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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.

teaching and research

mathematics


  • this example shows how to solve the eigenvalue problem of the laplace operator on an l-shaped region.

  • this example shows how to solve a partial differential equation (pde) of nonlinear heat transfer in a thin plate.

  • this example simulates a tsunami wave phenomenon by solving the partial differential equations that model the tsunami.

  • this example shows how to use the symbolic math toolbox functions jacobian and matlabfunction to provide analytical derivatives to optimization solvers.

  • symbolic math toolbox provides analytical plotting of mathematical expressions without explicitly generating numerical data.

physics


  • this example explores the physics of the damped harmonic oscillator by solving the equations of motion in the case of no driving forces.

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

  • this example shows how to use functional derivatives in symbolic math toolbox using the context of a wave equation.

  • solve differential equations of an rlc circuit by using laplace and inverse laplace transforms.

  • this example finds closed-form solutions for the coefficients of frequencies in an output signal.

  • this example shows how to work with units in physics calculations.

mathematical system modeling

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.

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.

this example uses to estimate the unknown capacitance and initial voltage of a symbolically derived algebraic model of a simple resistor-capacitor (rc) circuit.

create custom-equation-based components for the simscape library using symbolic math toolbox.

robotics

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

this example shows how to derive and apply inverse kinematics to a two-link robot arm by using matlab and symbolic math toolbox.

this example shows how to derive a continuous-time nonlinear model of a quadrotor using symbolic math toolbox.

quantitative finance

this example shows how to calculate the call option price using the black–scholes formula.

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

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.

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

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