steps explaining algebraic transformations or L’Hôpital’s Rule where applicable.

Integrate a scalar or vector field along a parametric path with MiniWebtool’s Line Integral Calculator. Two- and three-dimensional curves are supported, with symbolic steps, arc length, and a visualization of the chosen path.

Approximate a function near zero using MiniWebtool’s Maclaurin Series Calculator. Choose the expansion order to inspect polynomial terms, convergence information, and a remainder estimate, with partial-sum graphs showing the approximation’s behavior.

Follow tangent-line approximations toward a root in MiniWebtool’s Newton's Method Calculator. Enter a function and starting guess to inspect each Newton-Raphson iteration, the path on the graph, and convergence behavior.

Enter a function and the interval in MiniWebtool’s Numerical Integration Calculator to 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 with MiniWebtool’s Optimization Calculator for Calculus. Get critical points, intervals of increase and decrease, concavity analysis, inflection points and an interactive graph with worked steps.

Differentiate a multivariable expression while holding the other variables constant in MiniWebtool’s Partial Derivative Calculator. Specify variables and orders, including mixed derivatives, to see the result and applied differentiation rules.

Expand a function around a chosen center with MiniWebtool’s Power Series Calculator. Taylor or Maclaurin coefficients, convergence bounds, and endpoint analysis accompany partial-sum visualizations that show where the approximation follows the original function.

MiniWebtool’s Radius of Convergence Calculator determines 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.

Connect changing measurements in a familiar calculus setup with MiniWebtool’s Related Rates Solver. Choose a scenario such as a sliding ladder or filling cone, supply known values and rates, and follow the derivative-based solution.

Compare numerical integration methods in MiniWebtool’s Riemann Sum Calculator. A function, interval, and subdivision count produce left, right, midpoint, trapezoidal, or Simpson approximations, with visualizations and steps showing how the estimate is built.

MiniWebtool’s Runge-Kutta (RK4) Method Calculator approximates an initial-value differential equation using fourth-order Runge-Kutta steps. Specify the equation, starting point, step size, and endpoint to inspect k1–k4 values and a solution table of up to 1,000 steps.

MiniWebtool’s Second-Order ODE Solver works with linear equations defined by coefficients, a forcing expression, and initial values. View the closed-form solution, damping classification, and phase-plane behavior over a chosen x range.

Explore infinite-series behavior with MiniWebtool’s Series Convergence Test Calculator. Select a series and parameters to compare applicable convergence tests, follow the working, and inspect partial-sum graphs.

Approximate an integral with MiniWebtool’s Simpson's Rule Calculator. Choose the 1/3 or 3/8 rule and subdivisions, then inspect parabolic visualizations, calculation steps, and error or convergence estimates.

Differentiate a function of one variable with MiniWebtool’s Single Variable Derivative Calculator. Select the derivative order or an evaluation point and review the applied rules, calculation steps, and graph.

MiniWebtool’s Surface Integral Calculator evaluates scalar surface integrals and vector-field flux over parametric surfaces. Choose a preset or enter a parameterization, field, and bounds, then inspect normals and a three-dimensional surface view.

Explore a rotated curve with MiniWebtool’s Surface of Revolution Calculator. Supply f(x), bounds, and a rotation axis to estimate the resulting surface area, with formula steps and a three-dimensional visualization.

MiniWebtool’s System of ODEs Solver analyzes coupled differential equations or matrix-defined systems. Inspect eigenvalue calculations, equilibrium classifications, and trajectory phase portraits to understand the system’s local behavior.

Approximate a function near a point with MiniWebtool’s Taylor Series Calculator. Choose the expansion center and order to see derivative-based terms and compare the polynomial approximation with the function graph.

Approximate an integral with MiniWebtool’s Trapezoidal Rule Calculator from a function with bounds and subintervals, or from x and y data. Review worked steps and individual trapezoid areas.

Evaluate iterated integration with MiniWebtool’s Triple Integral Calculator. Enter a function, three integration variables, and optional bounds to obtain symbolic working for definite or indefinite triple integrals, with three-dimensional context.

MiniWebtool’s Volume of Revolution Calculator models solids formed by rotating curves. Choose disk, washer, or shell method, supply functions and bounds, and inspect the integral setup with a three-dimensional visualization.

MiniWebtool’s Wronskian Calculator builds a derivative matrix from supplied functions and evaluates its determinant. Follow the expansion and optional point evaluation when examining linear independence, interpreting zero results with the functions’ assumptions.

Compute one-sided Z-transforms and causal inverse Z-transforms with MiniWebtool’s Z-Transform Calculator. 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.