MATLAB Examples

This script demonstrates using the included Talbot and Euler algorithms for numerical approximations of the inverse Laplace transform. The examples cover functions with known inverses

This file contains an explanation of the difference between implicit and explicit time integration schemes. The content is intended for those who want to learn a bit more than what the

Use functional derivatives in the Symbolic Math Toolbox™ using the example of the wave equation. The wave equation for a string fixed at its ends is solved using functional derivatives. A

Create a 3-D surface by using fsurf .

Plot 3-D parametric lines by using fplot3 .

Plot equations and implicit functions using fimplicit .

Create a 2-D line plot by using fplot . Plot the expression x^3-6x^2+11x-6 .

Compute definite integrals using Symbolic Math Toolbox™.

Analytically find and evaluate derivatives using Symbolic Math Toolbox™. In the example you will find the 1st and 2nd derivative of f(x) and use these derivatives to find local maxima,

Learn calculus and applied mathematics using the Symbolic Math Toolbox™. The example shows introductory functions fplot and diff .

Provides an overview of the Symbolic Math Toolbox which offers a complete set of tools for computational and analytical mathematics.

This demonstration shows how to find extrema of functions using analytical and numerical techniques using the Symbolic Math Toolbox.

The fplot family accepts symbolic expressions and equations as inputs enabling easy analytical plotting without explicitly generating numerical data.

Derive the symbolic stationary distribution of a trivial Markov chain by computing its eigen decomposition.

Solve the eigenvalue problem of the Laplace operator on an L-shaped region.

Do rotations and transforms in 3D using Symbolic Math Toolbox™ and matrices.

Perform simple matrix computations using Symbolic Math Toolbox™.

Compute the inverse of a Hilbert matrix using Symbolic Math Toolbox™.

Extracts closed-form solutions for the coefficients of frequencies in an output signal. The output signal results from passing an input through an analytical nonlinear transfer

Use a Padé approximant in control system theory to model time delays in the response of a first-order system.

Explores basic arbitrage concepts in a single-period, two-state asset portfolio. The portfolio consists of a bond, a long stock, and a long call option on the stock.

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.

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

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

Use units to perform physics calculations in both SI and Imperial units. Compute with units the terminal velocity of a falling paratrooper by modeling the deacceleration of velocity due to

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.

Simulates and explores the behavior of a simple pendulum by deriving its equation of motion, and solving the equation analytically for small angles and numerically for any angle.

Solve differential algebraic equations (DAEs) of high differential index using Symbolic Math Toolbox™.

Simulates the tsunami wave phenomenon by using the Symbolic Math Toolbox™ to solve differential equations.

Solve parameterized algebraic equations using the Symbolic Math Toolbox.

Convert a second-order differential equation into a system of differential equations that can be solved using the numerical solver ode45 of MATLAB®.

Solve polynomial equations and systems of equations, and work with the results using Symbolic Math Toolbox™.

Demonstrates that the Symbolic Math Toolbox helps minimize errors when solving a nonlinear system of equations.

Use the Symbolic Math Toolbox™ functions jacobian and matlabFunction to provide analytical derivatives to optimization solvers. Optimization Toolbox™ solvers are usually more

Finds parameterized analytical expressions to model the displacement of a joint for a trivial cantilever truss structure in both static and frequency domains for use in Simscape.

Model a bouncing ball, which is a clasical hybrid dynamic system. This model includes both continuous dynamics and discrete transitions. It uses the Symbolic Math Toolbox to help explain

Create a custom equation based components for the Simscape Library using the Symbolic Math Toolbox.

Use variable-precision arithmetic to investigate the decimal digits of pi using Symbolic Math Toolbox™.

Get precise values for binomial coefficients and find probabilities in coin-tossing experiments using the Symbolic Math Toolbox.

Work with large integers and their decimal representation using the Symbolic Math Toolbox™.

Use variable-precision arithmetic to obtain high precision computations using Symbolic Math Toolbox™.

Use some elementary functions on sym objects using the Symbolic Math Toolbox™.

This code solves a test problem involving a Poisson equation on a square domain. The method relies on Lagrangian finite elements on a uniform triangular mesh. The solver is documented in the

INTRODUCTION

This code solves the test problem of a thermally driven flow in a rectangular enclosure with an aspect ration of 8:1, as described in Christon et al. (2002). The method relies on Taylor-Hood

This code solves a test problem involving a Burgers equation on a square domain, described in "Singler (2014). The method relies on linear Lagrangian finite elements on a uniform triangular

This example was authored by the MathWorks community.

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