Enhanced Calculus & Differential Equations

Version 10 adds many significant enhancements to its traditional strength in symbolic calculus. For the first time, symbolic solutions to hybrid differential equations with events and delay differential equations are possible. All discrete calculus operations are extended with newly developed algorithms motivated by probability and statistics. New dedicated commands for curve geometry as well as newly added special functions automate many tasks. Taken together, these developments will lead to smoother workflow for a wide range of applications, starting from college calculus to research level.

  • Obtain symbolic solutions to hybrid differential equations, with explicit events. »
  • Obtain symbolic solutions to delay differential equations.
  • Compute arbitrary expressions of solutions for differential equations. »
  • Obtain elegant results for discrete calculus operations on special functions. »
  • Directly compute arbitrary expressions of solutions for difference equations. »
  • Compute the curvature and arc length of parametrized curves. »
  • Use the classical Frenet–Serret system for curves in n dimensions. »
  • New differential-equation-related functions, including Scorer, associated Fresnel, and logistic functions.
  • Expanded number-theoretic functions, such as generalized Dirichlet L-functions and the Riemann function. »
  • Play with fractals using Cantor staircase, Minkowski , and Böttcher functions. »
  • Construct interpolating functions from data with quantities. »
  • Differentiate and integrate interpolating functions with quantities. »
  • Use quantities in symbolic differential equations.

Compute Symbolic Solutions for ODEs with Events »

Directly Obtain Solution Expressions for ODEs »

Find Symbolic Solutions for Delay Differential Equations »

Automatically Invoke NDSolve if DSolve Fails »

Rectify a Periodic Wave »

Model a Ball Bouncing down Steps »

Design a Proportional-Derivative Controller »

Visualize Chaos in a Delay Differential Equation »

Evaluate New Classes of Telescoping Sums and Products »

Compute Sums Involving Special Functions »

Obtain Simple Differences and Ratios for Special Functions »

Directly Obtain Solution Expressions for Difference Equations »

Color a Curve by Arc Length »

Compute the Curvature of Curves in Any Dimensions »

Visualize the TNB Basis of a Knot »
Animate the Tangent and Normal to a Function »

New Differential and Integral Equations Functions »

New Number-Theoretic Functions »

Draw Ford Circles »

Compute a Distribution Function for Rationals in the Unit Interval »

Interpolate Data with Quantities »

Differentiate and Integrate Interpolated Data with Quantities »

Compute Thermodynamic Values from Interpolated Data »

Plot the Planck Thermodynamic Potential of Water »