Calculus for Computer Science and AI

Calculus is fundamental to many areas of computer science, particularly in machine learning, computer graphics, optimization, and algorithm analysis. This chapter covers essential calculus concepts with practical applications in computing.

Why Calculus Matters in CS/AI

  • Machine Learning: Gradient descent, backpropagation, optimization
  • Computer Graphics: Curves, surfaces, animation, physics simulation
  • Algorithm Analysis: Growth rates, complexity analysis
  • Signal Processing: Fourier transforms, filtering
  • Optimization: Finding optimal solutions in algorithms
  • Physics Simulation: Game engines, robotics

Chapter Contents

  1. Limits and Continuity
  2. Derivatives and Applications
  3. Integration and Applications
  4. Multivariable Calculus
  5. Optimization in Machine Learning
  6. Numerical Methods

Prerequisites

  • Basic algebra and functions
  • Understanding of coordinate systems
  • Programming experience (helpful for examples)

Tools and Libraries

We’ll use Python with libraries like: - NumPy for numerical computations - SciPy for scientific computing - Matplotlib for visualization - SymPy for symbolic mathematics