MATLAB Examples

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

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

Work with large integers and their decimal representation using the 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

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

Perform simple matrix computations using Symbolic Math Toolbox™.

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

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

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

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

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

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

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

Solve parameterized algebraic equations using the Symbolic Math Toolbox.

Compute definite integrals 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

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.

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

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,

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

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

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.

Explores the physics of the damped harmonic oscillator by

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

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 .

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

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.

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

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

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.

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

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

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

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

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.

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

INTRODUCTION

This example was authored by the MathWorks community.

Basic physics courses at our universities are filled with a considerable amount of content, especially since the transition from Diploma to Bachelor's degree programs. They promote

A first step to theoretical physics is the mathematical description of space and time. This is based on coordinate systems consisting of an origin, basis vectors and coordinates.

We consider spherical coordinates \[\vec r = \left( {\begin{array}{*{20}{c}} {r\sin \theta \cos \varphi } \\ {r\sin \theta \sin \varphi } \\ {r\cos \theta } \end{array}} \right)\]

We parameterize a Mexican hat by

For the formulation of classical mechanics, Isaac Newton distinguished sharply between content and dynamics. His dynamic laws apply in general, regardless of any content. They are then

In contrast to water waves or sound waves, for light signals there is no medium to which the velocity of the signals can relate. There is only the observer, and nothing else. Light signals

Trajectories

Here we calculate the reflection and transmission of a plane quantum wave at a 1D Woods-Saxon potential.

Instead of coordinates of lines points, movements of the pen are specified. There are commands for forward movement, rotation, color and storage of states:

The Duffing oscillator is a one-dimensional driven oscillator with friction and a nonlinear potential. It is described by the

There are basically two types of chaotic systems

Man unterscheidet grundsätzlich zwei Arten von chaotischen Systemen

Die HJG drückt den Energisatz durch die Wirkung S aus und hat damit eine klare physikalische Bedeutung:

The suspension point {K_1} of a plane pendulum slides frictionless along the x-axis. The pendulum body {K_2} has the distance L from the suspension point. Both bodies have the same mass

We consider the dynamics of the Kepler problem

Der Duffing-Oszillator ist ein eindimensionaler, angetriebener Oszillator mit Reibung und einem nichtlinearen Potenzial. Er wird beschrieben durch die

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