Lecture 2: Vector Calculus

André E. Lazzaretti

​

Universidade Tecnológica Federal do Paraná (UTFPR) - Curitiba

Pós-Graduação em Engenharia Elétrica e Informática Industrial (CPGEI)

​

Differentiation of Univariate Functions

Partial Differentiation and Gradients

Partial Differentiation and Gradients

Partial Differentiation and Gradients

Partial Differentiation and Gradients

Gradients of Vector-Valued Functions

Gradients of Vector-Valued Functions

Gradients of Matrices

Useful Identities for Computing Gradients

Automatic Differentiation

• Automatic differentiation applies a series of elementary arithmetic operations, e.g., addition and multiplication and elementary functions, e.g., sin; cos; exp; log.
• By applying the chain rule to these operations, the gradient of quite complicated functions can be computed automatically.

​

Automatic Differentiation

Automatic Differentiation

Automatic Differentiation

Higher-Order Derivatives

Taylor Series

Multivariate Taylor Series