Symbolic & Numeric Calculus

Symbolic & Numeric Calculus in Mathematica 11

Mathematica Version 11 builds on its capabilities in calculus, with new symbolic and numeric features that enhance each other. Integral transforms are extended with the Mellin transform, along with related convolution and function simplification operations. The symbolic differential equation solver has been extended to support multiple types of integral and integro-differential equations. A new back end has been added to the numerical optimization engine for faster and more accurate solutions for large systems. Small tweaks include a new function for computing difference quotients and extending volume computations to understand non-Cartesian coordinates. Taken together, these enhancements make calculus faster, easier, and better at all levels of sophistication.

Key Features

  • Find the Mellin transforms of functions. »
  • Perform the Mellin convolutions for pairs of functions. »
  • Express functions in terms of Meijer's G function. »
  • Rapidly solve constrained numerical optimization problems with hundreds of variables. »
  • Compute ordinary and partial difference quotients. »
  • Obtain symbolic solutions for linear integral equations. »
  • Solve inhomogeneous differential equations using Green's functions. »
  • Compute areas and volumes using non-Cartesian coordinates. »

Related Examples

Compute a Mellin Transform »

Find an Inverse Mellin Transform »

Perform a Mellin Convolution »

Solve a SIAM Challenge Problem »

Compute Difference Quotients »

Evaluate a Derivative Using First Principles »

Generate a Gallery of Difference Quotients »

Visualize Secants and Tangents »

Find the Largest Small Polygon »

Find the Charge Distribution on a Sphere »

Optimize the Shape of a Cam »

Model a Hanging Chain »

Solve a Volterra Integral Equation »

Solve a Fredholm Integral Equation »

Solve an Integro-Differential Equation »

Solve the Tautochrone Problem »

Solve an Initial Value Problem Using a Green's Function »

Solve a Boundary Value Problem Using a Green's Function »

Solve the Wave Equation Using Its Fundamental Solution »

Find the Impulse Response of a Circuit »

Represent Functions in Terms of MeijerG »

Compute Definite Integrals Using G Reduction »

Compute Areas and Volumes in Non-Cartesian Coordinates »

Solve an ODE with a Ramp Forcing Function »