IE University · School of Science & Technology

Calculus for Computer Science.

An interactive web companion to the TI-84 Plus CE programming toolkit by Andrea Montana. Every module from the research paper, rebuilt as a live visualization you can play with right here.

11modules
2 + 3Dvisualizations
0install

What this is

The accompanying research paper — Calculus for Computer Science: TI-84 Programming Toolkit — designs eleven TI-BASIC programs that turn a graphing calculator into a lightweight computational assistant. Each program automates one piece of single- or multi-variable calculus.

This site is the same toolkit, in a browser. Each module shows the math, lets you change inputs, runs the same numerical method the calculator uses, and visualizes the result. The TI-BASIC source for every module is reproduced inside its section.

LIMTLimit estimationTwo-sided numeric table + DNE detector. CONTContinuity checkJump · removable · continuous classifier. DER1Derivative at a pointf′(a) and tangent line, draggable a. DER2Second derivativeConcavity and inflection candidates. IMPLImplicit diff.dy/dx = −Fx/Fy on a level curve. INT1Definite integralShaded area + Riemann sum overlay. MACLMaclaurin seriesPolynomial approximations up to degree 6. GRADGradient vector∇f on a 3-D surface and 2-D contour. DDERDirectional deriv.Duf, with auto-normalised direction. TANPTangent planePlane through a surface, drawn in 3-D. CRITCritical-point testSecond-derivative discriminant D = fxxfyy − fxy².

How to use a module

  1. Pick a module from the sidebar.
  2. Edit the function and any points / intervals. Examples from the paper's exam questions are preloaded.
  3. Press Compute (or just hit Enter). Numeric output and the plot update together.
  4. Each module shows the TI-BASIC source it mirrors, so you can compare the calculator workflow side by side.

Tip: function syntax uses ^ for powers, * for multiplication, and standard names sin, cos, exp, log, sqrt, abs. Use log for natural log (math.js convention).

LIMT

Numeric limit estimation

Estimate $\lim_{x \to a} f(x)$ by sampling from both sides, then flag whether the limit exists.

TI-BASIC source — PROGRAM:LIMT 

        

      

      

    

  


  
  

    

      CONT
      
Continuity check at $x = a$

      
Compares one-sided limits with $f(a)$ to classify: continuous, removable discontinuity, or jump.

    

    

      

        
        
        
        

        
TI-BASIC source — PROGRAM:CONT

      

      

    

  


  
  

    

      DER1
      
First derivative at a point

      
Computes $f'(a)$ numerically and draws the tangent line $y = f'(a)(x-a) + f(a)$.

    

    

      

        
        
        
        

        
TI-BASIC source — PROGRAM:DER1

      

      

    

  


  
  

    

      DER2
      
Second derivative & concavity

      
Plots $f$, $f'$ and $f''$ together; flags concavity and inflection candidates at $x=a$.

    

    

      

        
        
        
        

        
TI-BASIC source — PROGRAM:DER2

      

      

    

  


  
  

    

      IMPL
      
Implicit differentiation

      
For a curve defined by $F(x,y) = 0$, the slope is $\dfrac{dy}{dx} = -\dfrac{F_x}{F_y}$. The plot shows the level set and the tangent line.

    

    

      

        
        
        
        
        

        
TI-BASIC source — PROGRAM:IMPL

      

      

    

  


  
  

    

      INT1
      
Definite integral & Riemann sums

      
Computes $\int_a^b f(x)\,dx$ and compares the four classic Riemann approximations alongside the exact value.

    

    

      

        
        
        
        
        
        
        

        
TI-BASIC source — PROGRAM:INT1

      

      

    

  


  
  

    

      MACL
      
Maclaurin polynomial

      
Builds $P_n(x) = \sum_{k=0}^{n} \frac{f^{(k)}(0)}{k!}x^k$ from numerical derivatives at the origin, and plots successive approximations against $f$.

    

    

      

        
        
        
        
        

        
TI-BASIC source — PROGRAM:MACL

      

      

    

  


  
  

    

      GRAD
      
Gradient vector $\nabla f$

      
Computes $\nabla f = (f_x, f_y)$ at a point. Visualized on the 3-D surface and on the 2-D contour plot, where the gradient is always perpendicular to the level curve.

    

    

      

        
        
        
        
        

        
TI-BASIC source — PROGRAM:GRAD

      

      

        

        

      

    

  


  
  

    

      DDER
      
Directional derivative $D_u f$

      
Auto-normalises the direction $\mathbf{u}$, then computes $D_u f = \nabla f \cdot \hat{\mathbf{u}}$. The 3-D plot shows the slice taken in direction $\mathbf{u}$.

    

    

      

        
        
        
        
        
        
        

        
TI-BASIC source — PROGRAM:DDER

      

      

    

  


  
  

    

      TANP
      
Tangent plane to $z = f(x,y)$

      
$z = f(p,q) + f_x(p,q)(x-p) + f_y(p,q)(y-q)$. Drawn alongside the surface in 3-D.

    

    

      

        
        
        
        
        

        
TI-BASIC source — PROGRAM:TANP

      

      

    

  


  
  

    

      CRIT
      
Critical-point classification

      
Second-derivative test: $D = f_{xx}f_{yy} - f_{xy}^2$. Local min if $D>0, f_{xx}>0$; local max if $D>0, f_{xx}<0$; saddle if $D<0$.

    

    

      

        
        
        
        
        

        
TI-BASIC source — PROGRAM:CRIT

      

      

    

  


  
  

    

      ?
      
Syntax guide

      
All inputs are parsed by math.js. Same rules across every module.

    

    

      

        
You typeMeaning

        
x^2$x^2$ — powers use ^

        
3*x*y$3xy$ — multiplication is explicit with *

        
sqrt(x)$\sqrt{x}$

        
exp(x)$e^x$

        
log(x)$\ln x$ — natural log (math.js convention)

        
log10(x)$\log_{10} x$

        
sin, cos, tan, asin, ...Trig functions, radians

        
abs(x)$|x|$

        
pi, eConstants

        
(x^2-1)/(x-1)Use parentheses freely

      

      
Sample functions from the paper

      
    
        
  • Limit: sin(x)/x at a=0
    • 
        
  • Continuity: (x^2-1)/(x-1) at a=1 (removable)
    • 
        
  • Derivative: x^3 - 2*x at a=1
    • 
        
  • Integral: $\int_0^2 x^2\,dx = 8/3$
    • 
        
  • Gradient (problem 11): x^2*y + 3*y^2 at $(1,2)$
    • 
        
  • Critical pts (problem 13): x^3 - 3*x*y^2
    • 
        
  • Tangent plane (problem 15): log(x^2 + y + 2) at $(1,0)$
    •