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Lagrange Operators: Optimization with Constraints

Lagrange Operators: Optimization with Constraints

Finding maximums and minimums when rules must be obeyed

Course Description

This course introduces Lagrange multipliers (often called “Lagrange operators” by students), a powerful technique used to optimize functions subject to constraints. Students develop intuition through geometry, gradients, and constraint curves before mastering the formal method and building problem-solving fluency. The course balances conceptual understanding with algebraic precision and includes real-world applications in physics, economics, and engineering.

Target Audience

  • Grade 11–12 students in advanced mathematics
  • Students in IB Math AA HL / AP Calculus / first-year university preparation pathways
  • Physics, economics, and engineering-bound students who want stronger optimization tools

Prerequisites

To succeed in this course, students should already be comfortable with:

  • Partial derivatives
  • Gradients and level curves
  • Optimization of single-variable functions

💡 Tip: If you’re a bit rusty on gradients or partial derivatives, you can still take this course— just plan to review those topics during Unit 1.

The Physics of Diffraction: Slits, Gratings, and Patterns

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🌈 The Physics of Diffraction: Slits, Gratings, and Patterns

See how light bends, spreads, and forms brilliant fringes — step by step.

When light passes through a narrow slit or a diffraction grating, it doesn’t behave “straight-line simple” anymore. This focused course guides you through single-slit diffraction, double-slit interference, and diffraction gratings using clear visuals, intuitive explanations, and worked examples.

  • 🌊 Understand diffraction as wave spreading (when gap size ≈ wavelength)
  • 🔬 Explain single- and double-slit patterns (maxima, minima, fringe spacing)
  • 📐 Use diffraction equations to calculate wavelength and slit/grating spacing
  • 🌈 Connect diffraction gratings to real spectroscopy & modern tech
💰 $4.95 • 250 weeks access
🚀 Start the Course

Fractions, Ratios & Percentages (Without the Panic)

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🧩 Fractions, Ratios & Percentages — Made Calm

Understand the ideas clearly, practise step-by-step, and build confidence.

A short, guided mini-course that helps you make sense of fractions, ratios, and percentages — without rushing, guessing, or memorising tricks.

  • ✅ Simplify & compare fractions
  • ✅ Ratios (and what they actually mean)
  • ✅ Percentages as “out of 100” + conversions
  • 🔐 Final Vault Challenge + badge
💰 $2.95 • 250 weeks access
Start the Course

Solving Equations & Rearranging Formulae

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⚖️ Solving Equations Made Simple

Learn to rearrange formulae without stress or guesswork

Struggling with equations in math or science? This short, focused micro-course teaches you how to solve equations and rearrange formulae step by step — using clear visuals, interactive practice, and Vault-style challenges.

  • 🧠 Understand equations as balances
  • 🔁 Solve one-step and two-step equations
  • 🔬 Rearrange physics formulae with confidence
  • 🎮 Interactive Vault challenges & instant feedback

GAMES

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🎮 GAMES

Challenge your reflexes, strategy, and focus!

Play classic browser games like Tetris and more. Compete for top scores, track your progress, and explore the logic behind the fun.

  • 🎯 Score tracking
  • 🧠 Strategy meets speed
  • 🏆 Leaderboards & bragging rights

YE Site and Personal Finances

Ideas and notes for developing the YE site

Ideas relating to money management, and growth.

Dinner and Dessert Recipes

Welcome to our family’s favourite collection of comforting dinners and sweet treats! This course is a cozy digital recipe box featuring our tried-and-true meals—some simple, some indulgent, all full of heart. Whether you’re whipping up a quick weeknight pasta bake or baking lemon squares for a weekend gathering, you’ll find what you need here.

🍴 Recipes include:

  • Tuna & Corn (or Pea!) Pasta Bake – Crunchy Topped
  • Chocolate Lava Cakes for Two
  • Hearty Lentil Stew
  • Zesty Lemon Squares
🥄 Visit the Course