ANLIS - Analysis for Python

ANLIS is a Python package for analysis built on top of numpy and sympy. ANLIS provides a set of functions to perform analysis tasks. ANLIS is a work in progress and currently supports the following tasks:

• Series
  • Plotting any series
  • Arithmetic Series
    • Finding $a_n$ from two elements
  • Geometric Series
    • Finding $a_n$ from two elements
    • Finding the sum of an infinite series (based on ratio and first element or two elements)
• Convergence
  • Determining if a sequence is convergent (or divergent)
  • Convergence Tests
• Derivatives
  • Finding the critical points of a function
  • Finding the extrema of a function
• Vectors
  • Finding the magnitude of a vector
  • Finding the unit vector of a vector
  • Finding the dot product of two vectors
• Taylor Series
  • Finding the Taylor Series of a function
  • Finding the Taylor Polynomial of a function
  • Finding the Lagrange Remainder of a function
• Integrals
  • Left/Right Riemann Sums
  • Trapezoidal Rule
  • Simpson's Rule
• Differentials (e.g. for error analysis)
  • Absolute differential
  • Relative differential
• Multidimensional Calculus
  • Critical points
    • Finding critical points
    • Finding extrema
  • Derivatives
    • Finding the (or all) partial derivatives of a function
    • Finding partial derivatives of composite functions
    • Finding the gradient of a function
    • Finding the Jacobian of a function
    • Finding the determinant of a function
    • Finding the linearisation of a function
    • Solving with Newton-Raphson
    • Finding the directional derivative of a function
  • Contour Lines
    • Finding the contour lines of a function
    • Finding the tangent lines of contour lines
    • Plotting the contour lines of a function (2D or 3D)
  • Differentials (e.g. for error analysis)
    • Absolute differential
    • Relative differential
    • Total differential

The wiki contains more information on the functions along with examples and when to use them.