Symbolic Math Toolbox
Perform symbolic math computations
Symbolic Math Toolbox™ provides functions for solving, plotting, and manipulating symbolic math equations. You can create, run, and share symbolic math code using the MATLAB® Live Editor. The toolbox provides functions in common mathematical areas such as calculus, linear algebra, algebraic and ordinary differential equations, equation simplification, and equation manipulation.
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.
You can share your symbolic work with other MATLAB users as live scripts or convert them to HTML or PDF for publication. You can generate MATLAB functions, Simulink® function blocks, and Simscape™ equations directly from symbolic expressions.
Get Started:
Getting Started Resources
Mathematical Modeling with Symbolic Math Toolbox
Integration
Evaluate exact analytical solutions for definite or indefinite integrals. Perform high-precision numeric integrations using variable-precision arithmetic.
Compute the definite integral of a function and its maximum value using derivative.
Differentiation
Calculate derivatives of symbolic expressions or functions including functional derivatives.
Find the local maxima, minima, and inflection points of f(x) using the 1st and 2nd derivative.
Series Expansion, Integral Transformation, and Vector Analysis
Approximate functions using series expansions, compute common transforms and their inverses, and perform vector calculus operations.
Find the system response using Padé approximant of varying orders of accuracy.
Solve Algebraic and Differential Equations
Solve linear and nonlinear algebraic and differential equations analytically. Reduce differential algebraic equations.
Investigate the motion of a damped harmonic oscillator in the cases of under-, over-, and critical-damping.
Simplify and Rewrite Expressions
Simplify and rewrite symbolic expressions using different assumptions or options to manipulate expressions for various computations.
Simplify fractions using the simplify function.
Substitute Variables
Replace portions of expressions with specific symbolic or numeric values to evaluate symbolic expressions using substitution.
Substitute elements in symbolic matrices using the subs function.
Matrix Operation and Transformation
Analyze, transform, and decompose matrices to study the properties of linear equations.
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. 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.
Analytical Plotting
Use built-in functions to plot symbolic expressions and functions using extended MATLAB graphics capabilities.
Plot f=ex sin(20x), ex, and -ex using the fplot command.
Animation
Visualize the behavior of symbolic expressions using animations.
An animation of a moving automotive piston given a changing angular speed.
Precision and Computation Speed
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.
Improve the computation time of the Riemann zeta function by reducing precision.
Define, Create, and Convert Units
Create custom unit systems and convert between existing unit systems. Directly use over 2000 built-in units of measurement for physical quantities such as mass, time, velocity, and power.
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.
Verify the dimensions of a kinematic equation using the checkUnits function.
Interactive Computations
Interactively update and display symbolic math computations alongside MATLAB code, formatted text, equations, images, and hyperlinks using the MATLAB Live Editor.
Use MATLAB live scripts to display symbolic math computations alongside MATLAB code and other documentation.
Share MATLAB Code and Live Scripts
Create reproducible documentation by embedding code within a narrative. Publish and share your work as live scripts, generated PDFs or HTML documents.
Share your work with other MATLAB users as an executable notebook.
Generate code for MATLAB, Simulink, and Simscape
Generate MATLAB functions, Simulink function blocks, or custom equation-based Simscape components directly from symbolic expressions.
Extend the Simscape modeling environment by creating custom components from symbolic expressions.
Generate code for C, Fortran, LaTeX, and MathML
Generate C or Fortran code from symbolic expressions for numeric computations. Generate LaTeX or MathML for display.
Generate optimized C code with comments from symbolic expressions.
Live Editor Tasks
Interactively solve equations, simplify symbolic expressions, and generate MATLAB code in a live script
Differential Equations
Return solutions of differential equations in implicit form or truncated series expansion form
Number Theory
Evaluate the Euler phi function and Jacobi symbol, and find rational fraction approximations and primitive roots
Physical Units
Use new physical constants in compliance with 2019 redefinition of SI units
See the release notes for details on any of these features and corresponding functions.
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