Introduction to Calculus

Calculus serves as a fundamental tool in machine learning, offering the mathematical language to describe how algorithms learn and adapt. This chapter guides you through understanding the basic calculus concepts and their applications in machine learning. By the end, you'll grasp the essential calculus concepts important for analyzing and developing machine learning models.

We start by looking into limits, which help us comprehend the behavior of functions as they approach specific points or infinity. Next, we examine derivatives, the backbone of optimization techniques used to minimize error in machine learning algorithms. You'll learn how derivatives describe the rate of change and how this concept is used in adjusting model parameters for better performance.

Integrals, the inverse of derivatives, will also be covered, providing insights into areas under curves and summation of quantities. This knowledge is particularly useful for understanding cumulative distributions and calculating expected values.

Lastly, we'll introduce the chain rule, a strong tool for computing derivatives of composite functions. This is especially relevant in neural networks, where the chain rule is extensively used to update weights during backpropagation.

Throughout this chapter, we'll emphasize practical examples and intuitive explanations to ensure you understand these concepts and their relevance in machine learning. By the end, you'll be well-equipped to tackle calculus-based challenges as you get into the field.