The slope of a line, and its relationship to the tangent line of a curve is a fundamental concept in calculus. It is important for a general understanding of function derivatives. In this tutorial, you will discover what is the slope of a line and what is a tangent to a curve. After completing this […]
One of the most frequently used functions in machine learning and data science algorithms are polynomials or functions involving powers of x. It is therefore, important to understand how the derivatives of such functions are calculated. In this tutorial, you will discover how to compute the derivative of powers of x and polynomials. After completing […]
The concept of the derivative is the building block of many topics of calculus. It is important for understanding integrals, gradients, Hessians, and much more. In this tutorial, you will discover the definition of a derivative, its notation and how you can compute the derivative based upon this definition. You will also discover why the […]
The concept of the limit of a function dates back to Greek scholars such as Eudoxus and Archimedes. While they never formally defined limits, many of their calculations were based upon this concept. Isaac Newton formally defined the notion of a limit and Cauchy refined this idea. Limits form the basis of calculus, which in […]
There is no denying that calculus is a difficult subject. However, if you learn the fundamentals, you will not only be able to grasp the more complex concepts but also find them fascinating. To understand machine learning algorithms, you need to understand concepts such as gradient of a function, Hessians of a matrix, and optimization, […]
We have previously seen that calculus is one of the core mathematical concepts in machine learning that permits us to understand the internal workings of different machine learning algorithms. Calculus, in turn, builds on several fundamental concepts that derive from algebra and geometry. The importance of having these fundamentals at hand will become even more […]
Calculus is one of the core mathematical concepts in machine learning that permits us to understand the internal workings of different machine learning algorithms. One of the important applications of calculus in machine learning is the gradient descent algorithm, which, in tandem with backpropagation, allows us to train a neural network model. In this tutorial, […]
The measurement of the rate of change is an integral concept in differential calculus, which concerns the mathematics of change and infinitesimals. It allows us to find the relationship between two changing variables and how these affect one another. The measurement of the rate of change is also essential for machine learning, such as in […]
Calculus is the mathematical study of change. The effectiveness of calculus to solve a complicated but continuous problem lies in its ability to slice the problem into infinitely simpler parts, solve them separately, and subsequently rebuild them into the original whole. This strategy can be applied to study all continuous elements that can be sliced […]
Differential evolution is a heuristic approach for the global optimisation of nonlinear and non- differentiable continuous space functions. The differential evolution algorithm belongs to a broader family of evolutionary computing algorithms. Similar to other popular direct search approaches, such as genetic algorithms and evolution strategies, the differential evolution algorithm starts with an initial population of […]
