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This lecture introduces the fundamental ideas of calculus — the mathematics of change and accumulation — setting the stage for differential and integral calculus.

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📋 At a Glance

• [ ] Understand what calculus is and why it matters for computer science
• [ ] Grasp the two central problems: tangent lines and areas under curves
• [ ] Review functions, domains, ranges, and function composition
• [ ] Understand the concept of a rate of change
• [ ] Distinguish between average and instantaneous rates of change
• [ ] Review key function families: polynomials, exponentials, logarithms, trigonometric
• [ ] Understand the intuition behind limits as the foundation of calculus
• [ ] Connect calculus concepts to real-world applications

1. What is Calculus?

Calculus is the mathematical study of continuous change. It has two main branches:

1. Differential calculus — concerned with rates of change (slopes, velocities)
2. Integral calculus — concerned with accumulation (areas, totals)

These two branches are connected by the Fundamental Theorem of Calculus (covered later).

2. Why Calculus Matters for Computer Science

Applications