This lesson provides a complete foundation in Orders of Growth within Algorithm Analysis and Design, covering relative rates of growth, logarithmic, polynomial, exponential and factorial functions, limits-based comparisons, L’Hôpital’s Rule, Stirling’s Formula, and Big-O classifications.

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What’s Included

💡 Full Orders of Growth Slide Deck (PPT + PDF)
💡 Growth comparison graphs and figures
💡 Worked mathematical examples using limits
💡 Algorithm runtime estimation examples
💡 Ready for in-person, online, or hybrid classrooms

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WHAT STUDENTS WILL LEARN

✏️ Orders of Growth
✏️ Relative rates of growth
✏️ Logarithmic functions
✏️ Polynomial functions
✏️ Exponential functions
✏️ Factorial functions
✏️ Comparing orders of growth using limits
✏️ L’Hôpital’s Rule
✏️ Stirling’s Formula
✏️ Growth comparison graphs
✏️ O(1)
✏️ O(log n)
✏️ O(n)
✏️ O(n log n)
✏️ O(n²)
✏️ O(n³)
✏️ O(2ⁿ)
✏️ O(n!)
✏️ Same, lower, and higher order of growth
✏️ Summation notation (Σ)
✏️ Useful summation formulas
✏️ Runtime analysis of for loops
✏️ Runtime analysis of nested loops
✏️ Runtime analysis of while loops
✏️ Tracing loop execution
✏️ Runtime estimation of non-recursive algorithms
✏️ Best-case and worst-case growth comparison

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