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Feature List

1. Pure Math Functions

  • Addition, subtraction, multiplication, division, parentheses
  • Exponentiation (including non-integer, rational and real exponents), and logarithms. Special buttons are:
    • Square, cube, sqrt, cbrt
    • Exponential function and 10^x
    • Natural log and log10
  • Constants: pi, e
  • Trigonometric and inverse trigonometric functions (just sin, cos, tan and their inverses should do)
  • Complex numbers (and complex-compatible arithmetic operations), along with:
    • Conjugation, real and imaginary parts, argument, magnitude
  • Numerical derivative calculation at a given point
  • Numerical (definite) integration over a given interval (perhaps including nesting, which is not supported on TI-84)
  • Sigma notation evaluation (perhaps including nesting, which is not supported on TI-84)
  • Counting functions: factorial, nPr, nCr

2. Statistics

Everything under the 'distr' and 'stat' pages on the TI-84 Plus CE.

Distributions:

  • Normal: PDF, CDF, inverse
  • Student's t: PDF, CDF, inverse
  • Chi-squared: PDF, CDF
  • F-distribution: PDF, CDF
  • Binomial: PDF, CDF, inverse
  • Poisson: PDF, CDF
  • Geometric: PDF, CDF

Statistical calculations:

  • Entering of data into lists + sorting lists in ascending and descending order
  • Univariate and bivariate statistics, namely:
    • Sample mean of each variable (x̄)
    • Sum of values for each variable (Σx)
    • Sum of squares of values for each variable (Σx²)
    • Sum of products of variables (Σxy)
    • Sample variance: Bessel-corrected (s²) and non-Bessel-corrected (σ²)
    • Number of samples (n)
    • Minimum and maximum value of each variable (min(X), max(X))
  • Regression:
    • Least-squares:
      • Linear, quadratic, cubic, quartic
      • Logarithmic, exponential, power (ax^b), logistic (c / (1 + ae^(-bx)))
      • Sinusoidal
    • Median-median (unique to Texas Instruments GCs)
    • Manual-fit linear regression (optional)

Statistical tests:

  • TODO: complete this section

3. Solvers

  • Polynomial root finder (up to degree 10)
    • Solutions should be given in rational form when possible, especially for polynomials of up to degree 3 (replicates TI-84 Plus CE functionality)
  • Simultaneous linear equation solver (up to 10 equations and unknowns)
    • Note: should support the case where number of equations < number of unknowns, in which case some unknowns are expressed in terms of other unknowns.
  • Root finding for arbitrary function through graphing

4. Graphing

  • Should support plotting of multiple arbitrary univariate functions on the same coordinate plane
  • Additional calculations:
    • Find value of function at given x-value
    • Numerical root-finding within a given interval
      • There exist a wealth of algorithms for this, including naive bisection (binary search to within some accuracy bound), the Newton-Raphson method, and several others you can probably find online.
    • Finding of local maxima and minima within a given interval
    • Graph intersection finding (trivial; simply find a root of the difference between the two functions)
    • Derivative and definite integral calculation (same as under section 1)
      • Consider highlighting area under graph if integral function is called when in graphing mode