# Applications

Perform application-specific workflows using Symbolic Math Toolbox™

Symbolic Math Toolbox provides tools to solve, plot, and manipulate mathematical expressions, both analytically and numerically with high precision. From the results of symbolic computations, you can also generate MATLAB® functions, Simulink® Function blocks, and Simscape™ equations to use with other toolboxes. Use these tools to perform application-specific workflows.

## Mathematical System Modeling

Animation and Model of Automotive Piston

This example shows how to model the motion of an automotive piston by using MATLAB and Symbolic Math Toolbox.

This example shows how to use a Padé approximant in control system theory to model time delays in the response of a first-order system.

Analytical Model of Cantilever Truss Structure for Simscape

This example shows how to find parameterized analytical expressions for the displacement of a joint of a cantilever truss structure in both the static and frequency domains.

Estimate Model Parameters of a Symbolically Derived Plant Model in Simulink

This example uses Simulink Design Optimization™ to estimate the unknown capacitance and initial voltage of a symbolically derived algebraic model of a simple resistor-capacitor (RC) circuit.

Customize and Extend Simscape Libraries for a Custom DC Motor

Create custom-equation-based components for the Simscape library using Symbolic Math Toolbox.

## Robotics

Analytical Solutions of the Inverse Kinematics of a Humanoid Robot

This example shows how to derive analytical solutions for the inverse kinematics of the head chain of a humanoid robot.

Derive and Apply Inverse Kinematics to Two-Link Robot Arm

This example shows how to derive and apply inverse kinematics to a two-link robot arm by using MATLAB and Symbolic Math Toolbox.

Derive Quadrotor Dynamics for Nonlinear Model Predictive Control

This example shows how to derive a continuous-time nonlinear model of a quadrotor using Symbolic Math Toolbox.

## Quantitative Finance

The Black–Scholes Formula for Call Option Price

This example shows how to calculate the call option price using the Black–Scholes formula.

Explore Single-Period Asset Arbitrage

Explore basic arbitrage concepts in a single-period, two-state asset portfolio.

Simulate a Stochastic Process Using the Feynman–Kac Formula

This example obtains the partial differential equation that describes the expected final price of an asset whose price is a stochastic process given by a stochastic differential equation.

Markov Chain Analysis and Stationary Distribution

This example shows how to derive the symbolic stationary distribution of a trivial Markov chain by computing its eigen decomposition.