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MIT 18.01/18.02: Calculus

Descriptions

  • Offered by: MIT
  • Prerequisites: High school math (functions, trigonometry, exponentials)
  • Difficulty: 🌟🌟🌟
  • Class Hour: 80+

MIT 18.01 (Single Variable Calculus) and 18.02 (Multivariable Calculus) are required math courses for science and engineering students at MIT.

Calculus is the foundation of understanding change and optimization. In AI, gradient descent, backpropagation, and probability density functions all build on calculus.

Course Resources

MIT 18.01: Single Variable Calculus

MIT 18.02: Multivariable Calculus

Course Content

18.01: Single Variable Calculus

  • Limits and continuity
  • Derivatives and differentiation
  • Mean value theorem
  • Integration and the Fundamental Theorem of Calculus
  • Techniques of integration
  • Infinite series

18.02: Multivariable Calculus

  • Vectors and analytic geometry
  • Partial derivatives and total differential
  • Directional derivatives and gradients
  • Multiple integrals
  • Line and surface integrals
  • Green's, Stokes', and Divergence theorems

Self-Study Tips

Study single variable before multivariable. Concepts like gradients and directional derivatives from multivariable calculus are heavily used in AI.

Pair with 3Blue1Brown's Essence of Calculus.

Focus on derivatives, integrals, gradients, and the chain rule. These are the most used calculus knowledge in AI and ML.

Notes

If time is limited, complete at least 18.01 (single variable calculus), since derivatives and integrals are fundamental to optimization algorithms like gradient descent.

Topics from 18.02 (multivariable calculus) such as gradients, directional derivatives, and Lagrange multipliers are used in machine learning optimization theory.