The toolbox provides functions in common mathematical areas such as calculus, linear algebra, algebraic and ordinary differential equations, equation simplification, and equation manipulation.
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Symbolic Math Toolbox lets you analytically perform differentiation, integration, simplification, transforms, and equation solving. You can perform dimensional computations and conversions using SI and US unit systems.
Your computations can be performed either analytically or using variable-precision arithmetic, with the results displayed in mathematical typeset. Evaluate exact analytical solutions for definite or indefinite integrals.
Perform high-precision numeric integrations using variable-precision arithmetic. Find the local maxima, minima, and inflection points of f x using the 1 st and 2 nd derivative. Approximate functions using series expansions, compute common transforms and their inverses, and perform vector calculus operations.
Solve linear and nonlinear algebraic and differential equations analytically.
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Reduce differential algebraic equations. Investigate the motion of a damped harmonic oscillator in the cases of under-, over-, and critical-damping. Simplify and rewrite symbolic expressions using different assumptions or options to manipulate expressions for various computations.
Replace portions of expressions with specific symbolic or numeric values to evaluate symbolic expressions using substitution.
Solve systems of linear equations in matrix or equation form. Compute matrix properties, such as the eigenvalues, norm, determinant and characteristic polynomial to study systems of linear equations. Derive the symbolic stationary distribution of a trivial Markov chain and determine the transition probabilities.
Analytically plot symbolic expressions, create animations, and customize visualizations. Explicitly set the number of significant digits to avoid hidden round-off errors. Increase the speed of calculations by reducing the precision with variable-precision arithmetic. Create custom unit systems and convert between existing unit systems. Directly use over built-in units of measurement for physical quantities such as mass, time, velocity, and power.
Create reproducible documentation by embedding code within a narrative. Translate symbolic equations into functions or blocks for use in numeric simulations and engineering design. Extend the Simscape modeling environment by creating custom components from symbolic expressions.
Generate C or Fortran code from symbolic expressions for numeric computations. Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select:.
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Much more than documents.
Watch video. Download a free trial. Get Started:. Documentation and Resources Try or Buy. Get examples and videos. Calculus Define and perform operations on symbolic expressions, equations, numbers, and variables. Integration Evaluate exact analytical solutions for definite or indefinite integrals. Compute Definite Integrals.
Compute the definite integral of a function and its maximum value using derivative. Differentiation Calculate derivatives of symbolic expressions or functions including functional derivatives.
Analytically Find and Evaluate Derivatives. Functional Derivatives Tutorial. Find Asymptotes, Critical, and Inflection Points.
Perform symbolic math computations
Series Expansion, Integral Transformation, and Vector Analysis Approximate functions using series expansions, compute common transforms and their inverses, and perform vector calculus operations. Plot the Gradient of a Function.
Equation Solving, Simplification, and Substitution Manipulate, simplify, and solve symbolic expressions. Solve Algebraic and Differential Equations Solve linear and nonlinear algebraic and differential equations analytically.
Equation Solving. Simplify and Rewrite Expressions Simplify and rewrite symbolic expressions using different assumptions or options to manipulate expressions for various computations.
Simplify Symbolic Expressions. Choose Function to Rearrange Expression.
Substitute Variables Replace portions of expressions with specific symbolic or numeric values to evaluate symbolic expressions using substitution. Substitute Variables in Symbolic Expressions. Explore Single-Period Asset Arbitrage. Substitute elements in symbolic matrices using the subs function. Linear Algebra Perform linear algebra operations on symbolic vectors and matrices.
Matrix Operation and Transformation Analyze, transform, and decompose matrices to study the properties of linear equations. Eigenvalues of the Laplace Operator. Matrix Rotations and Transformations.
Investigate the singular value of a 3-by-3 Hilbert matrix. Solve Systems of Linear Equations Solve systems of linear equations in matrix or equation form.
Solve System of Linear Equations. Markov Chain Analysis and Stationary Distribution. Visualization Analytically plot symbolic expressions, create animations, and customize visualizations. Analytical Plotting with Symbolic Math Toolbox. Create Plots. Animation Visualize the behavior of symbolic expressions using animations. Animation and Model of Automotive Piston. Animation and Solution of Double Pendulum Motion.
Symbolic Math Toolbox
An animation of a moving automotive piston given a changing angular speed. Variable-Precision Arithmetic Control precision of computations with variable-precision arithmetic.
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Precision and Computation Speed Explicitly set the number of significant digits to avoid hidden round-off errors. Increase Precision of Numeric Calculations. Recognize and Avoid Round-Off Errors. Numerical Computations With High Precision.
Increase Speed by Reducing Precision. Improve the computation time of the Riemann zeta function by reducing precision. Units and Dimensional Analysis Perform dimensional computations using built-in or custom unit systems. Define, Create, and Convert Units Create custom unit systems and convert between existing unit systems. Units and Unit Systems List. Define New Unit and Rewrite Unit. Visualize the velocity of a paratrooper as they approach terminal velocity.
Perform Dimensional Analysis Verify the dimensional compatibility and consistency of units in physics calculations. Units of Measurement Tutorial. Unit Conversions and Unit Systems. Verify the dimensions of a kinematic equation using the checkUnits function. Computational Mathematics in Symbolic Math Toolbox.
Learn Calculus in the Live Editor.
Live Scripts and Functions. Share Live Scripts and Functions.
Code Generation Translate symbolic equations into functions or blocks for use in numeric simulations and engineering design. Generate C or Fortran code from Symbolic Expressions. Generate optimized C code with comments from symbolic expressions. Additional Symbolic Math Toolbox Resources.