User Guide

Learn how to use Calcora effectively for calculus computations and step-by-step explanations.

Getting Started

Option 1: Desktop App (Recommended)

Windows Desktop App

  1. Download Calcora.exe from GitHub Releases
  2. Click "More info" → "Run anyway" (SmartScreen warning is expected for unsigned apps)
  3. Browser opens automatically to http://localhost:PORT
  4. Start computing! No installation needed.
Tip: The desktop app runs 100% offline. No data leaves your computer.

Option 2: Web Demo

Try Calcora instantly in your browser: Live Demo

Option 3: Python Package

pip install calcora

Use Calcora as a Python library or run the web interface locally:

calcora serve  # Starts web server at http://localhost:5000

Basic Operations

Differentiation

Input Syntax

Enter expressions using standard mathematical notation:

  • x**2 — x squared (power)
  • sin(x), cos(x), tan(x) — Trigonometric functions
  • exp(x) or e**x — Exponential
  • log(x) — Natural logarithm
  • sqrt(x) or x**(1/2) — Square root

Examples

Input: x**2 + 3*x + 2
Output: 2*x + 3

Input: sin(x)*cos(x)
Output: cos(x)**2 - sin(x)**2

Input: e**(x**2)
Output: 2*x*e**(x**2)

Integration

Indefinite Integrals

Calcora supports 10 integration techniques:

  • ✅ Power rule
  • ✅ U-substitution
  • ✅ Integration by parts (LIATE heuristic)
  • ✅ Partial fractions
  • ✅ Trigonometric identities
  • ✅ Inverse trig patterns
  • ✅ Hyperbolic functions
  • ✅ Exponentials and logarithms

Definite Integrals

Specify lower and upper bounds:

Input: x**2, from 0 to 2
Output: 8/3 ≈ 2.667

Includes area visualization under the curve!

Matrix Operations

Supported Operations

  • Determinant — Matrix determinant
  • Inverse — Matrix inverse (if exists)
  • Eigenvalues — Eigenvalue computation
  • RREF — Reduced row echelon form
  • LU Decomposition — Lower-upper factorization
  • Rank — Matrix rank

Example

Matrix: [[1, 2], [3, 4]]
Determinant: -2
Inverse: [[-2, 1], [1.5, -0.5]]

Verbosity Modes

Calcora offers three explanation detail levels:

Concise Mode

Best for: Quick answers, intermediate students

Shows: Final result + key transformation steps

d/dx[x**2 + 3*x]
= 2*x + 3

Detailed Mode (Default)

Best for: Learning, homework verification

Shows: Every rule applied + intermediate steps

d/dx[x**2 + 3*x]
Step 1: Apply sum rule: d/dx[f + g] = f' + g'
Step 2: Apply power rule to x**2: 2*x
Step 3: Apply constant multiple rule to 3*x: 3
Result: 2*x + 3

Teacher Mode

Best for: Teaching, exam prep, deep understanding

Shows: Definitions, theorems, pedagogical notes

d/dx[x**2 + 3*x]
**Sum Rule:** If f and g are differentiable, then d/dx[f + g] = f' + g'
**Power Rule:** For any real number n, d/dx[x^n] = n*x^(n-1)
...detailed explanation with theorem citations...

Tips & Best Practices

✅ DO:

  • Use parentheses for clarity: sin(2*x) not sin 2x
  • Use ** for powers: x**2 not x^2
  • Check step-by-step explanations to understand the process
  • Verify results against known solutions
  • Use Teacher Mode when learning new concepts

⚠️ AVOID:

  • Very complex expressions (>50 terms) — performance may suffer
  • Using Calcora for graded work without understanding the steps
  • Assuming 100% accuracy — always verify critical computations
  • Relying solely on answers — focus on understanding the method

Keyboard Shortcuts

Shortcut Action
Ctrl/Cmd + Enter Compute (submit expression)
Ctrl/Cmd + K Clear input
Ctrl/Cmd + D Toggle dark mode
Ctrl/Cmd + V Cycle verbosity modes

Troubleshooting

Desktop App Issues

Windows SmartScreen Warning

Issue: "Windows protected your PC" message

Solution: Click "More info" → "Run anyway". This is expected for unsigned open-source apps. See Code Signing Guide for details.

Browser Doesn't Open

Solution: Manually open browser and navigate to the URL shown in the console window (e.g., http://localhost:54782)

Computation Issues

"Cannot compute integral"

Reason: Expression requires advanced techniques not yet implemented (e.g., trigonometric substitution)

Workaround: Try simplifying the expression or use SymPy directly

Incorrect Result

Action: Report on GitHub Issues with:

  • Input expression
  • Expected result
  • Actual result
  • Verbosity mode used

Privacy & Security

🔒 Your Data is Private

  • ✅ Desktop app runs 100% offline (no internet required)
  • ✅ No data collection or telemetry
  • ✅ All computations happen locally on your device
  • ✅ No accounts or sign-up required
  • ✅ Open source — audit the code yourself!

Web Demo Note: The live demo on Netlify does send requests to a server, but does not log or store any data.

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