liminfoMathematica Reference
Free reference guide: Mathematica Reference
About Mathematica Reference
This Mathematica Reference is a searchable cheat sheet for the Wolfram Language, organized into eight categories: Basics, Math, Lists, Graphics, Equations, Calculus, Linear Algebra, and Programming. Each entry includes the function syntax, a description, and runnable code examples.
The reference covers fundamental operations like variable assignment, delayed assignment (f[x_] := expr), lists, conditionals (If), loops (Do), and Module for local variables, along with symbolic math functions including Solve, Simplify, Expand, Factor, and N for numerical approximation.
Advanced topics include 2D/3D plotting (Plot, Plot3D, ListPlot, ParametricPlot, Histogram), differential equation solving (DSolve, NDSolve, FindRoot, Reduce, NSolve), calculus operations (D, Integrate, Limit, Series), linear algebra (Eigenvalues, Det, Inverse, LinearSolve, Dot, Cross), and programming constructs (Nest, NestList, pure functions, pattern matching, Import/Export).
Key Features
- Complete Wolfram Language syntax reference with 42+ entries across 8 categories
- Math functions: Solve, Simplify, Expand, Factor, and N for symbolic and numerical computation
- List operations: Table, Map, Select, Sort, Reverse, Total, Mean, and Median
- Graphics: Plot, Plot3D, ListPlot, ListLinePlot, ParametricPlot, Histogram, and BarChart
- Equation solving: DSolve, NDSolve, FindRoot, Reduce, NSolve for algebraic and differential equations
- Calculus: D (derivatives), Integrate (definite/indefinite), Limit, and Series (Taylor expansion)
- Linear algebra: Eigenvalues, Eigenvectors, Det, Inverse, Transpose, LinearSolve, Dot, Cross
- Programming: For/While loops, Nest/NestList, pure functions (#, &), pattern matching, and Export/Import
Frequently Asked Questions
What Mathematica topics does this cheat sheet cover?
It covers eight categories: Basics (variables, delayed assignment, lists, If, Do, Module), Math (Solve, Simplify, Expand, Factor, N), Lists (Table, Map, Select, Sort, Total, Mean), Graphics (Plot, Plot3D, ListPlot, ParametricPlot, Histogram), Equations (DSolve, NDSolve, FindRoot, Reduce, NSolve), Calculus (D, Integrate, Limit, Series), Linear Algebra (Eigenvalues, Det, Inverse, LinearSolve, Dot, Cross), and Programming (loops, Nest, pure functions, pattern matching, Import/Export).
What is the difference between = and := in Mathematica?
The single equals (=) is immediate assignment, evaluated once at definition time. The colon-equals (:=) is delayed assignment, re-evaluated each time the symbol is used. For function definitions, use f[x_] := expr so the expression is freshly evaluated with each call argument.
How do I solve equations in Mathematica?
Use Solve[eqn, x] for exact symbolic solutions, NSolve[eqn, x] for numerical solutions, FindRoot[f, {x, x0}] for iterative root finding, Reduce[expr, vars] for conditional solving including inequalities, DSolve for differential equations, and NDSolve for numerical ODE/PDE solving.
How do I create plots in Mathematica?
Use Plot[f, {x, a, b}] for 2D function graphs, Plot3D for 3D surfaces, ListPlot/ListLinePlot for data points, ParametricPlot for parametric curves, and Histogram/BarChart for statistical visualizations. Add options like PlotLabel, AxesLabel, and PlotMarkers for customization.
What calculus operations are available?
D[f, x] computes derivatives and partial derivatives, Integrate[f, x] finds indefinite integrals, Integrate[f, {x, a, b}] evaluates definite integrals, Limit[f, x -> a] computes limits, and Series[f, {x, a, n}] generates Taylor series expansions around a point.
How do I work with matrices in Mathematica?
Define matrices as nested lists: {{1, 2}, {3, 4}}. Use Det for determinants, Inverse for matrix inverse, Transpose, Eigenvalues/Eigenvectors, LinearSolve[A, b] for solving Ax=b, Dot (.) for matrix multiplication, Cross for cross product, and MatrixForm for display formatting.
What are pure functions in Mathematica?
Pure functions use # for arguments and & to close the function body. For example, #^2 & squares its argument. Use with Map: Map[#^2 &, {1, 2, 3}] returns {1, 4, 9}. Multiple arguments use #1, #2, etc. Pure functions are ideal for short, inline operations.
Is this Mathematica reference free?
Yes, completely free with no usage limits and no account required. All content runs locally in your browser with instant search and category filtering. Works on desktop, tablet, and mobile with dark mode support.