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Symbolic Computations in MATLAB

Symbolic variables, expressions, functions, conversions between symbolic and numeric

Symbolic Math Toolbox™ enables you to perform symbolic computations from the MATLAB^® command line by defining a special data type — symbolic objects. Functions are called using the familiar MATLAB syntax and are available for integration, differentiation, simplification, equation solving, and other mathematical tasks. Symbolic computations augment the numeric capabilities of MATLAB. You can convert symbolic results to numeric results and use them outside Symbolic Math Toolbox.

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Featured Examples

The Physics of the Damped Harmonic Oscillator

Explores the physics of the damped harmonic oscillator by solving the equations of motion in the case of no driving forces. This example investigates the cases of under-, over-, and critical-damping.

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Simulate the Motion of the Periodic Swing of a Pendulum

Solve the equation of motion of a simple pendulum analytically for small angles and numerically for any angle.

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Evaluating the Average Power Delivered by a Wind Turbine

Uses Symbolic Math Toolbox™ and the Statistics and Machine Learning Toolbox™ to explore and derive a parametric analytical expression for the average power generated by a wind turbine.

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Developing an Algorithm for Undistorting an Image

Develops a mathematical model using the Symbolic Math Toolbox™ to undistort an image and features a local function in the live script.

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Electric Dipole Moment and Radiation Power

Finds the average radiation power of two attracting charges moving in an elliptical orbit (an electric dipole).

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Validate Simulink Model Using Symbolic Math Toolbox

Model a bouncing ball, which is a classical hybrid dynamic system. This model includes both continuous dynamics and discrete transitions. It uses the Symbolic Math Toolbox™ to help explain some of the theory behind ODE solving in the Simulation of a Bouncing Ball.

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