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Topics

Univariate Calculus

• Limit, Differentiation, Chain Rule

Multivariate Calculus

• Partial Derivatives, Gradient, Jacobian, Hessian

Vector Calculus

• Directional Derivative, Taylor Expansion, Divergence, Curl

Study Resources & Scope Used to Study

[1] Mathematics for Machine Learning - Deisenroth, Faisal, and Ong

• Vector Calculus
  • 5.2 Partial Differentiation and Gradients
  • 5.3 Gradients of Vector-Valued Functions
  • 5.4 Gradients of Matrices
  • 5.5 Useful Identities for Computing Gradients
• Continuous Optimization
  • 7.2 Constrained Optimization and Lagrange Multipliers
  • 7.3 Convex Optimization

[2] Calculus - James Stewart

• Univariate and Multivariate Calculus
  • Chapters 2–4: Limits, Derivatives, Chain Rule
  • Chapters 14–15: Partial Derivatives, Gradients, Directional Derivatives
  • Chapter 16: Vector Calculus (Divergence, Curl)

[3] Python/NumPy/PyTorch Implementations

• Code examples for computing gradients, Hessians, and implementing gradient descent.