Calculus of several variables
Abstract
In this chapter, we start with basic ideas of limits of functions in higher dimensions, and then move to directional and partial derivatives, gradients and extreme points of real-valued functions of many variables. We tie these ideas to the Hessian matrix and Newton's method, since minimizing functions such as a cost function or error function is important in optimization problems. Using a higher dimensional version of the sigmoid function, we give examples of uses of calculus in AI. We finish the chapter with a discussion of the chain rule with an application to the simplest version of a neural network.
Fields of Study & Subjects
Mathematical and Computational Methods
Neural Networks and Applications
Stochastic Gradient Optimization Techniques
Publication details
- Journal / source
- Chapman & Hall/CRC eBooks
- Pages
- 34–65
- Publication date
- 4 February 2026
- Language
- EN
- Document type
- Book chapter